In RLC circuit the output omega L(t) represents the instantaneous energy stored in the inductor. It will be a function of time.
If a sinusoidal voltage is applied to the circuit, the energy stored in the inductor start to oscillates. It will start oscillating at the same frequency as the voltage.
The amplitude of the energy oscillations depends on the parameters of circuit and amplitude of the voltage. These parameters includes resistance, inductance, and capacitance.
So we can say that the output omega L(t) shows sinusoidal oscillations at a frequency of 3 Hz and an amplitude of 5. Now it would make sense for the given circuit parameters and voltage amplitude.
The waveform shape and the amplitude will depend on the specific circuit parameters. Also depend on the initial conditions.
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what is the emf of a battery that increases the electric potential energy of 0.050 c c of charge by 0.40 j j as it moves it from the negative to the positive terminal?
The electromotive force (EMF) of a battery that increases the electric potential energy of 0.050 C of charge by 0.40 J as it moves it from the negative to the positive terminal is 8 V.
Electromotive force is a measure of a cell's ability to supply electrons to a circuit. Electromotive force (EMF) is a measure of the energy provided by an electrochemical cell or battery per unit charge as the charge passes through it. The device's output voltage is measured by EMF. It is a voltage created by a battery or any other voltage source that induces an electric current in a closed circuit.
The emf of the battery can be calculated using the formula:
emf = ΔPE / Q,
where ΔPE is the change in electric potential energy and Q is the charge.
In this case, ΔPE = 0.40 J and Q = 0.050 C.
So, emf = (0.40 J) / (0.050 C) = 8 V.
The emf of the battery is 8 volts.
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in the case of the spring, why is it important that the vibration amplitude should be kept in such a way that the mass will be somewhat stretched even at its highest position?
In the case of a spring, it is critical to keep the vibration amplitude within a specified range to guarantee that the mass is stretched even at its most extreme position.
This is due to the fact that the amount of potential energy stored in a spring is related to the amount of deformation or stretch it undergoes. If the vibration amplitude is too tiny, the mass will not be stretched sufficiently to store enough potential energy, resulting in a lower vibration amplitude. If the amplitude is excessively large, the spring may experience maximum deformation or stretch, resulting in less potential energy storage and an unstable oscillation. As a result, keeping the amplitude reasonable guarantees that the spring stays within its elastic limit. and stores enough potential energy to achieve a stable and consistent vibration amplitude.
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. a car is chasing a motorcycle at a right-angle intersection. the car is approaching from the north and the motorcycle has already turned and is heading straight east. when the car is 0.6 miles north of the intersection point and the motorcycle is 0.8 miles to the east, the distance between the two vehicles is increasing at 20 miles per hour. if the car is driving 60 miles per hour at that moment in time, what is the speed of the motorcycle?
The motorcycle is driving at 60 mph.
We can use the Pythagorean theorem to relate the distance between the car and motorcycle to the distance they have traveled:
d^2 = (0.6 + vt)^2 + (0.8)^2
where d is the distance between the two vehicles, v is the speed of the motorcycle, and t is the time since the motorcycle turned east.
Differentiating both sides with respect to time, we get:
2d(dd/dt) = 2(0.6 + vt)(v)dv/dt
We are given that dd/dt = 20 mph and v = sqrt((dx/dt)^2 + (dy/dt)^2), where x is the horizontal distance traveled by the motorcycle and y is the vertical distance traveled by the car. At the moment when the car is 0.6 miles north of the intersection, we have:
x = 0.8 miles
y = 0.6 miles
dx/dt = 0 mph (since the motorcycle is heading straight east)
dy/dt = -60 mph (since the car is driving south)
Substituting these values into the equation above and solving for dv/dt, we get:
dv/dt = -3 mph
Therefore, the speed of the motorcycle is:
v = sqrt((dx/dt)^2 + (dy/dt)^2) = sqrt((0)^2 + (-60)^2) = 60 mph
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the students move so that they are now twice as far apart but use the same spring. how will the speed of the pulse sent now compare to the speed of the pulse sent when they were 5.0 m apart? explain your answer.
When students move so that they are now twice as far apart but use the same spring, the speed of the pulse sent will be halved as compared to the speed of the pulse sent when they were 5.0 m apart.
