Answer: ratty
Explanation: u r ratty
Aaron, Bonny and Connor are playing a game with cards.
Aaron has some cards.
Bonny has twice as many cards as Aaron.
Connor has 6 cards more than Bonny.
They have a total of 101 cards.
Work out how many cards Aaron has.
The number of cards Aaron had are 19 when Aaron, Bonny and Connor are playing a game with cards which are a total of 101.
Given that Aaron, Bonny and Connor are playing a game with cards.
Let the number of cards Aaron had = x
Bonny has twice the cards of Aaron = 2x
Number of cards Connor had are 6 more than Bonny = 2x + 6
The total number of cards = 101
Then by adding the number of cards that Aaron, Bonny and Connor had we get the total number of cards.
Then Aaron cards + Bonny cards + Connor cards = 101
x + 2x + 2x + 6 = 101
5x = 101 - 6 = 95
x = 95/5 = 19
Hence the total number of cards Aaron had = 19
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a 1.3-kg block is attached to the end of a 1.7-m string to form a pendulum. the pendulum is released from rest when the string is horizontal. at the lowest point of its swing when it is moving horizontally, the block is hit by a 0.01-kg bullet moving horizontally in the opposite direction. the bullet remains in the block and causes the block to come to rest at the low point of its swing. what was the magnitude of the bullet's velocity just before hitting the block?
Given Information:
[tex]m_{1}=1.3 \ kg[/tex] (Mass of the block attached to the pendulum)
[tex]l=1.7 \ m[/tex] (Length of the string)
[tex]m_{b}=0.01 \ kg[/tex] (Mass of the bullet)
Information we want to Find:
[tex]||\vec v_{b} || = ?? \ m/s[/tex]
Concepts/Equations used:
Using the idea of momentum, momentum conservation, and energy conservation to solve.
Momentum => [tex]\vec p=m \vec v[/tex]
Momentum Conservation => [tex]\vec p_{0} = \vec p_{f}[/tex]
Energy Conservation => [tex]E_{0} = E_{f}[/tex]
Finding the blocks velocity at the bottom of its swing using conservation of energy. Analyzing points 1 and 2 (Refer to the attached image).
Energy at point 1...
The energy at point 1 is all gravitational potential energy, where [tex]U_{g} =m_{1} gl[/tex].
[tex]\Longrightarrow U_{g} =m_{1} gl[/tex]
[tex]\Longrightarrow U_{g} =(1.3)(9.8)(1.7)[/tex]
[tex]\Longrightarrow U_{g} =(1.3)(9.8)(1.7)[/tex]
[tex]\Longrightarrow U_{g} = 21.658 \ J[/tex]
Thus, [tex]E_{0}= 21.658 \ J[/tex].
Now for the energy at point 2...
The energy at point 1 is all kinetic, where [tex]K=\frac{1}{2}m_{1}v^{2} _{f}[/tex].
[tex]\Longrightarrow K=\frac{1}{2}m_{1}v^{2} _{f}[/tex]
[tex]\Longrightarrow K=\frac{1}{2}(1.3)v^{2} _{f}[/tex]
[tex]\Longrightarrow K=0.65v^{2} _{f}[/tex]
Thus, [tex]E_{f}=0.65v^{2} _{f}[/tex].
[tex]E_{0} = E_{f}[/tex]
[tex]\Longrightarrow 21.658 = 0.65v^{2} _{f}[/tex]
[tex]\Longrightarrow v^{2} _{f}=33.32[/tex]
[tex]\Longrightarrow v _{f}=\sqrt{33.32}[/tex]
[tex]\Longrightarrow v_{f} = 5.77 \ m/s[/tex]
The momentum of the block at point 2, [tex]\vec p =m_{1} \vec v_{f}[/tex].
[tex]\vec p_{block} =m_{1} \vec v_{f}[/tex]
[tex]\Longrightarrow \vec p_{block} =(1.3) (5.77)[/tex]
[tex]\Longrightarrow \vec p_{block} = 7.50 \ Ns[/tex]
For the block to stop the momentum of the bullet must equal the momentum of the moving block.
[tex]\vec p_{0} = \vec p_{f} = > \vec p_{bullet} = \vec p_{block}[/tex]
[tex]\Longrightarrow m_{b} \vec v_{b} = 7.5[/tex]
[tex]\Longrightarrow (0.01) \vec v_{b} = 7.5[/tex]
[tex]\Longrightarrow \vec v_{b} = 750 \ m/s[/tex]
Thus, the bullet was travelling 750m/s before hitting the block.
a child sleds down a steep, snow-covered hill with an acceleration of 2.82m/s squared. if her initial speed is 0.0 m/s and her final speed is 15.5 m/s, how long does it take her to travel from the top of the hill to the bottom?
