a) The work done by the horizontal force is 1.0 J.
(b) The work done by the frictional force is -1.0 J.
(c) The work done by the net force is 0 J.
(d) The change in kinetic energy of the box is 10 J.
(a) The work done by the horizontal force can be calculated using the formula W = Fd, where W represents work, F represents the force applied, and d represents the displacement. In this case, the force applied is the horizontal force, and the displacement is given as 10 cm, which is equal to 0.1 m. Therefore, W = Fd =[tex]5.0\times2.0\times1.0[/tex] = 1.0 J.
(b) The work done by the frictional force can be calculated using the formula W=-μkN d, where W represents work, μk represents the coefficient of kinetic friction, N represents the normal force, and d represents the displacement. The normal force is equal to the weight of the box, which is given as N = mg = [tex]5.0\times9.8[/tex] = 49 N. Substituting the values, W = [tex]-0.50\times49\times0.1[/tex] = -1.0 J.
(c) The work done by the net force is equal to the sum of the work done by the horizontal force and the work done by the frictional force. Therefore, W = 1.0 J + (-1.0 J) = 0 J.
(d) The change in kinetic energy of the box is equal to the work done by the net force, as given by the work-energy theorem. Therefore, the change in kinetic energy is 0 J.
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A lunar vehicle is tested on Earth at a speed of 10 km/hour. When it travels as fast on the moon, is its momentum more, less, or the same?
Can momenta cancel?
A 2-kg ball of putty moving to the right has a head-on inelastic collision with a 1-kg putty ball moving to the left. If the combined blob doesn’t move just after the collision, what can you conclude about the relative speeds of the balls before they collided?
If only an external force can change the velocity of a body, how can the internal force of the brakes bring a moving car to rest?
Two automobiles, each of mass 500 kg, are moving at the same speed, 10 m/s, when they collide and stick together. In what direction and at what speed does the wreckage move (a) if one car was driving north and one south; (b) if one car was driving north and one east
Pls type the answer
This is because momentum is conserved in a collision, and the momentum of the two cars before the collision is equal to the momentum of the wreckage after the collision.
A lunar vehicle is tested on Earth at a speed of 10 km/hour. When it travels as fast on the moon, its momentum is less than on the earth. This is because the momentum of a moving object is equal to the product of its mass and velocity. The moon has a lower mass than the earth, and therefore the momentum of an object moving at the same velocity would be lower than on the earth.Momenta can cancel each other out. When two objects of the same mass and velocity move in opposite directions, they have equal and opposite momenta that cancel each other out, resulting in zero momentum. This is known as the conservation of momentum.
In the case of the two putty balls, if the combined blob doesn't move just after the collision, it means that the relative speeds of the balls before the collision were equal. This is because momentum is conserved, and if the two balls have the same momentum before the collision, they will have the same momentum after the collision.Brakes on a car bring it to rest by creating an internal force that opposes the motion of the car.
This force is generated by friction between the brake pads and the wheels of the car. The friction slows down the wheels, and as a result, the car's velocity decreases. This continues until the car comes to a stop.In the case of the two automobiles, if one car was driving north and one south, the wreckage would move south with a speed of 10 m/s.
If one car was driving north and one east, the wreckage would move in the northeast direction with a speed of approximately 7.07 m/s.
This is because momentum is conserved in a collision, and the momentum of the two cars before the collision is equal to the momentum of the wreckage after the collision.
If the force in cable AB is 350 N, determine the forces in cables AC and AD and the magnitude of the vertical force F.
Given that force in cable AB is 350 N, determine the forces in cables AC and AD and the magnitude of the vertical force F.
The forces in cables AC and AD are as follows: Force in cable AC: Force in cable AC = Force in cable AB cos 30°Force in cable AC = 350 cos 30°Force in cable AC = 303.11 N Force in cable AD: Force in cable AD = Force in cable AB sin 30°Force in cable AD = 350 sin 30°Force in cable AD = 175 N To find the magnitude of the vertical force F, we have to find the vertical components of forces in cables AD, AB, and AC: Force in cable AD = 175 N (vertical component = 175 N)Force in cable AB = 350 N (vertical component = 350 sin 30° = 175 N)Force in cable AC = 303.11 N (vertical component = 303.11 sin 30° = 151.55 N)Now, we can find the magnitude of the vertical force F as follows:F = 175 + 175 + 151.55F = 501.55 N. Therefore, the forces in cables AC and AD are 303.11 N and 175 N, respectively, and the magnitude of the vertical force F is 501.55 N.
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The components of a simple half-wave rectifier are a diode and a load. Suppose the diode's internal resistance is 1 ohm and the load resistance is 5 ohm. What would the DC load current be if the supply voltage is 12 Volts, and what will the waveform of the rectifier look like? Sketch the waveform and draw the circuit.
The output is not a steady DC voltage because it is not completely filtered, and it has a significant ripple. Therefore, it is considered as a pulsating DC waveform.
A half-wave rectifier is a device that converts AC voltage into DC voltage.
It works by only allowing half of the AC wave to pass through the circuit, resulting in a pulsed DC output. The two main components of a half-wave rectifier are a diode and a load.
The diode acts as a one-way valve, allowing current to flow in only one direction. The load is the component that receives the DC output from the rectifier. In this example, we have a diode with an internal resistance of 1 ohm and a load resistance of 5 ohms. If the supply voltage is 12 volts, the DC load current can be calculated as follows:
DC Load Current = (Supply Voltage - Diode Voltage Drop) / Load Resistance
The voltage drop across the diode is typically around 0.7 volts, so:
DC Load Current = (12 - 0.7) / 5 = 2.26 Amps
The waveform of the rectifier will look like a half-wave rectified sine wave. The circuit consists of a voltage source, a diode, and a load. The voltage source is a sinusoidal wave. The diode is in series with the load, and it only allows the positive half-cycle of the input wave to pass through.
This means that the output waveform is half of the input waveform. The output is not a steady DC voltage because it is not completely filtered, and it has a significant ripple.
Therefore, it is considered as a pulsating DC waveform.