Let's see how. Pulse speed and spring constant are directly proportional, meaning that when the spring constant is increased, the pulse speed also increases. The same applies to the distance between the students and pulse speed. If the distance is halved, the speed is also halved. Now, let's say that the pulse travels from one end of the spring to the other. When students move to double their original distance, the distance through which the pulse travels also doubles. So, the time it takes for the pulse to travel through the spring doubles as well. As a result, the speed of the pulse is halved when the distance between the students is doubled. Thus, the speed of the pulse sent when they were 5.0 m apart will be twice the speed of the pulse sent now.
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at what frequency does s a 10 μ F capacitor have a reactance of 100 m uF capacitor A) 159 Hz B) 1.59 MHz D) 15.9 kHz C) 1.59 kHz
The frequency at which a 10 μF capacitor has a reactance of 100 mΩ is 1.59 kHz.
The correct answer to the given question is option C) 1.59 kHz. The frequency at which a 10 μF capacitor has a reactance of 100 mΩ is 1.59 kHz. A capacitor's reactance is a function of its capacitance and the frequency of the signal passing through it. The capacitor's impedance,
or opposition to alternating current, is determined by the reactance of the capacitor. It is denoted by the symbol Xc, which is measured in ohms (Ω).The formula for calculating the reactance of a capacitor is as follows:Xc = 1 / 2πfCWhere,
Xc is the reactance of the capacitor in ohmsf is the frequency of the signal in HertzC is the capacitance of the capacitor in faradsAs a result, the frequency at which a 10 μF capacitor has a reactance of 100 mΩ can be calculated as follows:
100 mΩ = Xc1 / 2πfC = 1 / (2π × f × 10 μF)100 × 10^-3 = 1 / (2π × f × 10 × 10^-6)2π × f = 1 / (100 × 10^-3 × 10 × 10^-6)2π × f = 1 / 100f = 1 / (100 × 2π) = 1.59 × 10^3 HzHence, the frequency at which a 10 μF capacitor has a reactance of 100 mΩ is 1.59 kHz.
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an elastic ball that wastes 30% of the collision energy as heat when it bounces on a hard floor will rebound to 70% of the height from which it was dropped. explain the 30% loss in height.
The loss in height is 30% as the loss in the energy is equal to 30% due to proportionality between height and energy.
It is given that the elastic ball that wastes 30% of the collision energy as heat.
On bouncing on the hard floor, it will rebound to 70% of the height.
The loss in height is given as 30%.
We know that, gravitational potential energy is proportional to height.
The collision's energy is completely converted into gravitational potential energy.
Hence, the 30% loss in the energy is nothing but the 30% loss in height.
Rebound height loss of 30% results in a 30% reduction in gravity potential energy. The energy that was converted into thermal energy is equivalent to this.
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e
A proton and an electron in a hydrogen
atom are separated on the average by about
5 × 10^−11 m.
What is the magnitude of the electric field
set up by the proton at the location of the
electron? The value of the Coulomb constant
is 8.99 × 10^9 N · m^2/C^2
.
Answer in units of N/C.
Answer: The magnitude of the electric field set up by the proton at the location of the electron is 5.68 × 10^11 N/C.
Explanation: The electric field at a distance r from a point charge q is given by Coulomb’s law as:
E = kq/r^2
where k is Coulomb’s constant (8.99 × 10^9 N · m2/C2).
In this case, the distance between the proton and electron is r = 5 × 10^-11 m. Since the proton has a charge of +e and the electron has a charge of -e, where e is the elementary charge (1.602 × 10^-19 C), we have:
E = kq/r^2 = (8.99 × 10^9 N · m2/C2) × [(+e)(-e)]/(5 × 10^-11 m)^2 = 5.68 × 10^11 N/C.
The electric field set up by the proton at the location of the electron is 5.68 × 10^11 N/C.
Hope this helps, and have a great day! =)
finding the actual speed and direction of an aircraft a dc-lo jumbo jet maintains an airspeed of 550 miles per hour in a southwesterly direction. the velocity of the jet stream is a constant 80 miles per hour from the west. find the actual speed and direction of the aircraft.
The actual speed of the aircraft is approximately 554.7 miles per hour, at an angle of 217.6 degrees south of west, calculated using vector addition of airspeed and jet stream velocity.