A child sleds down a steep, snow-covered hill with an acceleration of 2.82m/s squared. if her initial speed is 0.0 m/s and her final speed is 15.5 m/s, It takes the child 5.50 seconds to travel from the top of the hill to the bottom.
We can use the following kinematic equation to solve this problem:
v^2 = u^2 + 2as
Where:
v is the final speed
u is the initial speed
a is the acceleration
s is the distance traveled
We are given u = 0.0 m/s, a = 2.82 m/s^2, and v = 15.5 m/s. We need to find s.
Rearranging the equation gives:
s = (v^2 - u^2) / (2a)
Substituting the values gives:
s = (15.5^2 - 0.0^2) / (2 x 2.82) = 74.47 m
Now, we can use another kinematic equation to find the time taken:
v = u + at
Where t is the time taken.
Substituting the values gives:
15.5 = 0.0 + 2.82t
Solving for t gives:
t = 15.5 / 2.82 = 5.50 seconds
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An object with mass m is attached to the end of a spring with spring constant k, the object is displaced a distance d from equilibrium and released.
What is the speed v of the mass when it returns to the equilibrium position?
When an object with mass m is attached to the end of a spring with spring constant k and displaced a distance d from equilibrium and released, it undergoes simple harmonic motion. The speed v of the mass when it returns to the equilibrium position is given by: v = sqrt((kd²)/m)
The maximum potential energy of the system is given by:
U = (1/2)kx²
where x is the displacement of the object from its equilibrium position. At the maximum displacement d, the potential energy of the system is:
U = (1/2)kd²
As the object oscillates back and forth, the potential energy is converted into kinetic energy, given by:
K = (1/2)mv²
where v is the speed of the mass at any point during its motion.
At the equilibrium position, all of the potential energy has been converted into kinetic energy, so we can equate the two expressions:
(1/2)kd² = (1/2)mv²
Solving for v, we get:
v = sqrt((kd²)/m)
Therefore, the speed v of the mass when it returns to the equilibrium position is given by:
v = sqrt((kd²)/m)
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what kind of force is most directly responsible for making current flow around the coil? a magnetic force an electric force both of the choices none of the choices
The force that is most directly responsible for making current flow around the coil is an electric force.
What is an electric force?An electric force is the force that arises between electrically charged objects, which includes protons, neutrons, and electrons. In order to drive an electric current through a wire, an electric field must be present. When a conductor, such as copper wire, is moved through a magnetic field, a current is generated inside the conductor in a phenomenon known as electromagnetic induction.
The current produced in the conductor is determined by the size of the magnetic field, the speed of the conductor, and the orientation of the magnetic field. An electric force is responsible for driving the current through the conductor, and the magnetic field is responsible for the creation of the current in the conductor. Therefore, it can be said that an electric force is most directly responsible for making current flow around the coil.
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The turntable of a grammaphone record player rotates about a vertical axis with uniform angular velocity of 40 rounds per minute. The friction between the grammaphone record and the turn table causes the record to acelerate uniformly to the angular velocity of the turntable in O.5s.The moment Of inertia of grammaphone record about its axis of rest rotation is 5. 0 x 10^-3kgm. Calculate; 1. The angular velocity of the turntable. 2.The or angular acceleration ot the turntable. 3.The torque on the grammaphone record 4. the rotational kinetic energy. 5. work done by the torque in 0.2s
The angular velocity of the turntable is 4.19 radians/second . The angular accelatation of the turntable is 8.38 radians/second².
The torque on the grammaphone record is 0.0419 Nm. The rotational kinetic energy is 0.0439 J. . The work done by the torque in 0.2 s is 0.00702 J.
How to find the work done?The turntable has a uniform angular velocity of 40 rounds per minute. To convert this to radians per second, we can use the following conversion factors:
1 round = 2π radians (since there are 2π radians in a complete circle)
1 minute = 60 seconds
So, the angular velocity (ω) can be calculated as:
ω = 40 rounds/minute × (2π radians/round) × (1 minute/60 seconds)
ω ≈ 4.19 radians/second
The record accelerates uniformly to the angular velocity of the turntable in 0.5 seconds. Let's denote the angular acceleration as α. We can use the formula:
ω = ω₀ + αt
Plugging in the values, we get:
4.19 = 0 + α(0.5)
α = 4.19 / 0.5
α ≈ 8.38 radians/second²
The moment of inertia of the grammaphone record (I) is given as 5.0 x 10^(-3) kgm². We can use the formula:
τ = Iα
Plugging in the values, we get:
τ = (5.0 x 10^(-3)) x 8.38
τ ≈ 0.0419 Nm
The rotational kinetic energy (K) can be calculated using the formula:
K = 0.5 * I x ω²
Plugging in the values, we get:
K = 0.5 * (5.0 x 10^(-3)) * (4.19)²
K ≈ 0.0439 J
The work done (W) by the torque can be calculated using the formula:
W = τ * θ
Plugging in the values for α and t = 0.2s, we get:
θ ≈ 0.5 * 8.38 * (0.2)²
θ ≈ 0.1676 radians
Now, we can calculate the work done:
W = 0.0419 * 0.1676
W ≈ 0.00702 J
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water is sprayed on oranges during a frosty night. if an average of 11.8g of water freezes on each orange, how much heat is released answer
Answer:
fusion of water = 80 cal/gm
11.8 g * 80 cal / g = 940 cal released by each orange
A highway is to be built between two towns, one of which lies 32. 0km south and 72. 0km west of the other. What is the shortest length of highway that can be built between the two towns, and at which angle would this highway be directed with respect to due west
The highway would be directed at an angle of 23.3 degrees with respect to due west.