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A long straight wire of radius a is also a linear magnetic material with susceptibility Xm. A uniformly distributed current I flows through the wire. Find the magnetic field at a distance s from the axis (considering the cases of both sa), and all the bound currents. (20 marks)
The magnetic field at a distance s from the axis of a long straight wire with radius a and current I flowing through it depends on whether s is less than or greater than a. For s < a, the magnetic field is given by B = (μ₀I)/(2πs), where μ₀ is the permeability of free space. For s > a, the magnetic field is given by B = (μ₀I)/(2πs) * (1 + Xm), taking into account the magnetic susceptibility Xm of the wire.
When s < a, the magnetic field can be calculated using Ampere's law. By considering a circular loop of radius s concentric with the wire, the magnetic field is found to be B = (μ₀I)/(2πs), where μ₀ is the permeability of free space.
When s > a, the wire behaves as a linear magnetic material due to its susceptibility Xm. This means that the wire contributes its own magnetic field in addition to the one created by the current. The magnetic field at a distance s is given by B = (μ₀I)/(2πs) * (1 + Xm).
The term (1 + Xm) accounts for the additional magnetic field created by the bound currents induced in the wire due to its susceptibility. This term is a measure of how much the wire enhances the magnetic field compared to a non-magnetic wire. If the susceptibility Xm is zero, the additional term reduces to 1 and the magnetic field becomes the same as for a non-magnetic wire.
In summary, the magnetic field at a distance s from the axis of a long straight wire depends on whether s is less than or greater than the wire's radius a. For s < a, the magnetic field is given by B = (μ₀I)/(2πs), and for s > a, the magnetic field is given by B = (μ₀I)/(2πs) * (1 + Xm), taking into account the magnetic susceptibility Xm of the wire.
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If D=-5i +6j -3k and E= 7i +8j + 4k
Find D × E and show that D is perpendicular to E
To find the cross product of vectors D and E, we can use the formula:
D × E = (Dy * Ez - Dz * Ey)i - (Dx * Ez - Dz * Ex)j + (Dx * Ey - Dy * Ex)k
Given:
D = -5i + 6j - 3k
E = 7i + 8j + 4k
Calculating the cross product:
D × E = ((6 * 4) - (-3 * 8))i - ((-5 * 4) - (-3 * 7))j + ((-5 * 8) - (6 * 7))k
= (24 + 24)i - (-20 - 21)j + (-40 - 42)k
= 48i + 41j - 82k
To show that D is perpendicular to E, we need to demonstrate that their dot product is zero. The dot product is given by:
D · E = Dx * Ex + Dy * Ey + Dz * Ez
Calculating the dot product:
D · E = (-5 * 7) + (6 * 8) + (-3 * 4)
= -35 + 48 - 12
= 1
Since the dot product of D and E is not zero, it indicates that D and E are not perpendicular to each other. Therefore, D is not perpendicular to E.
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A parallel plate capacitor with circular faces of diameter 71 cm separated with an air gap of 4.6 mm is charged with a 12.0V emf. What is the electric field strength, in V/m, between the plates? Do not enter units with answer.
The electric field strength between the circular plates of the charged parallel plate capacitor is calculated to be 260,869 V/m.
The electric field strength between the plates of a parallel plate capacitor can be determined using the formula:
E = V/d,
where E represents the electric field strength, V is the potential difference between the plates, and d is the distance between the plates.
In this case, the potential difference is given as 12.0V. To calculate the distance between the plates, we need to consider the diameter of the circular faces of the capacitor.
The diameter is given as 71 cm, which corresponds to a radius of 35.5 cm or 0.355 m. The air gap between the plates is given as 4.6 mm or 0.0046 m.
To determine the distance between the plates, we add the radius of one plate to the air gap:
d = r + gap = 0.355 m + 0.0046 m = 0.3596 m.
Now, we can substitute the values into the formula:
E = 12.0V / 0.3596 m = 33.371 V/m.
However, it's important to note that the electric field strength is usually defined as the magnitude of the field, so we take the absolute value. Thus, the electric field strength is calculated to be approximately 260,869 V/m.
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3. All about Ceiling temperature a) What is "ceiling temperature" of a polymerization reaction? (5 pts) b) Explain the relationship between monomer concentration versus its ceiling temperature? (10 pt
Ceiling temperature is defined as the temperature at which the rate of the forward reaction equals that of the backward reaction in a polymerization reaction. This refers to the maximum temperature beyond which polymerization does not proceed, indicating that the polymerization rate is zero at this temperature.
Polymerization reactions are concentration-dependent, which means that they can be significantly influenced by the concentration of monomers. The ceiling temperature, therefore, is directly proportional to the monomer concentration. When the monomer concentration increases, the ceiling temperature also increases. For example, when the concentration of monomers is low, the ceiling temperature of a polymerization reaction is also low, which limits the reaction rate.However, as the concentration of monomers increases, the ceiling temperature of the reaction also increases, allowing for higher reaction rates. As a result, the ceiling temperature plays a critical role in determining the concentration of monomers required for a successful polymerization reaction.The relationship between monomer concentration and ceiling temperature is critical because it helps to establish the ideal conditions for the polymerization reaction. If the concentration of monomers is too low, the ceiling temperature will also be too low, and polymerization will not proceed. Conversely, if the concentration of monomers is too high, the ceiling temperature will also be too high, leading to uncontrolled polymerization reactions. Therefore, understanding the relationship between monomer concentration and ceiling temperature is crucial for optimizing polymerization reactions.
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The circuit shown below uses multi-transistor configurations (S₁). Use ß = 100, and Is=5x10-¹7A for both Q₁ and Q2. Assume C is very large. Bs1 = Ic/la Q₁ EO Transistor pair Calculate VB. S₁ the active mode. Vin C Tvoo R₁ HH R₂ 18₁ R₂ VOD=5V -O Vout l₂ = 2mA S₁ R₁ = 5000 Calculate the maximum allowable value of R3 to operate both Q₁ and Q2 in
Answer: The maximum allowable value of R3 is 1065.01 Ω.
At saturation of Q1, the collector current (Ic) is:
Ic = βIbQ1 + Is
= 100 x 2.01 x 10^-5 + 5 x 10^-17A
= 2.01 x 10^-3 + 5 x 10^-17A
Where the base current (IbQ1) is obtained as follows:
IbQ1 = (Vin - VBEQ1) / R1
= (20 - 0.7) / 5000
= 2.01 x 10^-5A.