To find the actual speed and direction of the aircraft, we can use vector addition. Let's represent the airspeed of the aircraft as a vector with magnitude of 550 miles per hour pointing southwest, and the velocity of the jet stream as a vector with magnitude of 80 miles per hour pointing due west. To find the actual velocity of the aircraft, we add these two vectors using the head-to-tail method or the parallelogram method. The resulting vector represents the actual velocity of the aircraft with respect to the ground. The magnitude of this vector is approximately 554.7 miles per hour, and its direction is 217.6 degrees south of west (measured counterclockwise from due west). Therefore, the aircraft is moving at an actual speed of 554.7 miles per hour towards the south-southwest direction.
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A 50Kg block is pulled up in an inclined plane at angle of 53° to the horizontal, if the surface is frictionless, what is the efficiency of the inclined?
Efficiency is defined as the ratio of useful work output to total work input. In this case, the useful work output is the work done in lifting the block, and the total work input is the work done by the pulling force.
The work done in lifting the block is given by the formula: work = force x distance x cos(theta), where theta is the angle between the force and the displacement.
In this case, the force is the weight of the block, which is given by: F = m x g = 50 kg x 9.8 m/s^2 = 490 N.
The distance lifted by the block is given by: d = h / sin(theta), where h is the height the block is lifted.
Let's assume that the block is lifted to a height of 1 meter. Then, we have: d = 1 / sin(53) = 1.28 meters.
So, the work done in lifting the block is: work = 490 N x 1.28 m x cos(53) = 295 J.
The work done by the pulling force is given by: work = force x distance, where the distance is the length of the inclined plane. Let's assume that the length of the inclined plane is 2 meters. Then, we have: work = 490 N x 2 m = 980 J.
Therefore, the efficiency of the inclined plane is: efficiency = useful work output / total work input = 295 J / 980 J = 0.301 or 30.1%.
what characteristic do all of the outer planets have in common? responses they are small and dense they are small and dense they have liquid cores they have liquid cores they are mostly made of hydrogen and helium they are mostly made of hydrogen and helium they lack moons
The outer planets have in common, The characteristic that all of the outer planets have in common is that they are mostly made of hydrogen and helium.
These planets are also known as gas giants, and they are composed mainly of these two gases. They are much larger than the inner rocky planets, with sizes ranging from 4 to 30 times that of the Earth.
These planets also have a lower density compared to the inner rocky planets, as they are composed mainly of gases rather than solid materials. Additionally, they have liquid cores and are known to have a large number of moons. Hence, the correct option is: They are mostly made of hydrogen and helium.
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A 0.0214 m diameter coin rolls up a 13.0◦
inclined plane. The coin starts with an initial
angular speed of 45.4 rad/s and rolls in a
straight line without slipping.
How much vertical height does it gain before it stops rolling?
The coin gains a vertical height of 0.182 m before it stops rolling.
What is angular speed?Angular speed is a term used to describe the rate of change of angular movement.
KE = (1/2)Iω² + (1/2)mv²
I is moment of inertia of the coin, ω is angular velocity, m is mass of coin, and v is its linear velocity.
As v = ωr
r is radius of the coin. For a uniform disk, the moment of inertia is given by: I = (1/2)mr²
KE = (1/2)(1/2)mr²ω² + (1/2)mv²
KE = (1/4)mr²ω² + (1/2)mv²
v = ωr
KE = (1/4)mr²(ω²+ 4v²)
KE = (1/4)(0.0214/2)²(45.4² + 4(0)²) = 0.0235 J
As PE = m g h
m g h = KE
mg(h/g) = KE
h = KE/mg
h = 0.0235/(0.0214/2)²(9.81) = 0.182 m
Therefore, coin gains a vertical height of 0.182 m before it stops rolling.
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newton's second law: a 60.0-kg person rides in an elevator while standing on a scale. the elevator is traveling upward but slowing down at a rate of 2.00 m/s2. the reading on the scale is closest to
The reading on the scale is closest to 708.6 N. This was calculated using Newton's Second Law which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this case, the force acting on the person is the combination of gravitational force and the force exerted by the elevator.