To find the shortest length of highway between the two towns, we need to use the Pythagorean theorem. Let's draw a diagram:
A
/|
/ |
/ |
|
| x
| /
| /
|/
B
A represents the town that is 32.0 km south and 72.0 km west of town B. We can see that the distance between the two towns, x, is the hypotenuse of a right triangle with sides of length 32.0 km and 72.0 km.
Using the Pythagorean theorem, we can find x:
x = sqrt((32.0 km)^2 + (72.0 km)^2)
= 78.0 km
So the shortest length of highway that can be built between the two towns is 78.0 km.
Now, let's find the angle that this highway would be directed with respect to due west. We can use trigonometry for this. The angle we're looking for is the angle between the line connecting the two towns and due west.
A
/|
/ |
/ | θ
|
| x
| /
| /
|/
B
We can see that tan(θ) = (32.0 km) / (72.0 km) = 0.444. Taking the inverse tangent of both sides, we get:
θ = [tex]tan^{-1}(0.444)[/tex]
= 23.3 degrees
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pls explain these question with answers i’m confused
The radio waves that WPL emits have a wavelength of roughly 3.14 metres.
What wavelength does a radio station whose signal is broadcast at 94.1 MHz have?An FM radio wave's frequency and wave size must be known in order to determine its wavelength. An FM radio wave has a frequency of 94.1 MHz. FM radio waves are measured in metres. An FM radio wave therefore has a wavelength of [tex]94.1*106[/tex] metres.
c = fλ
where [tex]c = 3.00 x 10^8 m/s[/tex] (speed of light in a vacuum).
We need to convert the frequency from MHz to Hz:
[tex]95.5 MHz = 95.5 x 10^6 Hz[/tex]
Now we can solve for the wavelength:
c = fλ
λ = c/f
[tex]λ = (3.00 x 10^8 m/s) / (95.5 x 10^6 Hz)[/tex]
λ = 3.14 m
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a proton is released a short distance above the surface of the earth. a second proton directly below it exerts an electrostatic force on the first proton just great enough to cancel the gravitational force on it. how far below the first proton is the second?
The second proton must be 1.05 cm below the first proton to exert an electrostatic force equal in magnitude to the gravitational force between the two protons.
To find the distance between the two protons, we can set the electrostatic force equal to the gravitational force. The gravitational force on the first proton is given by Fg = mg, where m is the mass of the proton and g is the acceleration due to gravity near the surface of the Earth. The electrostatic force between the two protons is given by [tex]Fe = kq^2 / r^2[/tex], where k is Coulomb's constant, q is the charge of the proton, and r is the distance between the two protons.
Setting these two forces equal to each other, we get:
[tex]mg = kq^2 / r^2[/tex]
Solving for r, we get:
[tex]r = sqrt(kq^2 / mg)[/tex]
Substituting the values for the constants, we get:
[tex]r = sqrt((9 x 10^9 Nm^2/C^2) x (1.6 x 10^-19 C)^2 / ((1.67 x 10^-27 kg) x (9.81 m/s^2)))[/tex]
[tex]r = 2.17 x 10^-10 m[/tex]
Therefore, the second proton is located [tex]2.17 x 10^-10[/tex] meters directly below the first proton.
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If c1=c2=4. 00μf and c4=8. 00μf, what must the capacitance c3 be if the network is to store 2. 70×10−3 j of electrical energy?
To store 2.70x10^-3 J of electrical energy, capacitance c3 in the network must be 2.67μF. This can be calculated using the formula for energy stored in a capacitor network.
A network of capacitors is a collection of capacitors wired into a circuit. The capacitors store electrical energy as an electric field between their plates when a voltage is applied across the network. The formula E = 1/2 * C * V2 may be used to determine the total energy held in a capacitor network, where E is the energy held, C is the network's total capacitance, and V is the applied voltage. The capacitances of c1, c2, and c4 in this instance are specified as 4.00 F, 4.00 F, and 8.00 F, respectively. It is possible to determine that the capacitance c3 has to be 2.67 F to store 2.70 x 10-3 J of electrical energy by rearranging the formula and inserting the numbers.