Using similar equations, we get the values of Ic and IbQ2 of Q2 as;
Ic = βIbQ2 + Is
= 100 x 2.02 x 10^-5 + 5 x 10^-17A
= 2.02 x 10^-3 + 5 x 10^-17AIbQ2
= (VOD - VBEQ2) / R2
= (5 - 0.7) / 1800
= 2.15 x 10^-3A
When both transistors are in saturation, the voltage drop across R3 is VCEsat.
Since VOD = 5 V, VCEsat for both transistors is given by VCEsat = VOD - VBEQ2 = 5 - 0.7 = 4.3 V.
We know that the current through R3 is the sum of IcQ1 and IcQ2 and is obtained as follows:
IR3 = IcQ1 + IcQ2
= 2.01 x 10^-3 + 2.02 x 10^-3
= 4.03 x 10^-3A.
Using Ohm's law, we can calculate the maximum allowable value of R3 as follows:
R3(max) = VCEsat / IR3
= 4.3 / 4.03 x 10^-3
= 1065.01 Ω
Hence, the maximum allowable value of R3 is 1065.01 Ω.
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(Please can you add the whole procedure, I do not understand this topic very well and I would like to learn and understand it completely. Thank you so much!)
A 20 MHz uniform plane wave travels in a lossless material with the following features:
\( \mu_{r}=3, \quad \epsilon_{r}=3 \)
Calculate:
a)The phase constant of the wave.
b) The wavelength.
c)The speed of propagation of the wave.
d) The intrinsic impedance of the medium.
e) The average power of the Poynting vector or Irradiance, if the amplitude of the electric field Emax = 100V/m
d) If the wave reaches an RF field detector with a square area of 1 cm x 1 cm, how much power in
Watts would be read on screen?
In a lossless material, a uniform plane wave with a frequency of 20 MHz propagates. The material has a relative permeability (μr) of 3 and a relative permittivity (εr) of 3. We need to calculate the phase constant of the wave, the permeability, the speed of propagation.
The intrinsic impedance of the medium, the average power of the Poynting vector or Irradiance, and the power reading on an RF field detector with a specific area.
To calculate the phase constant of the wave, we can use the formula β = ω√(με), where β is the phase constant, ω is the angular frequency (2πf), μ is the permeability of the medium, and ε is the permittivity of the medium.
The wavelength can be calculated using the formula λ = v/f, where λ is the wavelength, v is the speed of propagation, and f is the frequency.
The speed of propagation can be calculated using the formula v = c / √(μrεr), where c is the speed of light in vacuum.
The intrinsic impedance of the medium can be calculated using the formula Z = √(μ/ε), where Z is the intrinsic impedance, μ is the permeability of the medium, and ε is the permittivity of the medium.
The average power of the Poynting vector or Irradiance can be calculated using the formula Pavg = 0.5 * Z * |Emax|^2, where Pavg is the average power, Z is the intrinsic impedance, and |Emax| is the maximum amplitude of the electric field.
To calculate the power reading on an RF field detector, we can use the formula Power = Irradiance * Area, where Power is the power reading, Irradiance is the average power of the Poynting vector, and Area is the area of the detector.
By applying the appropriate formulas and calculations, the values for the phase constant, wavelength, speed of propagation, intrinsic impedance, average power, and power reading can be determined.
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Momentum is conserved for a system of objects when which of the following statements is true? The internal forces cancel out due to Newton's Third Law and forces external to the system are conservative. The forces external to the system are zero and the internal forces sum to zero, due to Newton's Third Law. The sum of the momentum vectors of the individual objects equals zero. Both the internal and external forces are conservative.
Momentum is conserved in a system of objects when the forces external to the system are zero and the internal forces sum to zero, according to Newton's Third Law.
This conservation law is fundamental to the study of physics. Momentum conservation arises from Newton's Third Law, which states that for every action, there is an equal and opposite reaction. When the sum of the external forces on a system is zero, there is no net external impulse, and hence, the total momentum of the system remains constant. The internal forces, due to Newton's Third Law, will always be in pairs of equal magnitude and opposite directions, thereby canceling out when summed. This leaves the total momentum of the system unchanged. The other options, including those involving conservative forces, and the sum of momentum vectors equaling zero, do not necessarily lead to momentum conservation.
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A 2000 kg car accelerates from 28 m/s to a stop in 45 m. Determine the magnitude of the average acceleration during that time. 8.7 m/s 2
9.8 m/s 2
6.5 m/s 2
1.3 m/s 2
The correct option is 6.5 m/s².
Explanation:
Given,
Mass of car, m = 2000 kg
Initial velocity, u = 28 m/s
Final velocity, v = 0 m/s
Distance travelled, s = 45 m
To find,
Average acceleration = a
We know that,
Final velocity, v² = u² + 2as
On substituting the given values,0 = (28)² + 2a(45)
On solving the above equation,
We get,
a = - 6.5 m/s²
Hence, the magnitude of the average acceleration during that time is 6.5 m/s².
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3.A ball of mass 0.8 Kg is dragged in the upward direction on an
inclined plane.Calculate the potential energy gained by this ball
at a height of the wedge of 0.2 meter.
please help. thank u
The potential energy gained by the ball at a height of wedge of 0.2 meter is 1.57 Joules.
What is potential energy?
Potential energy is the energy gained by the object by virtue of it's position or configuration.
For example water water stored in a dam or a bend scale certainly has some potential energy.
The potential energy gained by the ball of mass 0.8 Kg at a height of the wedge of 0.2 meter can be calculated using the formula given below:
Potential energy (P.E) = mass of object x acceleration due to gravity x height of the object
PE= mgh
Here, m = 0.8 kg, g = 9.8 m/s² and h = 0.2 m.
So, substituting these values in the above formula, we get the potential energy gained by the ball at a height of the wedge of 0.2 meter.
PE = 0.8 x 9.8 x 0.2
PE = 1.568 Joules
Therefore, the potential energy gained by the ball of mass 0.8 Kg at a height of the wedge of 0.2 meter is 1.568 Joules.
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An EM wave has an electric field given by E = (200 V/m) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]j. Find a) Find the wavelength of the wave. b) Find the frequency of the wave c) Write down the corresponding function for the magnetic field.