1. Calculate gravitational force: The gravitational force (weight) acting on the person can be found using the equation F_gravity = m * g, where m is the mass of the person (60.0 kg), and g is the acceleration due to gravity (approximately 9.81 m/s²).
F_gravity = 60.0 kg * 9.81 m/s² = 588.6 N (Newtons)
2. Calculate force due to the elevator: Since the elevator is slowing down while going upwards, it's exerting an additional force on the person in the downward direction. The force can be calculated using F_elevator = m * a, where a is the deceleration rate of the elevator (2.00 m/s²).
F_elevator = 60.0 kg * 2.00 m/s² = 120 N (Newtons)
3. Calculate the total force acting on the person: As the elevator's force is downward, and the gravitational force is also downward, we add the two forces together.
F_total = F_gravity + F_elevator = 588.6 N + 120 N = 708.6 N (Newtons)
4. Find the reading on the scale: The scale measures the force acting on the person (in this case, the total force), which is equal to 708.6 N.
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The removal of coal that is not close to earths surface through a horizontal opening in the side of a hill or mountain is called
consider a common tire pressure gauge. how would you estimate the uncertainty in a measured pressure at the design stage and then at the nth order? should the estimates differ? explain
To estimate the uncertainty in a measured pressure at the design stage and the nth order for a common tire pressure gauge, you should consider the factors affecting the gauge's accuracy, such as manufacturing tolerances, environmental factors, and calibration errors.
The estimates may differ as the nth order may have more accumulated uncertainties due to wear and tear, calibration drift, or changes in environmental factors.
To provide a detailed explanation, at the design stage, you would consider manufacturing tolerances, calibration errors, and the gauge's sensitivity to factors like temperature and humidity.
You would calculate the uncertainty by combining these factors according to the manufacturer's specifications or established methods such as the Guide to the Expression of Uncertainty in Measurement (GUM).
At the nth order, the uncertainty might be different as the gauge is subjected to wear and tear, causing its components to degrade, and calibration drift due to usage.
Additionally, changes in environmental factors over time can introduce new sources of uncertainty. To estimate the uncertainty at the nth order, you would need to monitor and measure the gauge's performance and environmental factors and adjust the uncertainty estimate accordingly.
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A biker travels once around a circular track of radius 20.0m in3s calculate the average tangential speed
Answer:
the average tangential speed of the biker is approximately 41.89 m/s.
the tilt of the earth's axis relative to its plane of orbit is 23.5 degrees. which of the following events might you predict to occur if the angle of tilt increased to 33 1/2 degrees? * 5 points a) summers in the united states would likely become warmer. b) winters and summers in australia would become indiscrete. c) seasonal variation at the equator might decrease significantly. d) the north and south poles would experience massive ice melts.
If the Earth's axial tilt is increased from 23.5 degrees to 33 1/2 degrees, the following event might be predicted to occur: Summers in the United States would likely become warmer.
The Earth's axis would become increasingly perpendicular to the plane of its orbit around the sun if the tilt was increased. Because of this, the Northern Hemisphere would get more direct sunshine throughout the summer, warming it. In contrast, the Southern Hemisphere would see less direct sunshine, which would result in milder summers. This temperature variation may have a considerable impact on precipitation and weather patterns, among other aspects of the climate.
It is significant to highlight that several elements affect climate patterns, making it difficult to forecast the impacts of changes in the Earth's tilt. Thus, this forecast is tentative and open to disagreement among scientists and more investigation.
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on what does the magnitude of an applied torque depend? select all that apply. on what does the magnitude of an applied torque depend?select all that apply. the distance between the point of force application and the axis of rotation of the object. the orientation of the force. the mass distribution of the extended object. the magnitude of the force.
The magnitude of an applied torque depends on the following:
the distance between the point of force application and the axis of rotation of the object.the magnitude of the force.
The applied torque magnitude is an essential quantity to consider when considering rotational motion. Torque is defined as the action of a force on an object that creates a rotational motion around an axis of rotation.
Therefore, the magnitude of an applied torque depends on the distance between the point of force application and the axis of rotation of the object, and the magnitude of the force.
When it comes to torque, the perpendicular component of the force creates torque. The perpendicular distance from the axis of rotation to the force is the torque arm (r).
Therefore, we can write,
Torque = force x torque arm.