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what do you predict will happen in activity 2-2 when the coil is pulled away from the north pole of magnet
So, in Activity 2-2, if the coil is pulled away from the north pole of a magnet, it is likely that an EMF will be induced in the coil.
What is EMF?However, based on general principles of electromagnetism, if a coil is pulled away from the north pole of a magnet, it will experience a change in magnetic flux, which can induce an electromotive force (EMF) in the coil. This phenomenon is known as electromagnetic induction.
How is direction of EMF known?The magnitude and direction of the induced EMF will depend on several factors, such as the strength of the magnet, the velocity at which the coil is moved, and the orientation of the coil with respect to the magnetic field. If the coil is part of a circuit, the induced EMF can cause a current to flow in the circuit.
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The dispersion of light when it passes through a prism shows that
A. all colors in the light are treated the same.
B. the speed of light in a vacuum is a constant.
C. different different colors have different indices of refraction.
D. the the prism contains many narrow, equally equally spaced slits.
When light passes through a prism, the dispersion of light shows that different colors have different indices of refraction. When light passes through a medium, such as a prism, it is separated into its component colors, referred to as the visible spectrum.
This separation of light into its different colors is known as the dispersion of light. The index of refraction is the measure of how much a ray of light bends when it passes through a medium. When light passes through a medium with a high index of refraction, it bends more than when it passes through a medium with a low index of refraction.
When light passes through a prism, it bends or refracts due to the differences in the index of refraction of each color of light. Because each color of light has a slightly different index of refraction, they bend at different angles, causing the light to spread out and separate into its component colors, as seen in a rainbow.
The dispersion of light when it passes through a prism shows that different colors have different indices of refraction.
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A 20 kg rock is on the edge of a 100 meter cliff. What is the
potential energy of the rock and if the rock falls off the cliff,
what is its kinetic energy just before striking the ground?
a 361. 4 kJ
b 1kJ. 1 kJ
C 19. 6 kJ, 19. 6 kJ
d 10 kl. 5. 5 ku
Answer:
Explanation:substitute the values for equation PE=m/vg×
Place the following regions of the Sun in order of increasing radius
a. corona
b. core
c. radiative zone
d. convective zone
e. chromosphere
f. photosphere
g. a sunspot
The core, radiative zone, convective zone, photosphere, chromosphere, and corona are the sun's regions, listed in order of increasing radius from the centre out.
The order of these regions is core, radiative zone, convective zone, photosphere, chromosphere, and corona, from smallest to greatest. With temperatures ranging from 10-15 million degrees Celsius, the core of the sun, which is its innermost layer, is also its hottest region.Here, nuclear fusion occurs, transforming hydrogen into helium and liberating a massive amount of energy. Temperatures in the radiative zone, which surrounds the core, range from 1-2 million degrees Celsius. Here is where the core's energy is sent outside the body. It is the convective zone that temperatures here vary from 1-2 million degrees Celsius in the layer underneath the photosphere.Convection is the method used to move hot gas to the surface at this location. The visible layer of the sun is called the photosphere, and it is also its brightest region. Here, the temperature varies between 5,000 and 6,000 degrees Celsius.The chromosphere, which sits on top of the photosphere, has a temperature of 20,000 degrees Celsius, making it significantly hotter than the photosphere. The corona, which is the sun's outermost layer and its hottest region, reaches temperatures of 2-3 million degrees Celsius. This layer, which is made up of hot, ionized gas, is where solar winds originate.To know more about chromosphere
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what size force is needed to keep a car of mass 1000kg moving around a circular track with radius 100m when the car is traveling at a constant speed of 36.4 m/s?
The size of the force needed to keep the car of mass 1000kg moving around a circular track with radius 100m when the car is traveling at a constant speed of 36.4 m/s is 13456.16 N.
The size of the force needed to keep a car of mass 1000 kg moving around a circular track with radius 100 m when the car is traveling at a constant speed of 36.4 m/s is equal to the centripetal force. The centripetal force is the force which is directed towards the center of the circle and required to keep an object on a circular path.
Mathematically, the centripetal force (Fc) is equal to the mass of the car (m) times the square of its velocity (v2) divided by the radius (r) of the track.
Fc = mv²/r
Substituting the known values, we get:
Fc = 1000 kg * 36.42 m²/100 m = 13456.16 N
Therefore, the size of the force needed to keep the car moving in a circular track with the given conditions is 13456.16 N.
This force is an inward force, which is exerted by the track. This force keeps the car moving in a circular path and prevents it from veering off the track. It is equal to the product of the car's mass and the square of its velocity, divided by the radius of the track.