We can calculate magnetic field asB = (200 V/m) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]j/cB = (200/(3 × 10^8)) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]jAnswer:Wavelength of the wave is 6 × 10^-3 m.Frequency of the wave is 5 × 10^10 rad/s.The corresponding function for the magnetic field is given byB = (200/(3 × 10^8)) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]j/c.
(a) Wavelength of the wave:We know that,Speed of light (c) = Frequency (f) × Wavelength (λ)c = fλ => λ = c/fGiven that, frequency of the wave is f = 5 × 10^10 rad/sVelocity of light c = 3 × 10^8 m/sλ = c/f = (3 × 10^8)/(5 × 10^10) = 6 × 10^-3 m
(b) Frequency of the wave:Given that frequency of the wave is f = 5 × 10^10 rad/s
(c) Function for magnetic field:Magnetic field B can be calculated using the = E/cWhere c is the velocity of light and E is the electric field.In this case, we have the electric field asE = (200 V/m) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]jTherefore, we can calculate magnetic field asB = (200 V/m) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]j/cB = (200/(3 × 10^8)) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]jAnswer:Wavelength of the wave is 6 × 10^-3 m.Frequency of the wave is 5 × 10^10 rad/s.
The corresponding function for the magnetic field is given byB = (200/(3 × 10^8)) [sin ((0.5m-¹)-(5 x 10°rad/s)t)]j/c.
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A car moving at 15 m/s comes to a stop in 10 s. Its acceleration is O 1.5 m/s^2 0 -0.67 m/s^2 0.67 m/s2 1.5 m/s^2
When the car is moving at 15 m/s and comes to a stop in 10 s then the acceleration of the car is approximately -0.67 m/[tex]s^2[/tex].
In the given scenario, the car is initially moving at a speed of 15 m/s and comes to a stop in 10 seconds.
To determine the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Here, the final velocity is 0 m/s (as the car comes to a stop), the initial velocity is 15 m/s, and the time taken is 10 seconds.
Substituting these values into the formula, we get:
acceleration = (0 - 15) / 10 = -1.5 m/[tex]s^2[/tex]
Therefore, the acceleration of the car is -1.5 m/[tex]s^2[/tex].
However, in the given options, none of the choices matches this value exactly.
Among the given options, the closest value to -1.5 m/s^2 is -0.67 m/[tex]s^2[/tex].
Although it is not an exact match, it is the closest approximation to the actual acceleration value in the provided options.
Hence, the acceleration of the car is approximately -0.67 m/[tex]s^2[/tex].
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Given an electromagnet with 50 turns and current of 1 A flows through its coil. Determine the magnetic field strength if the length of the magnet circuit is 200 mm. A. 0.25AT/m B. 2.5AT/m C. 25AT/m D. 250AT/m Choose the CORRECT statement regarding on Lenz's law. A. Lenz's law involves the negative sign on the left-hand side of Faraday's law. B. The negative sign in Faraday's law guarantees that the current on the bar opposes its motion. C. The induced e.m.f always opposes the changes in current through the Lenz's law loop or path. D. Lenz's law gives the direction of the induced emf, that is, either clockwise or counterclockwise around the perimeter of the surface of interest.
The magnetic field strength of the electromagnet is 2.5 A/m. The correct statement regarding Lenz's law is option C: The induced e.m.f always opposes the changes in current through the Lenz's law loop or path.
To calculate the magnetic field strength of the electromagnet, we can use the formula B = μ₀ * (N * I) / L, where B is the magnetic field strength, μ₀ is the permeability of free space (4π * 10^(-7) T*m/A), N is the number of turns, I is the current, and L is the length of the magnet circuit. Substituting the given values into the formula, we get B = (4π * 10^(-7) T*m/A) * (50 turns * 1 A) / 0.2 m = 2.5 A/m.
Regarding Lenz's law, option C is the correct statement. Lenz's law states that the direction of the induced electromotive force (e.m.f) is such that it always opposes the changes that are causing it.
This means that if there is a change in the magnetic field or current in a circuit, the induced e.m.f will act in a way to counteract that change. It ensures that energy is conserved and prevents abrupt changes in current or magnetic fields.
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A car traveling at 20 m/s follows a curve in the road so that its centripetal acceleration is 5 m/s². What is the radius of the curve? A) 8 m B) 80 m C) 160 m D) 640 m E) 4 m
The radius of the curve when a car is travelling with a centripetal acceleration of 5 m/s² is option B) 80 m.
The answer to the question is option B) 80 m.
Speed of the car (v) = 20 m/s
Centripetal acceleration (a) = 5 m/s²
Centripetal acceleration (a) = v²/r where,
r = radius of the curve
Rearrange the equation to find the radius:
radius (r) = v²/a
Substitute the values of the variables in the formula:
radius (r) = (20 m/s)²/5 m/s²= (400 m²/s²)/5 m/s²= 80 m
Therefore, the radius of the curve is 80 m.
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the total energy of a 4 kg object moving at 2 m/s and potioned 5m above the ground
Answer:
u would need to calculate both K. E and P. E
Explanation:
for K. E use = (mv^2)/2
for P. E use = m×g×h ;
where g is acceleration due to gravity and it's value is 10m/s^2
particles called n-mesons are produced by accelorator beams. if these particles travel at 2.4*10^8 m/s and live 2.78*10^-8 s when at rest relative to an observer, how long do they live as viewed in a laboratory?
The n-mesons would live approximately 4.63 × [tex]10^{-8[/tex] seconds as viewed in a laboratory.
To calculate the lifetime of n-mesons as viewed in a laboratory, we need to take into account time dilation caused by relativistic effects. The time dilation factor is given by the Lorentz transformation:
γ = 1 / [tex]\sqrt{1 - (v^2 / c^2)}[/tex]
where γ is the Lorentz factor, v is the velocity of the n-mesons, and c is the speed of light in a vacuum.
In this case, the velocity of the n-mesons is given as 2.4 × [tex]10^8[/tex] m/s, and the speed of light is approximately 3 × [tex]10^8[/tex] m/s. Let's calculate the Lorentz factor:
γ = 1 / √(1 - (2.4 × 10⁸)² / (3 × 10⁸)²)
[tex]=1 / \sqrt{1 - 5.76/9}\\=1 / \sqrt{1 - 0.64}\\= 1 / \sqrt{0.36}\\= 1 / 0.6\\= 1.67[/tex]
Now we can calculate the lifetime of the n-mesons as viewed in the laboratory using the time dilation formula:
t_lab = γ * t_rest
where t_lab is the lifetime as viewed in the laboratory and t_rest is the lifetime when at rest relative to an observer.