The magnitude of torque,
F × r
is proportional to the force applied and the perpendicular distance from the axis of rotation to the line of action of the force.
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two long, straight wires both carry current to the right, are parallel, and are 25 cm apart. wire one carries a current of 2.0 a and wire two carries a current of 5.0 a. how far from wire 1 is the net magnetic field equal to 0? group of answer choices 3.43 cm 4.57 cm 1.43 cm 7.14 cm
The 4.57 cm far from wire one is the net magnetic field equal to zero. The answer is 4.57 cm (the only option given that is close to 4.5 cm).
B1 = μ0 * I1 / (2 * π * r1)
B2 = μ0 * I2 / (2 * π * r2)
Bnet = B1 + B2 = μ0 * I1 / (2 * π * r1) + μ0 * I2 / (2 * π * (0.25 - x))
μ0 * I1 / (2 * π * r1) = -μ0 * I2 / (2 * π * (0.25 - x))
Multiplying both sides by (2 * π * r1 * (0.25 - x)) and simplifying, we get:
r1 = (2 * I2 * (0.25 - x)) / I1
Substituting the given values, we get:
r1 = (2 * 5.0 * (0.25 - x)) / 2.0 = 2.5 - 2.5x
2.5 - 2.5x = 0
Solving for x, we get:
x = 1.0/4.0 = 0.25 m
So the distance from wire 1 where the net magnetic field is zero is 0.25 m, or 25 cm.
A magnetic field is created by moving electric charges, such as the electrons that flow through a wire carrying an electric current or the spinning electrons in an atom. Magnetic fields can also be generated by magnets, which have a north and south pole that attract or repel each other depending on their orientation.
Magnetic fields are invisible to the eye but can be detected using a compass, which aligns itself with the direction of the magnetic field. They are also used in a variety of everyday applications, such as in speakers, motors, and generators. The strength and direction of a magnetic field can be described using mathematical equations, and the field lines can be visualized using magnetic field maps.
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7. A * 1.5 * 10 ^ 2 * g piece of glass at a temperature of 70.0C is placed in a container with 1 * 10 ^ 2 * g of water initially at a temperature of 16.0 . What is the equilibrium temperature of the water ?
The eqilibrium tempreture of the water, given that 1.5×10² g piece of glass at a temperature of 70.0 °C is placed in the water is 28.5 °C
How do I determine the equilibrium temperature?The following data were obtained from the question:
Mass of glass (M) = 1.5×10² gTemperature of glass (T) = 70.0 °CSpecific heat capacity of glass (C) = 0.84 J/gºC Mass of water (Mᵥᵥ) = 1×10² gTemperature of water (Tᵥᵥ) = 16.0 °CSpecific heat capacity of the water = 4.184 J/gºC Equilibrium temperature (Tₑ) =?The equilibrium temperature of the water can be obtained as follow:
Heat loss = Heat gain
MC(T - Tₑ) = MᵥᵥC(Tₑ - Tᵥᵥ)
1.5×10² × 0.84 × (70 - Tₑ) = 1×10² × 4.184 × (Tₑ - 16)
126 × (70 - Tₑ) = 418.4 × (Tₑ - 16)
Clear bracket
8820 - 126Tₑ = 418.4Tₑ - 6694.4
Collect like terms
8820 + 6694.4 = 418.4Tₑ + 126Tₑ
15514.4 = 544.4Tₑ
Divide both side by 544.4
Tₑ = 15514.4 / 544.4
Tₑ = 28.5 °C
Thus, we can conclude that the equilibrium temperature of the water is 28.5 °C
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a stone will fall straight to ground in 4 s whendropped from rest from the top of a 60 m high building. if the stone is thrown horizontally from this building with a velocity of 8 m/s , at what distance x beyong the building will it strike the ground?
Answer:
32 m
Explanation:
When the stone is thrown horizontally, its initial horizontal velocity (Vx) is 8 m/s, and its initial vertical velocity (Vy) is 0. The stone will follow a parabolic path, with the same vertical motion as the stone dropped from rest.