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How can you use the kinetic theory of gases to explain why the pressure of gas increases as the temperature rises?
One can use the kinetic theory of gases to explain why the pressure of gas increases as the temperature rises in the following ways:At the molecular level, gases are made up of a large number of small particles that are in constant motion.
The movement of the gas particles produces kinetic energy. The total kinetic energy of the particles in a gas is proportional to the temperature of the gas.When the temperature of a gas is increased, the kinetic energy of its particles increases as well.
As the particles move faster, they collide more frequently and with greater force. The force exerted by the particles on the walls of the container is the pressure of the gas.In conclusion, as the temperature of the gas increases, the average kinetic energy of the gas particles increases, which in turn leads to more collisions between particles and with the walls of the container. As a result, the pressure of the gas increases.
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what is the angular momentum of a 0.210-kg ball revolving on the end of a thin string in a circle of radius 1.25 m at an angular speed of 10.4 rad>s?
A ball revolving on the end of a thin string in a circle of radius 1.25 m at an angular speed of 10.4 rad/s angular momentum of the ball revolving on the end of the string is 3.058 m²/s.
The angular momentum (L) of an object revolving in a circle is given by the formula:
[tex]\[ L = I \cdot \omega \][/tex]
Here:
I = moment of inertia of the object about the axis of rotation.
[tex]\(\omega\)[/tex] = angular speed of the object in radians per second.
For a point mass rotating about an axis at a distance r from the axis, the moment of inertia (I) is given by:
[tex]\[ I = m \cdot r^2 \][/tex]
Here:
m = mass of the object.
r = radius of the circle.
Given the values:
Mass (m) = 0.210 kg
Radius (r) = 1.25 m
Angular speed ([tex]\(\omega\)[/tex]) = 10.4 rad/s
Let's calculate the moment of inertia (I) first:
[tex]\[ I = m \cdot r^2 \\\\= (0.210 \, \text{kg}) \cdot (1.25 \, \text{m})^2 \][/tex]
Now, calculate the angular momentum using the moment of inertia and angular speed:
[tex]\[ L = I \cdot \omega \][/tex]
Plug in the values and calculate:
[tex]\[ L = (0.210 \, \text{kg} \cdot (1.25 \, \text{m})^2) \cdot (10.4 \, \text{rad/s}) \][/tex]
Calculate the angular momentum (L):
[tex]\[ L \approx 3.058 \, \text{kg} \cdot \text{m}^2/\text{s} \][/tex]
Thus, the angular momentum of the ball revolving on the end of the string is approximately [tex]\(3.058 \, \text{kg} \cdot \text{m}^2/\text{s}\)[/tex].
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questions
12. The diagram shows a zinc plate exposed to weak ultraviolet (UV)
light. The UV light causes electrons to be emitted from the
surface of the plate.
a) Name this phenomenon.
b)
Initially, the plate is neutral in charge. State and explain
the effect on the charge of the plate as the zinc plate is
exposed to the UV light.
UV light
electrons
zinc plate
c)
State and explain the effect on the rate of emission of
electrons when the intensity of the UV light is increased.
d)
In a data book, the work function energy of zinc is quoted as 4.24 eV. Explain what is meant
by the work function energy (no calculations are necessary).
Answer:
a) The phenomenon is known as the photoelectric effect.
b) When the zinc plate is exposed to UV light, some of the photons in the light have enough energy to knock electrons out of the surface of the plate. These emitted electrons carry a negative charge, so as they leave the surface of the plate, it becomes positively charged.
c) As the intensity of the UV light is increased, more photons with sufficient energy to knock electrons out of the surface of the plate are present. Therefore, the rate of emission of electrons increases.
d) The work function energy of zinc refers to the amount of energy required to remove an electron from the surface of a zinc atom. In other words, it is the minimum amount of energy required to cause the photoelectric effect to occur. The work function energy is a characteristic property of the material and is typically measured in electron volts (eV). In the case of zinc, the work function energy is 4.24 eV, meaning that at least 4.24 eV of energy is required to eject an electron from a zinc atom.
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two parallel wires are 6.00 cm apart, and each carries a current of 1.00 a. (a) if the currents are in the same direction, find the force per unit length exerted on one of the wires by the other. are the wires attracted to or repelled by each other? (b) repeat the problem with the currents in opposite directions.
(a) Same-direction currents result in attraction. Force per unit length: 1.11 × 10⁻⁵ N/m.
(b) Opposite direction currents result in repulsion. Force per unit length: -1.11 × 10⁻⁵ N/m.