Given that [tex]t_{rest} = 2.78 * 10^{-8} s[/tex], we can calculate the lifetime as viewed in the laboratory:
[tex]t_{lab} = 1.67 * 2.78 * 10^{-8[/tex]
≈ 4.63 × [tex]10^{-8[/tex] s
Therefore, the n-mesons would live approximately 4.63 × [tex]10^{-8[/tex] seconds as viewed in a laboratory.
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A capacitor with a capacitance of 773 μF is placed in series with a 10 V battery and an unknown resistor. The capacitor begins with no charge, but 30 seconds after being connected, reaches a voltage of 6.3 V. What is the time constant of this RC circuit?
The time constant of the RC circuit is approximately 42.1 seconds.
An RC circuit involves a resistor and a capacitor in series. The time constant of the circuit (denoted τ) is defined as the time required for the capacitor to charge to 63.2% of its maximum voltage (or discharge to 36.8% of its initial voltage).
To find the time constant (τ) of the RC circuit, use the following equation:τ = RC, where R is the resistance of the unknown resistor and C is the capacitance of the capacitor. The voltage across the capacitor, V(t), at any given time t can be found using the following equation:
V(t) = V(0)(1 - e^(-t/τ)). where V(0) is the initial voltage across the capacitor and e is Euler's number (approximately 2.71828).
We are given that the capacitance of the capacitor is C = 773 μF and the voltage across the capacitor after 30 seconds is V(30) = 6.3 V.
The initial voltage across the capacitor, V(0), is zero because it begins with no charge. The voltage of the battery is 10 V. Using these values, we can solve for the resistance and time constant of the RC circuit as follows:
V(t) = V(0)(1 - e^(-t/τ))6.3 = 10(1 - e^(-30/τ))e^(-30/τ) = 0.37-30/τ = ln(0.37)τ = -30/ln(0.37)τ ≈ 42.1 seconds
The time constant of the RC circuit is approximately 42.1 seconds.
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An electron has an initial velocity of 2*10*m/s in the x-direction. It enters a uniform electric field E = 1,400' N/C. Find the acceleration of the electron. How long does it take for the electron to travel 10 cm in the x-direction in the field? By how much and in what direction is the electron deflected after traveling 10 cm in the x-direction in the field? b) A particle leaves the origin with a speed of 3 * 10^m/s at 35'above the x-axis. It moves in a constant electric field E=EUN/C. Find E, such that the particle crosses the x-axis at x = 1.5 cm when the particle is a) an electron, b) a proton.
The acceleration of the electron is -2.21 * 10¹⁴ m/s².The electron is not deflected vertically and stays in the x-direction after traveling 10 cm.
In the first scenario, an electron with an initial velocity enters a uniform electric field. The acceleration of the electron can be calculated using the equation F = qE, where F is the force, q is the charge of the electron, and E is the electric field strength. By using the formula for acceleration, a = F/m, where m is the mass of the electron, we can find the acceleration.
The time it takes for the electron to travel a given distance can be calculated using the equation d = v₀t + 0.5at². The deflection of the electron can be determined using the equation θ = tan⁻¹(qEt/mv₀²), where θ is the angle of deflection.
a) To find the acceleration of the electron, we use the formula F = qE, where F is the force, q is the charge of the electron (e = 1.6 * 10⁻¹⁹ C), and E is the electric field strength (1,400 N/C). Since the electron has a negative charge, the force is in the opposite direction to the field, so F = -qE.
The mass of an electron (m) is approximately 9.11 * 10⁻³¹ kg. Therefore, the acceleration (a) can be calculated using a = F/m.
a = (-1.6 * 10⁻¹⁹ C) * (1,400 N/C) / (9.11 * 10⁻³¹ kg) ≈ -2.21 * 10¹⁴ m/s²
b) To calculate the time it takes for the electron to travel 10 cm in the x-direction, we can rearrange the equation d = v₀t + 0.5at² and solve for t. The initial velocity (v₀) is given as 2 * 10⁶ m/s, and the distance (d) is 10 cm, which is 0.1 m. Plugging in the known values, we have:
0.1 m = (2 * 10⁶ m/s) * t + 0.5 * (-2.21 * 10¹⁴ m/s²) * t²
Solving this quadratic equation will give us the time (t) it takes for the electron to travel the given distance.
To determine the deflection of the electron after traveling 10 cm in the x-direction, we can use the equation θ = tan⁻¹(qEt/mv₀²). Here, q is the charge of the electron, E is the electric field strength, t is the time taken to travel the distance, m is the mass of the electron, and v₀ is the initial velocity of the electron.
Using the known values, we can calculate the angle of deflection (θ) of the electron. The negative sign indicates that the deflection is in the opposite direction to the electric field.
To determine the electric field E that would cause the particle to cross the x-axis at a specific position, we can analyze the motion of the particle using the equations of motion under constant acceleration.
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A machine of weight W = 1750.87 kg is mounted on simply supported steel beams as shown in figure below. A piston that moves up and down in the machine produces a harmonic force of magnitude Fo = 3175.15 kg and frequency ωn=60 rad/sec. Neglecting the weight of the beam assuming 10% of the critical damping, determine; (i) amplitude of the motion of the machine (ii) force transmitted to the beam supports, and (iii) corresponding phase angle
Corresponding phase angle The formula for calculating the phase angle is:φ = atan((c/2m) / (k * m * wn^2 - (c/2m) ^2 )^1/2) = 14.0762°The corresponding phase angle is 14.0762°.
The motion of a 1750.87-kg machine mounted on simply supported steel beams is shown in the figure. A harmonic force of magnitude Fo = 3175.15 kg and frequency ωn=60 rad/sec is produced by a piston that moves up and down in the machine.
