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25 questions
The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated at the same angular speed about an axis perpendicular to the plane of the drawing at point P?
A
B
C
D
A solid cylinder and a hollow pipe with equal masses and radii are released simultaneously at the top of a ramp and roll to the bottom without slipping, which one will reach the bottom first?
solid cylinder
hollow pipe
Not enough information to answer.
They both reach the bottom at the same time.
An ice skater spins without friction on the ice with her arms extended. When she folds in her arms,
her moment of inertia increases and her angular speed decreases.
her moment of inertia decreases and her angular speed increases.
her moment of inertia increases and her angular speed increases.
her moment of inertia decreases and her angular speed remains the same.
Suppose you are designing an engineless car for a downhill coasting race (meaning that you want to maximize translational velocity). What type of wheels would be the best?
Solid disks.
Hoops.
Hollow cylinders.
Diamond encrusted triangles.
In order to do a lot of flips (raise angular speed) an Olympic diver would want:
A high moment of inertia
A low moment of inertia
A low linear acceleration
A low angular velocity
A dog of mass 10 kg sits on a skateboard of mass 2 kg that is initially traveling south at 2 m/s. The dog jumps off with a velocity of 1 m/s north relative to the ground. Which of the following is the best estimate of the velocity of the skateboard immediately after the dog has jumped?
17 m/s south
1 m/s north
1 m/s south
3 m/s south
7 m/s south
If the translational velocity of an carousel horse is 3 m/s, and is located a distance of 2 m from the axis of rotation, what is the horse's angular velocity?
0.67 rad/s
1.5 rad/s
5 rad/s
6 rad/s
A student conducts an experiment to verify that a collision is elastic. The two identical cubes involved, object X and object Y, travel toward each other at the same initial speed. Which of the following equations should the student consider using to verify that the collision is elastic, and why?
Equation I only, because the change in momentum of object X
will be equal to the negative change of momentum for object Y.
Equation II only, because the conservation of momentum must be verified for the system of object X and object Y.
Equation I and equation III, because the change in momentum of object X will be equal to the negative change of momentum for object Y, and the difference in the kinetic energy of the system before and after the collision should be determined.
Equation II and equation III, because the conservation of momentum must be verified for the system of object X
and object Y, and the difference in the kinetic energy of the system before and after the collision should be determined.
A student must conduct an experiment to verify the conservation of momentum for a closed two-cart system. Cart X and cart Y travel toward each other and eventually collide. The student has determined the following procedure.
Step 1: Measure the mass of cart X and cart Y with a balance.
Step 2: Use a motion sensor to record data of the velocity of each cart before, during, and after the collision.
Step 3: Use the data and ∑ pf= ∑ p0 to determine if the right-hand side of the equation is equal to the left-hand side of the equation.
Which of the following steps should the student add to the procedure so that the conservation of momentum can be experimentally verified?
Conduct the experiment on a smooth, level surface.
Attach adhesive strips to each cart so that they stick together after they collide.
Ensure that the mass of each cart is the same.
Ensure that the initial speed of each cart is the same.
An object of mass m attached to a spring with constant k oscillates with amplitude A. Assuming air resistance and the mass of the spring to be negligible, which of the following changes alone would cause the period of this oscillation to increase?
I. Increasing m
II. Increasing A
III. Using a spring with greater k
I only
II only
I or II only
I, II, and III
II or III only
Two people of unequal mass are initially standing still on ice with negligible friction. They then simultaneously push each other horizontally. Afterward, which of the following is true?
The kinetic energies of the two people are equal.
The speeds of the two people are equal.
The momenta of the two people are of equal magnitude.
The center of mass of the two-person system moves in the direction of the less massive person.
The less massive person has a smaller initial acceleration than the more massive person.
A student is observing an object of unknown mass that is oscillating horizontally at the end of an ideal spring. The student measures the object’s period of oscillation with a stopwatch.
While the object is continuously oscillating, the student determines the maximum speed of the object during two oscillations. The first speed is 3.5 m / s and the second speed is 2.7 m / s. Which of the following could account for the decrease in the object’s maximum kinetic energy?