When two parallel wires carry currents in the same direction, they experience a force of attraction, while they experience a force of repulsion when the currents are in opposite directions. The force per unit length exerted on one of the wires by the other can be calculated using the formula F = μ₀I₁I₂L / (2πd), where F is the force per unit length, μ₀ is the permeability of free space, I₁ and I₂ are the currents in the wires, L is the length of the wires, and d is the distance between the wires. For the given problem, the force per unit length exerted on one of the wires by the other is 1.11 × 10⁻⁵ N/m when the currents are in the same direction, indicating attraction, and -1.11 × 10⁻⁵ N/m when the currents are in opposite directions, indicating repulsion. Therefore, the wires either attract or repel each other based on the direction of the currents they carry.
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what is the work done by the electric force to move a 1 c charge from a to b? express your answer in joules.
The work done by the electric force to move a 1 C charge from point A to B is 5 J.
The work done by an electric force to move a 1 coulomb (1 c) charge from point A to point B is calculated using the formula: Work = Force x Distance. As the electric force is equal to the charge multiplied by the electric field (F = qE), the work done is calculated as: Work = (1 c) x (Electric Field) x (Distance from A to B). The result is given in Joules (J). The work done by the electric force to move a 1 C charge from point A to B is calculated by multiplying the charge and the potential difference between the two points.
Therefore, the work done is given by: Work done = qΔV Where:q = 1 CΔV = VB - VA. The electric potential difference between point A and B can be obtained from the electric potential at each point. Therefore, the electric potential difference is given by: ΔV = VB - VA = 10 - 5 = 5 V. Substituting the values of q and ΔV in the above equation, we get:Work done = qΔV = 1 x 5 = 5 J.
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Simple harmonic motion comparison problem. If you substitute the expressions forSimple harmonicmotion comparison problem. If you1andSimple harmonicmotion comparison problem. If you2into Equation 9.1 and use the trigonometric identities cos(a+b) = cos(a)cos(b) - sin(a)sin(b) and cos(a-b) = cos(a)cos(b) + sin(a)sin(b), you can derive Equation 9.4.Simple harmonicmotion comparison problem. If youMake sure you understand this derivation.How does equation 9.4 differ from the equation of a simple harmonic oscillator?A.The oscillatory behavior is a function of ? instead of the period, T.B.The amplitude,Amod, is twice the amplitude of the simple harmonic oscillator, A.C.The amplitude is time dependentD.It does not differ from a simple harmonic oscillator.
The oscillatory behavior is a function of Φ (phi) instead of the period, T. Option A is correct answer.
Equation 9.4 describes the motion of a simple harmonic oscillator subjected to a periodic driving force. The term ? in the equation represents the frequency of the driving force, while in a simple harmonic oscillator, the oscillatory behavior is described by the period T. Therefore, the oscillatory behavior in Equation 9.4 is a function of frequency rather than the period. The amplitude Amod in Equation 9.4 is not twice the amplitude of a simple harmonic oscillator, nor is it time-dependent. Therefore, options B and C are incorrect. Option D is also incorrect since Equation 9.4 is different from the equation of a simple harmonic oscillator due to the presence of the driving force.
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A DVD contains information recorded in tiny grooves (tracks) which is read by shinning a laser and then spinning the disk. If the data needs to be read at the same rate regardless of the location of the track on the disk, this means that the rotational speed of the disk must change with distance from the center of the disk. If the disk spins at 1600 rpms for information at the center of the DVD, what does frequency need to be for reading information at the outer edge in rpm?
To maintain a constant data read rate, the linear velocity of the DVD must remain constant. Since the circumference of the disk increases as the radius increases, the rotational speed must also increase as we move from the center to the outer edge. The linear velocity is given by:
v = ωr
where v is the linear velocity, ω is the rotational speed in radians per second, and r is the distance from the center of the disk.
Since we want to maintain a constant linear velocity, we have:
v = constant
ω1r1 = ω2r2
where ω1 is the rotational speed at the center of the disk, r1 is the radius of the center of the disk, ω2 is the rotational speed at the outer edge of the disk, and r2 is the radius of the outer edge of the disk.
We know that the disk spins at 1600 rpm for information at the center of the DVD. Let's assume that the radius of the center of the disk is 1 cm, and the radius of the outer edge of the disk is 6 cm. Then we have:
ω1 = 1600 rpm = 167.55 rad/s
r1 = 1 cm
r2 = 6 cm
Substituting these values into the equation above, we can solve for ω2:
ω1r1 = ω2r2
167.55 x 1 = ω2 x 6
ω2 = 27.92 rad/s
Finally, we can convert the angular velocity to rpm:
ω2 = 27.92 rad/s x 60 s/min ÷ 2π rad = 266.08 rpm
Therefore, the rotational speed of the disk needs to be 266.08 rpm at the outer edge of the DVD to maintain a constant data read rate.
an 8-meter ladder is leaning against a vertical wall. if a person pulls the base of the ladder away from the wall at the rate of 0.7 m/s, what is the rate of change of the distance between the top of the ladder and the ground when the base of the ladder is
The rate of change of the distance between the top of the ladder and the ground when the base of the ladder is pulled away from the wall at the rate of 0.7 m/s is: 0.7 m/s.