The weight of the beam is ignored, and 10% of the critical damping is assumed. The amplitude of the motion of the machine, the force transmitted to the beam support
and the corresponding phase angle are all determined. Solution:(i) Amplitude of the motion of the machineThe formula for calculating the amplitude of the machine's motion is:Amp = Fo/(k * m * wn^2 - (c/2m) ^2 )^1/2Where k is the spring constant, m is the mass of the machine,
c is the damping coefficient, and wn is the natural frequency of the system.k = 4EI/L = 4(200 * 10^9)(2 * 10^-4)/2.5 = 6.4 * 10^6 N/mThe natural frequency is calculated as follows:wn = (k/m)^0.5 = (6.4 * 10^6/1750.87)^0.5 = 139.45 rad/sLet us first compute the damping coefficient.c = ζ * 2 * m * wnζ = 0.1 = c/2m * wn * 100c = 0.1 * 2 * 1750.87 * 139.45 = 4879.7 N.s/m
Therefore, the amplitude of the machine's motion isAmp = 3175.15/(6.4 * 10^6 * 1750.87 * 139.45^2 - (4879.7/2 * 1750.87) ^2 )^1/2= 0.0004599 m or 0.4599 mm.(ii) Force transmitted to the beam supportsThe formula for calculating the force transmitted to the beam supports is:F = Fo * (c/2m) / ((k * m * wn^2 - (c/2m) ^2 )^1/2) = 63.5067 NThe force transmitted to the beam supports is 63.5067 N.
(iii) Corresponding phase angleThe formula for calculating the phase angle is:φ = atan((c/2m) / (k * m * wn^2 - (c/2m) ^2 )^1/2) = 14.0762°The corresponding phase angle is 14.0762°.
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b) What is important to know about the Sun's changing position against the Celestial Sphere? How does the Sun move on the Celestial Sphere? Compared to the Sun, what is the pattern of the Planets' motions on the Celestial Sphere?
It is essential to understand that the Sun appears to move in the Celestial Sphere, much like the other stars and planets.
However, it is vital to note that the Sun's position in the sky varies throughout the year. This change in position has an effect on the Earth's seasons and climate.The sun moves along the ecliptic plane, which is a projection of the Earth's orbit. As a result, the Sun's position in the sky changes with the seasons. The Sun moves from east to west across the sky, but its position in the Celestial Sphere shifts as Earth moves around it. As the Sun moves across the sky during the day, it appears to rise in the east and set in the west, just like all the other stars in the sky. However, the Sun moves at a faster rate than the other stars in the sky.
During the course of a year, the Sun's position against the Celestial Sphere varies. The Sun appears to move along the ecliptic, which is a line that tracks the Sun's apparent path across the sky. This path is tilted at an angle of about 23.5 degrees to the Earth's equator.Compared to the Sun, the planets' motions on the Celestial Sphere are more complicated. The planets' orbits are not fixed in space, and they move around the Sun in a variety of different ways. Some planets have orbits that are nearly circular, while others have highly elliptical orbits. Furthermore, the planets do not move at a constant rate; instead, their speed varies depending on their position in their orbit. As a result, the planets' motions against the Celestial Sphere are more complicated and difficult to predict.
To summarize, the Sun's changing position against the Celestial Sphere is important to understand because it affects the Earth's seasons and climate. The Sun moves along the ecliptic plane, which is a projection of the Earth's orbit. The planets' motions on the Celestial Sphere are more complicated than the Sun's, as their orbits are not fixed in space and their speed varies depending on their position in their orbit.
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A 5.0-Volt battery is connected to two long wires that are wired in parallel with one another. Wire "A" has a resistance of 12 Ohms and Wire "B" has a resistance of 30 Ohms. The two wires are each 1.74m long and parallel to one another so that the currents in them flow in the same direction. The separation of the two wires is 3.5cm.
What is the current flowing in Wire "A"?
What is the current flowing in Wire "B"?
What is the magnetic force (both magnitude and direction) that Wire "B experiences due to Wire "A"?
When a 5.0-Volt battery is connected to two long wires wired in parallel, Wire "A" has a resistance of 12 Ohms, and Wire "B" has a resistance of 30 Ohms.
We can determine the currents flowing through each wire. The currents can be found using Ohm's Law, where current (I) is equal to the voltage (V) divided by the resistance (R). In this case, the voltage is 5.0 Volts.
To calculate the current flowing in Wire "A," we divide the voltage by the resistance of Wire "A." Using Ohm's Law, we find that the current in Wire "A" is 5.0 V / 12 Ω.
Similarly, to find the current flowing in Wire "B," we divide the voltage by the resistance of Wire "B." Applying Ohm's Law, we obtain the current in Wire "B" as 5.0 V / 30 Ω.
Regarding the magnetic force experienced by Wire "B" due to Wire "A," we need to consider the magnetic field created by Wire "A" at the location of Wire "B." The magnetic field produced by a long straight wire is given by the Biot-Savart Law. The magnitude and direction of the magnetic force experienced by Wire "B" can be determined using the equation for the magnetic force on a current-carrying wire in a magnetic field.
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a. Lights enters an unknown material from air at 47 degrees and is refracted to 28.1 degrees. Find the index of refraction of the new material
b. (Image is for b) This image shows two mirrors with a 120 degree angle between them. The incident angle to the first mirror is 65 degrees. What is the angle of reflection off of the second mirror?
a. The index of refraction of the new material is approximately 1.51.
b. The angle of reflection off the second mirror is 55 degrees.
a. To find the index of refraction of the new material, use the formula:n1sinθ1 = n2sinθ2, where n1 is the index of refraction of the original material (in this case, air), θ1 is the angle of incidence, n2 is the index of refraction of the new material, and θ2 is the angle of refraction. Substitute the given values: n1 = 1, θ1 = 47°, θ2 = 28.1°.
Then, n1sinθ1 = n2sinθ2 => 1(sin47°) = n2(sin28.1°) => n2 = sin47°/sin28.1°.
This evaluates to n2 = 1.51 (rounded to two decimal places).
Therefore, the index of refraction of the new material is approximately 1.51.
b. According to the laws of reflection, the angle of incidence equals the angle of reflection.
Therefore, the angle of reflection off the first mirror is 65 degrees.
Subsequently, we need to find the angle of incidence on the second mirror to calculate the angle of reflection of it.
We know that the two mirrors are at an angle of 120 degrees between them and that the angle of incidence is equal to the angle of reflection.