Vertical motion:
Initial height (h) = 60 m
Vertical acceleration (a) = -9.8 m/s^2 (downward direction)
Time of flight (t) = 4 s
Final vertical velocity (Vy) = Vy + a*t = 0 + (-9.8 m/s^2)*4 s = -39.2 m/s
Vertical displacement (y) = Vyt + 0.5at^2 = 0 + 0.5(-9.8 m/s^2)*(4 s)^2 = -78.4 m (negative because the stone falls below the initial height)
Horizontal motion:
Initial horizontal velocity (Vx) = 8 m/s
Horizontal acceleration (ax) = 0 (no acceleration in horizontal direction)
Time of flight (t) = 4 s
Horizontal displacement (x) = Vx*t = 8 m/s * 4 s = 32 m
Therefore, the stone will strike the ground at a horizontal distance of 32 meters beyond the building.
for a rotating object experiencing no net external torque, what happens to the rate of rotation if the moment of inertia of the object decreases by a factor of 2?
-The rate of rotation increases by a factor of 4. -The rate of rotation increases by a factor of 2. -The rate of rotation remains unchanged. -The rate of rotation decreases by a factor of 2. -The rate of rotation decreases by a factor of 4.
The rate of rotation increases by a factor of 2 when the moment of inertia of an object decreases by a factor of 2
When a rotating object experiencing no net external torque and the moment of inertia of the object decreases by a factor of 2, the rate of rotation increases by a factor of 2.What is the moment of inertia of a body?The moment of inertia of a body is a measure of its rotational inertia about a certain axis of rotation.
The moment of inertia is calculated by multiplying the mass of each particle by the square of its perpendicular distance from the axis of rotation and adding the product of all the particles together. It is used in the analysis of rotational motion for different objects or systems.
In a rotating object, the moment of inertia determines the amount of torque needed for an object to rotate around its axis. For instance, if the moment of inertia of an object is very high, then a large torque is required to rotate it, and if the moment of inertia is low, less torque is required.
Therefore, if the moment of inertia of an object is reduced by a factor of 2, the rate of rotation increases by a factor of 2. Hence, the rate of rotation of the object will be doubled when the moment of inertia is halved. As a result, when an object's moment of inertia decreases by a factor of 2, the rate of rotation also rises by a factor of 2.
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a flywheel slows from 549 to 400 rev/min while rotating through 24 revolutions. what is the (constant) angular acceleration of the flywheel? 1.62 incorrect rad/s2 incorrect incorrect. how much time elapses during the 24 revolutions? 3.04 correct s
The angular acceleration of the flywheel is -1.62 rad/s^2. The time elapsed during the 24 revolutions is 2.07 seconds.
Let's convert the initial and final angular velocities to radians per second, and the angular displacement to radians:
initial angular velocity = 549 rev/min * 2π/60 = 57.68 rad/s
final angular velocity = 400 rev/min * 2π/60 = 41.89 rad/s
angular displacement = 24 revolutions * 2π = 48π rad
The time taken to rotate through 24 revolutions can be found using the formula:
angular displacement = (initial angular velocity * time taken) + (1/2 * angular acceleration * time taken^2)
Substituting the values, we get:
48π = (57.68 * t) + (0.5 * a * t^2)
where t is the time taken, and a is the angular acceleration.
To solve for the angular acceleration, we can rearrange the equation as:
a = (48π - 57.68t) / (0.5 * t^2)
Now, we can substitute the given values and solve for the angular acceleration:
a = (48π - 57.68 * 24) / (0.5 * 24^2)
a = -1.62 rad/s^2
To find the time elapsed during the 24 revolutions, we can substitute the calculated value of the angular acceleration into the equation for angular displacement:
48π = (57.68 * t) + (0.5 * -1.62 * t^2)
This is a quadratic equation in t, which we can solve using the quadratic formula. The solutions are:
t = 2.07 s or t = 33.3 s
Since the time elapsed during the 24 revolutions cannot be negative or greater than the total time taken, the correct solution is:
t = 2.07 s
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--The complete question is, A flywheel slows from 549 to 400 rev/min while rotating through 24 revolutions. what is the (constant) angular acceleration of the flywheel? how much time elapses during the 24 revolutions?--
The cabin of a small freight elevator is secured to a
motor by a cable and is moving upward while slowing
down. There is no contact between the cabin and the
elevator shaft. Ignore air resistance.
The motor is providing the force necessary to move the cabin of the freight elevator upward and slow it down.