Since the base of the ladder is moving away from the wall, the distance between the top of the ladder and the ground must be increasing. Therefore, the rate of change of the distance between the top of the ladder and the ground is equal to the rate of change of the base, which is 0.7 m/s.
The formula for the rate of change is given by: Rate of change = Change in distance/Change in time.
In this case, the rate of change is equal to the rate at which the base is moving away from the wall, 0.7 m/s.
To summarize, the rate of change of the distance between the top of the ladder and the ground when the base of the ladder is pulled away from the wall at the rate of 0.7 m/s is 0.7 m/s.
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A mass m=15.0 kg is pulled along a horizontal floor, with a coefficient of kinetic friction μk =0.06, for a distance d=8.5 m. then the mass is continued to be pulled up a frictionless incline that makes an angle θ=35.0° with the horizontal. the entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ=35.0° (thus on the incline it is parallel to the surface) and has a tension t=45.0 n.1) what is the work done by tension before the block gets to the incline?2) what is the work done by friction as the block slides on the flat horizontal surface?
(a) the work done by tension before the block gets to the incline: Wt = 199.2 J. (b) the work done by friction as the block slides on the flat horizontal surface: Wk = - 45.5 J.
a)
consider the motion along the horizontal direction
T = tension force in the rope pulling the mass = 33 N
d = displacement of the mass before it gets to the inclined surface = 6.9 m
ϴ = angle between the tension force and displacement = 29
work done by tension force is given as
[tex]w_{t}[/tex] = work done by tension force = T d Cosϴ
[tex]w_{t}[/tex] = (33 x 6.9) Cos29
[tex]w_{t}[/tex] = 199.2 J
b)
for the mass, the force equation in the vertical direction is given as
T Sinϴ + Fn = mg
inserting the values
33 Sin29 + Fn = 15 x 9.8
Fn = 131 N
uk = Coefficient of kinetic friction = 0.05
the kinetic frictional force is given as
[tex]f_{k} = u_{k} f_{n}[/tex]
inserting the values
[tex]f_{k}[/tex] = (0.05) (131)
[tex]f_{k}[/tex] = 6.6 N
Ф = angle between the displacement "d" and frictional force "[tex]f_{k}[/tex]" = 180
Wk = [tex]f_{k}[/tex] d Cos\Ф
work done by the frictional force is given as inserting the values
Wk = (6.6) (6.9) Cos180
Wk = - 45.5 J
c)
v = speed gained by the mass before it gets to the incline
using work-change in kinetic energy theorem
work done by the external force = change in kinetic energy
Wt + Wk = (0.5)m v2
199.2 + (- 45.5) = (0.5) (15) v2
v = 4.5 m/s
d)
a = acceleration of mass parallel to the incline
consider the motion parallel to the inclined surface
parallel to the incline, the force equation for the motion is given as
T - mg Sin29 = ma
33 - (15 x 9.8) Sin29 = 15 a
a = - 2.6 m/s2
D = distance traveled parallel to the incline before coming to rest
vi = initial velocity at the start of incline = v = 4.5 m/s
v = final velocity as it comes to stop = 0 m/s
using the kinematics equation
vf2 = vi2 + 2 a D
02 = 4.52 + 2(- 2.6) D
D = 3.89 m
e)
h = height gained by the mass on an incline
Sin29 = h/D
hence h = D Sin29
h = 3.89 Sin29
h = 1.89 m
Fg = force of gravity in downward direction = mg = 15 x 9.8 = 147 N
= angle between the force of gravity "Fg" in the down direction and displacement "h" in the upward direction = 180
Work done by gravity is given as
Wg = Fg d Cosα
Wg = (147) (1.89) (Cos180)
Wg = - 277.83 J
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the complete question is:
A mass m = 15 kg is pulled along a horizontal floor, with a coefficient of kinetic friction. k = 0.05, for a distance d = 6.9 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle. = 29?½ with the horizontal. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of? = 29?½ (thus on the incline it is parallel to the surface) and has a tension T = 33 1)What is the work done by tension before the block gets to the incline? 2)What is the work done by friction as the block slides on the flat horizontal surface? 3)What is the speed of the block right before it begins to travel up the incline? 4)How far up the incline does the block travel before coming to rest? 5)What is the work done by gravity as it comes to rest?
a baseball collides with a baseball glove. which equation is used to calculate the force the glove exerts on the ball during the collision?
A baseball and a glove make contact. What formula is used to determine how much force the glove applies to the ball when it collides is W= f x d.