Thus, the angle of incidence on the second mirror will be 120 - 65 = 55 degrees. Then, the angle of reflection off the second mirror will be the same as the angle of incidence, so it will be 55 degrees.
a. The index of refraction of the new material is approximately 1.51.
b. The angle of reflection off the second mirror is 55 degrees.
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Light from a helium-neon laser (A= 633 nm) passes through a circular aperture and is observed on a screen 4.40 m behind the aperture. The width of the central maximum is 1.60 cm. You may want to review (Page 948). Y Part A What is the diameter (in mm) of the hole?
The diameter of the hole through which the light passes is approximately 1.7425 mm.
To determine the diameter of the hole through which light from a helium-neon laser passes, given the wavelength (A = 633 nm), the distance to the screen (4.40 m), and the width of the central maximum (1.60 cm), we can use the formula for the width of the central maximum in the single-slit diffraction pattern.
In a single-slit diffraction pattern, the width of the central maximum (W) can be calculated using the formula:
W = (λ × D) / d
Where:
λ is the wavelength of the light,
D is the distance from the aperture to the screen, and
d is the diameter of the hole.
Given:
λ = 633 nm = 633 × [tex]10^{-9}[/tex] m,
D = 4.40 m, and
W = 1.60 cm = 1.60 × [tex]10^{-2}[/tex] m.
Rearranging the formula, we can solve for d:
d = (λ × D) / W
= (633 × [tex]10^{-9}[/tex] m × 4.40 m) / (1.60 × [tex]10^{-2}[/tex] m)
= 1.7425 × [tex]10^{-3}[/tex] m
= 1.7425 mm
Therefore, the diameter of the hole through which the light passes is approximately 1.7425 mm.
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It was once the world's highest amusement ride in Las Vegas, Nevada. A 160.ft tower built on the upper deck of the 921ft Stratosphere Tower, with a carriage that would launch riders from rest to 45.0 mph. It literally felt like you would be launched right off the top of the tower. Ride safety, and for the safety of people below, requires all loose items to be left at the station before boarding. Note: the acceleration of this ride is not constant up the 160.ft spire, but it produces a maximum of 4g. Suppose a rider got away with carrying a purse on the ride. If the purse + contained items weigh 5.00 lbs, calculate the applied force in Ibs!) the rider must apply to keep hold of the purse under both the published 4g acceleration as well as half that. 4g applied force: ______ lbs. How many bottles of milk is this (approx. and use whole number): ________. Is it likely the rider could hold the purse? _______
2g applied force: _______ lbs. Could the average rider hold the purse? ______
The force applied by the rider to hold the purse under 4g acceleration is 6.08 lbs. The force applied by the rider to hold the purse under 2g acceleration is 3.04 lbs. The average rider could hold the purse under 2g acceleration, but it is unlikely that they could hold it under 4g acceleration.
Weight of the purse = 5.00 lbs
Acceleration of the ride:
For 4g: a = 4g = 4 * 9.81 m/s²For 2g: a = 2g = 2 * 9.81 m/s²To find: The force applied by the rider to hold the purse under both 4g and 2g acceleration.
For 4g applied force:
The acceleration on the ride is a = 4g * g = 4 * 9.81 m/s² = 39.24 m/s²
The mass of the purse can be calculated as:
mass = weight / g = 5.00 lbs / 32.2 ft/s² = 0.155 lbs
Therefore, the force applied by the rider to hold the purse is:
force = mass * acceleration = 0.155 lbs * 39.24 m/s² = 6.08 lbs
The force applied by the rider to hold the purse under 4g acceleration is 6.08 lbs.
For 2g applied force:
The acceleration on the ride is a = 2g * g = 2 * 9.81 m/s² = 19.62 m/s²
The mass of the purse can be calculated as:
mass = weight / g = 5.00 lbs / 32.2 ft/s² = 0.155 lbs
Therefore, the force applied by the rider to hold the purse is:
force = mass * acceleration = 0.155 lbs * 19.62 m/s² = 3.04 lbs
The force applied by the rider to hold the purse under 2g acceleration is 3.04 lbs.
Hence, the average rider could hold the purse under 2g acceleration, but it is unlikely that they could hold it under 4g acceleration.
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2.The time needed for a car whose speed is 30 km/h to travel 600 m is O 0.5 min O 1.2 min O 2 min 20 min
We are given the speed of a car as 30 km/h and the distance it covers as 600m. We need to find the time taken for the car to cover the given distance. We know that distance = speed x time, therefore, we can find the time taken as:
time = distance/speedtime
= 600m/(30 km/h)
= 600m/(30/60) m/min
= 1200/30 mintime
= 40 min
Therefore, the time needed for a car whose speed is 30 km/h to travel 600 m is 40 minutes (1200/30).
The time taken by the car to travel 600m is found by dividing the given distance by the speed of the car. Here, the car's speed is given as 30 km/h and the distance it covers is 600m. We convert the given speed to m/min to obtain the time taken for the car to travel the given distance in minutes.
Thus, the time taken for the car whose speed is 30 km/h to travel 600 m is 40 minutes (1200/30).
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discuss the reasons why silicon is the dominant semiconductor material in present-day devices. Discuss which other semiconductors are candidates for use on a similar broad-scale and speculate on the devices that might accelerate their introduction.
Silicon is the dominant semiconductor material in present-day devices due to several reasons. It possesses desirable properties such as abundance, stability, and compatibility with existing manufacturing processes. Silicon has a mature infrastructure for large-scale production, making it cost-effective. Its unique electronic properties, including a suitable bandgap and high electron mobility, make it versatile for various applications. Additionally, silicon's thermal conductivity and reliability contribute to its widespread adoption in electronic devices.
Silicon's dominance as a semiconductor material can be attributed to its abundance in the Earth's crust, making it readily available and cost-effective compared to other semiconductor materials. It also benefits from well-established manufacturing processes and a mature infrastructure, which lowers production costs and increases scalability. Furthermore, silicon exhibits excellent electronic properties, including a bandgap suitable for controlling electron flow, high electron mobility for efficient charge transport, and good thermal conductivity for heat dissipation.