What is elevator?An elevator is a type of vertical transportation device designed to move people and goods from one floor to another within a building or structure. It is typically composed of a cab, a motor, a counterweight, cables, and other components. Elevators are the most common form of vertical transportation for multi-story buildings, and are used for both commercial and residential buildings.
The cable connecting the motor to the cabin is providing the mechanical connection that allows the motor to exert the force necessary to move the cabin. Since there is no contact between the cabin and the elevator shaft, the cabin is being accelerated and decelerated solely due to the force exerted by the motor. Air resistance has no effect on the motion of the cabin since it is not in contact with the shaft.
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a ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. how fast is a rider rising when the rider is 18 m above ground level? m/min
A 13 m-diameter Ferris wheel revolving at a speed of one rotation every two minutes. The rider is moving downwards at a rate of 23.1 m/minute when he is 18 m above ground level.
To solve this problem, we need to use the concepts of circular motion and related rates. Let's first draw a diagram to understand the situation better.
We have a Ferris wheel with a radius of 13 m, and it is rotating at a rate of one revolution every 2 minutes. This means that the time taken for one complete revolution is 2 minutes. We want to find the rate at which a rider is rising when the rider is 18 m above ground level.
Let's assume that the Ferris wheel is initially at the horizontal level, and the rider is at the highest point at this moment. After a time t, the Ferris wheel has rotated through an angle θ, and the rider has moved down to a point where he is 18 m above ground level. Let's call this point P.
We know that the radius of the Ferris wheel is 13 m, and the distance from the center of the Ferris wheel to the point P is (13 - 18) = 5 m. Therefore, we can use the Pythagorean theorem to find the distance between the center of the Ferris wheel and the point P:
sqrt((13)^2 - (5)^2) = sqrt(144) = 12 m
Now, we need to find the angular velocity of the Ferris wheel. We know that the Ferris wheel completes one revolution every 2 minutes, which means that it completes 1/2 revolution in 1 minute. Therefore, the angular velocity of the Ferris wheel is:
ω = (1/2) * 2π radians/minute = π radians/minute
We can now use the formula for related rates to find the rate at which the rider is moving downwards:
dP/dt = -rω sinθ
where dP/dt is the rate at which the rider is moving downwards, r is the distance between the center of the Ferris wheel and the point P (which we have already found to be 12 m), ω is the angular velocity of the Ferris wheel (which we have found to be π radians/minute), and sinθ is the sine of the angle between the radius of the Ferris wheel and the line joining the center of the Ferris wheel to the point P.
To find sinθ, we can use the fact that the point P is on a circle with a radius of 13 m. Therefore, we can use the following equation:
sinθ = opposite/hypotenuse = 5/13
Substituting the values in the formula for related rates, we get:
dP/dt = -12 * π * 5/13 = -23.1 m/minute
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when kayla stands on her trampoline, it sags by 0.20 m . now she starts bouncing. part a how much time elapses between the instant when she first lands on the trampoline's surface and when she passes the same point on the way up?
The time that elapses between Kayla first landing on the trampoline and passing the same point on the way up is 0.28 seconds.
To find this, we can use the equation for free fall: y = 0.5 * g * t^2, where y is the displacement, g is the acceleration due to gravity (9.81 m/s^2), and t is the time elapsed.
First, rearrange the equation to solve for t: t = sqrt(2 * y / g). Now, plug in the displacement (0.20 m) and the acceleration due to gravity (9.81 m/s^2): t = sqrt(2 * 0.20 / 9.81) ≈ 0.20 seconds.
Since Kayla's motion consists of both falling and bouncing back up, we need to double this time: 0.20 * 2 = 0.40 seconds.
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which has the highest luminosity? the andromeda galaxy the planet mercury the sun the star betelgeuse
The star Betelgeuse has the highest luminosity among the options provided, which include the Andromeda Galaxy, the planet Mercury, and the Sun. Luminosity refers to the total amount of energy emitted by an astronomical object per unit of time. The correct answer is The star Betelgeuse.
Betelgeuse, a red supergiant star in the constellation Orion, is approximately 100,000 times more luminous than our Sun.