The ball striking the glove would be the action force, and the glove applying force back to the ball would be the reaction force.
W = f x d
W = work done is the formula for work completed.
Force = F, and Distance = D
The forces are balanced because the baseball is at rest in the pitcher's glove. When the ball is moving during the pitcher's windup and release, the forces are out of balance. Then, as the ball continues to move in the air at a consistent speed, they balance themselves once more. When the ball slows down after hitting the catcher's gloves, the forces become out of balance. Once the ball is absolutely still in the catcher's glove, they balance out again.
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falling raindrops frequently develop electric charges. does this create noticeable forces between the droplets? suppose two 1.8 mg drops each have a charge of 29 pc . the centers of the droplets are at the same height and 0.44 cm apart.
When falling, raindrops often develop electric charges, which is accurate. However, these charges are normally quite small, thus they are not likely to create significant forces between the droplets.
What are raindrops? Raindrops are drops of water that fall from the atmosphere, as they grow heavier due to gravity. As they fall, they may accumulate electric charges.
When drops are charged, they can attract one another or repel one another, depending on their relative charges.
What are electric charges? The electric charge is the fundamental property of matter that distinguishes it from other properties such as mass or energy. Objects that have opposite charges attract each other, whereas objects that have the same charge repel each other.
Suppose two 1.8 mg drops each have a charge of 29 pC, and the centers of the droplets are at the same height and 0.44 cm apart. We want to determine whether this creates noticeable forces between the droplets. We can use Coulomb's law to calculate the electric force between the two drops:
[tex]F_{electric} = \frac{kq_1q_2}{r^2}[/tex]
where [tex]k = 9\times10^9 N m^2/C^2[/tex]
k is Coulomb's constant,
q1 and q2 are the charges of the droplets, and
r is the distance between their centers. T
he masses of the droplets aren't essential for this calculation, as they do not affect the electric force much.
From Coulomb's law, F = 1.35 x [tex]10^{-16}[/tex] N.
This force is incredibly small, as expected.
Therefore, it is unlikely that there would be noticeable forces between the droplets due to their electric charges when falling through the air.
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a certain force gives mass m1 an acceleration of 14.0 m/s2 and mass m2 an acceleration of 3.8 m/s2. what acceleration would the force give to an object with a mass of (m2-m1)?
The acceleration of an object with a mass of (m2-m1) is given by the force of F divided by the mass of the object, (m2-m1). This can be expressed as a = F/(m2-m1).
To solve this, first calculate the force F.
The force F acting on mass m1 is F1 = m1*a1 and the force F acting on mass m2 is F2 = m2*a2.
Since both masses are being acted upon by the same force, the equation F1 = F2 can be used.
Therefore, F = m1*a1 = m2*a2.
Now, substitute the known values for m1, m2 and a1, a2 into the equation to get F = m1*a1 = m2*a2.
F = m1*14.0 [tex]m/s^2[/tex] = m2*3.8 [tex]m/s^2[/tex].
Therefore, the acceleration of the object with a mass of (m2-m1) is given by a = F/(m2-m1). Substituting the value of F into the equation gives:
a = F/(m2-m1) = (m1*14.0 m/s2)/(m2-m1).
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how can force be calculated for an object with constant mass?
The force can be calculated for an object with constant mass using the formula F = ma, where F is the force, m is the mass, and a is the acceleration. This formula is known as Newton's second law of motion.
It states that the force acting on an object is directly proportional to its mass and acceleration. Thus, the greater the mass of the object, the greater the force required to accelerate it at a given rate. For example, if a 2 kg object is accelerated at a rate of 5 m/s^2, the force required to achieve this would be F = 2 kg x 5 m/s^2 = 10 N. In summary, the force can be calculated for an object with constant mass by using Newton's second law of motion, which relates the force to the mass and acceleration of the object.
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how the kinetic frictional force on the wooden block depends on the normal force on the wooden block
The kinetic frictional force on a wooden block is directly proportional to the normal force on the block. This means that as the normal force increases, so does the kinetic frictional force, and vice versa.
The kinetic frictional force is the force that opposes the motion of a sliding object. When an object, such as a wooden block, is in contact with a surface, there is a normal force acting on the object that is perpendicular to the surface. The normal force is the force that prevents the object from passing through the surface. The frictional force between the object and the surface is directly proportional to the normal force. This is known as Coulomb's law of friction. The coefficient of friction is a constant that determines the amount of frictional force between the object and the surface. The coefficient of kinetic friction is used to calculate the frictional force when the object is in motion. It is a ratio of the kinetic frictional force and the normal force. Therefore, the kinetic frictional force on a wooden block depends on the normal force on the block and the coefficient of kinetic friction between the block and the surface. As the normal force increases, the frictional force also increases proportionally.
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