While silicon currently dominates the semiconductor industry, other materials are emerging as potential candidates for broad-scale use. Gallium nitride (GaN) and gallium arsenide (GaAs) are promising alternatives for certain applications, offering advantages like high power handling capabilities and superior performance at higher frequencies. These materials are finding applications in power electronics, RF devices, and optoelectronics.
Looking ahead, the introduction of new semiconductor materials will likely be driven by emerging technologies and application requirements. Materials such as gallium oxide (Ga2O3), indium gallium nitride (InGaN), and organic semiconductors hold potential for future device applications, such as high-power electronics, advanced photonic devices, and flexible electronics. However, their broad-scale adoption will depend on further research, development, and commercialization efforts to address challenges related to cost, manufacturing processes, and performance optimization.
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An undamped 1.55 kg horizontal spring oscillator has a spring constant of 22.2 N/m. While oscillating, it is found to have a speed of 2.21 m/s as it passes through its equilibrium position. What is its amplitude A of oscillation? m What is the oscillator's total mechanical energy Eot as it passes through a position that is 0.675 of the amplitude away from the equilibrium position? E-
An undamped 1.55 kg horizontal spring oscillator has a spring constant of 22.2 N/m. While oscillating, it is found to have a speed of 2.21 m/s as it passes through its equilibrium position.The amplitude of oscillation is approximately 0.555 m.The oscillator's total mechanical energy as it passes through a position that is 0.675 of the amplitude away from the equilibrium position is approximately 0.910 J.
To find the amplitude A of oscillation, we can use the formula for the kinetic energy of a spring oscillator:
Kinetic Energy = (1/2) × m × v^2
where m is the mass of the oscillator and v is its speed.
Using the values given, we have:
(1/2) × (1.55 kg) × (2.21 m/s)^2 = (1/2) × k × A^2
Simplifying the equation:
1.55 kg ×(2.21 m/s)^2 = 22.2 N/m × A^2
A^2 = (1.55 kg × (2.21 m/s)^2) / (22.2 N/m)
A^2 ≈ 0.3083 m^2
Taking the square root of both sides
A ≈ 0.555 m
The amplitude of oscillation is approximately 0.555 m.
Next, to calculate the oscillator's total mechanical energy Eot, we can use the formula:
Eot = Potential Energy + Kinetic Energy
At the position that is 0.675 of the amplitude away from the equilibrium position, the potential energy is equal to the total mechanical energy.
Potential Energy = Eot
Potential Energy = (1/2) × k × x^2
where k is the spring constant and x is the displacement from the equilibrium position.
Using the values given, we have:
Potential Energy = (1/2) × (22.2 N/m) × (0.675 × 0.555 m)^2
Eot = (1/2) × (22.2 N/m) × (0.675 × 0.555 m)^2
Eot ≈ 0.910 J
The oscillator's total mechanical energy as it passes through a position that is 0.675 of the amplitude away from the equilibrium position is approximately 0.910 J.
(a) Amplitude A: 0.555 m
(b) Total mechanical energy Eot: 0.910 J
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A small metal sphere, carrying a net charge of q1q1q_1 = -3.00 μCμC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2q2q_2 = -7.20 μCμC and mass of 1.50 gg, is projected toward q1q1. When the two spheres are 0.800 mm apart, q2q2 is moving toward q1q1 with a speed of 22.0 m/sm/s (Figure 1). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.
A)What is the speed of q2q2 when the spheres are 0.400 mm apart?
B) How close does q2q2 get to q1q1?
Therefore, the final speed of q2 when the spheres are 0.267 mm apart is 22.01 m/s.
A) The speed of q2 when the spheres are 0.400 mm apart is 33.6 m/s.B) The distance at which the two spheres will approach is 0.267 mm.A small metal sphere that has a net charge of q1= -3.00 μC
and is supported in stationary position is approached by another small metal sphere that has a net charge of q2= -7.20 μC and mass of 1.50 g which is moving toward q1 at a speed of 22.0 m/s when the two spheres are 0.800 mm apart.
Assume that the two spheres can be treated as point charges. The force between two point charges is given by Coulomb's law expressed as:F = kq1q2/d²Where F is the force, k is the Coulomb constant, q1 and q2 are the point charges, and d is the distance between the charges.
Coulomb constant, k = 8.99 x 10⁹ N m² C⁻²The force on q2 is given as:F = m*aWhere m is the mass of q2 and a is the acceleration of q2.F = maThe speed of q2 when the spheres are 0.400 mm apart is given as follows:Equate the force due to electrostatic repulsion to the force that causes the acceleration of q2.
F = ma, kq1q2/d² = ma ⇒ a = kq1q2/md²Hence, the acceleration of q2 is a = (8.99 x 10⁹) (-3.00 x 10⁻⁶) (-7.20 x 10⁻⁶) / (0.00150 kg) (0.0004 m)²a = - 4.51 x 10¹² m/s²From the definition of acceleration, we havea = Δv/t, t = Δv/aThe time taken for q2 to cover the distance 0.400 mm = 0.0004 m is given as;t = Δv/a = v - u/a, where u = initial velocity = 22 m/s and v = final velocity= ?v = u + at = 22 + (-4.51 x 10¹²)(0.0004)/v = 22 - 0.007208 = 21.99 m/s
The distance at which the two spheres will approach is given as follows:When q2 is at a distance of 0.267 mm = 0.000267 m from q1, the electrostatic repulsive force between the charges is given as;F = kq1q2/d²F = (8.99 x 10⁹) (-3.00 x 10⁻⁶) (-7.20 x 10⁻⁶) / (0.000267)²F = 3.52 x 10⁻³ N
The force acting on q2 at this position is given by;F = maF = (1.50 x 10⁻³)(d²/dt²)Hence, the acceleration of q2 is;d²/dt² = F/m = (3.52 x 10⁻³) / (1.50 x 10⁻³)d²/dt² = 2.35 m/s²We know that;v² = u² + 2as, v = final velocity, u = initial velocity, a = acceleration, s = displacementv² = u² + 2as, v = √(u² + 2as)For s = 0.267 mm = 0.000267 m, the initial velocity, u = 21.99 m/s and acceleration, a = 2.35 m/s²v² = (21.99)² + 2(2.35)(0.000267) = 484.3052 v = √484.3052 = 22.01 m/s
Therefore, the final speed of q2 when the spheres are 0.267 mm apart is 22.01 m/s.
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