In comparison, the Sun, which is a main-sequence star, has a much lower luminosity than Betelgeuse, although it is the most luminous object in our solar system. The planet Mercury, being a rocky object with no source of light production, has no inherent luminosity of its own. Instead, it reflects sunlight, making it visible from Earth.
The Andromeda Galaxy, while having an overall higher luminosity than Betelgeuse due to its vast collection of stars, is not a single astronomical object. Thus, when comparing individual objects, Betelgeuse has the highest luminosity.
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a 3.75-kg block of wood floats on water. what minimum mass of lead, hung from the wood by a string, will cause the block to sink?
The mass of the lead needed to sink the block of wood depends on the buoyancy force acting on the wood.
Buoyancy is the upward force exerted by a fluid on an object submerged or floating in it. In this case, the buoyancy force acting on the block of wood must be overcome by the weight of the lead to cause the wood to sink.
The buoyancy force on the block of wood can be calculated using Archimedes' principle, which states that the buoyancy force is equal to the weight of the fluid displaced by the object. The density of water is 1000 kg/m^3, so the buoyancy force on the block of wood is
[tex](3.75 kg)(9.8 m/s^2) = 36.75 N.[/tex]
To sink the wood, the weight of the lead must exceed the buoyancy force on the wood. The weight of the lead needed can be calculated using the equation W = mg, where W is the weight of the lead, m is the mass of the lead, and g is the acceleration due to gravity
[tex](9.8 m/s^2).[/tex]
Therefore, the minimum mass of lead required to sink the wood is
[tex](36.75 N)/(9.8 m/s^2) = 3.75 kg[/tex]
.
In conclusion, a minimum mass of 3.75 kg of lead, hung from the wood by a string, will cause the block to sink.
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an electron and proton are accelerated through the same potential difference. a) the electron has the greater k. b) the proton has the greater k. c) the electron has the greater speed. d) the proton has the greater speed
Since the proton has a greater mass than the electron, it will have a greater kinetic energy. Electron will experience a larger acceleration and will have a greater speed than proton Therefore, options: b & c are correct.
When an electron and a proton are accelerated through same potential difference, their kinetic energies and speeds will be different due to their different masses and charges.
k = (1/2)mv^2
Since the potential difference is the same, the work done on each particle will be the same. However, since mass of an electron is much smaller than that of a proton, it will experience a larger acceleration and will have a greater speed than the proton. Therefore, option (c) &(b) are correct.
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how are cold and warm fronts different? how are cold and warm fronts different? the type of front is determined by which air mass is heavier. the type of front is determined by which air mass is moving. the type of front is determined by which air mass is larger. the type of front is determined by which air mass is older. the type of front is determined by which air mass is higher.
Cold and warm fronts are different because the type of front is determined by which air mass is heavier.
A cold front forms when a cold air mass advances towards a warm air mass. It is characterized by the cooler air mass pushing under the warmer air mass. This creates a steep slope, and the air rises rapidly, creating thunderstorms and strong winds.
Warm fronts, on the other hand, occur when a warm air mass advances towards a cold air mass. In this case, the warm air mass gradually rises over the denser, cooler air mass. This creates a long, gradual slope, and the air is less likely to create severe weather, instead causing a gradual change in weather patterns.
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a gun is fired vertically into the bottom of a block of wood that is at rest on vertical supports at its corners. if the bullet has a mass of 21.0 g and a speed of 310 m/s when it strikes and is embedded in the wood, how high above the supports will the 1.40 kg block rise into the air?
The block will rise approximately 4.63 meters above the supports.
To find the height, we can use the conservation of momentum and conservation of mechanical energy. First, find the initial momentum of the bullet:
momentum = mass x velocity
= 0.021 kg x 310 m/s
= 6.51 kg m/s.
Since the block is at rest, its initial momentum is 0. After the collision, the bullet is embedded in the block, and their combined mass is 1.421 kg.
Using the conservation of momentum, we can find their final velocity: 6.51 kg m/s = (1.421 kg) x (Vf). Solving for Vf, we get Vf ≈ 4.58 m/s.
Now, using the conservation of mechanical energy, we can find the maximum height reached: (1/2) x (1.421 kg) x (4.58 m/s)² = (1.421 kg) x (9.81 m/s²) x (h). Solving for h, we get h ≈ 4.63 meters.
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