Energy was transferred from the object to the spring, which increased the maximum potential energy of the spring.
Energy was transferred from the spring to the object, which decreased the maximum potential energy of the spring.
As energy was transferred back and forth between the object and the spring, a greater average share of the energy became potential energy of the spring.
The object-spring system lost energy to its surroundings.
Object X of mass 4 kg travels with a speed of 3 m/s toward object Y of mass 2 kg that is initially at rest. Object X then collides with and sticks to object Y. After the collision, object X and object Y remain stuck together as they move. By how much does the kinetic energy of this system change, if at all?
It decreases by 6 J.
It increases by 12 J.
It remains constant.
It decreases to zero.
A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest. A sphere of mass m2, which is suspended from a string of length l is displaced to the right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion.
Which of the following is true for both spheres?
The maximum kinetic energy is attained as the sphere passes through its equilibrium position.
The maximum kinetic energy is attained as the sphere reaches its point of release.
The minimum gravitational potential energy is attained as the sphere passes through its equilibrium position.
The maximum gravitational potential energy is attained when the sphere reaches its point of release.
The maximum total energy is attained only as the sphere passes through its equilibrium position.
A block of mass 2.0kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 100N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0 m. The block is then pulled to x=0.5 m and released from rest so that the block-spring system oscillates between x=−0.5 m and x=0.5 m, as shown in the figure. Which of the following predictions is correct regarding the energy of the system?
If the mass of the block is changed to 0.5kg
and all other quantities are held constant, the maximum kinetic energy of the system will be half of the value from the original situation.
If the spring is changed so that its spring constant is 200 N/m
and all other quantities are held constant, the maximum kinetic energy of the system will be twice the value from the original situation.
If the block is pulled to x=2.0 m and released from rest and all other quantities are held constant, the maximum kinetic energy of the system will be four times the value from the original situation.
If the mass of the block is changed to 1.0kg
and the spring is changed to so that its spring constant is 50N/
m, the maximum kinetic energy of the system will be the same as the value from the original situation.
A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger, as shown in the figure.
Students are provided with data in which an experiment was conducted to determine the relationship between the length of the pendulum and the period of oscillation. The data include a pendulum of length 0.5m, for which it took 81 s for the pendulum bob to oscillate 10 times. However, the experiment was conducted at a location that is not near Earth’s surface. The gravitational field strength where the experiment was conducted is most nearly...?
0.003N/kg
0.024N/kg
0.30N/kg
2.40N/kg
Three different experiments are conducted that pertain to the oscillatory motion of a pendulum. For each experiment, the length of the pendulum and the mass of the pendulum are indicated. In all experiments, the pendulum is released from the same angle with respect to the vertical.
If the students collect data about the kinetic energy of the pendulum as a function of time for each experiment, which of the following claims is true?
The data collected from Experiment 1 will be the same as the data collected from Experiment 2.
The data collected from Experiment 1 will be the same as the data collected from Experiment 3.
The data collected from Experiment 2 will be the same as the data collected from Experiment 3.
The data collected from each experiment will be different.
A pendulum has a length l and a bob of mass m. Which of the following is true of the linear momentum of the bob as it swings from its highest to lowest point?
It remains constant because momentum is always conserved.
It increases in magnitude and changes direction.
It decreases in magnitude and does not change direction.
It is converted to angular momentum.
It is converted to kinetic energy.
A student must determine how the mass of a block affects the period of oscillation when the block is attached to a vertical spring. The value of the spring constant is known. The student writes the following experimental procedure.
1) Use an electronic balance to measure the mass of the block.
2) Attach the block to the vertical spring.
3) Displace the block from the system’s equilibrium position to a new vertical position.
4) Release the block from rest.
5) Use a meterstick to measure the vertical displacement of the center of mass of the block from the system’s equilibrium position to its maximum vertical position above the equilibrium position.
6) Use a stopwatch to measure the time it takes for the system to make ten complete oscillations.
7) Repeat the experiment for different vertical displacements and block masses.
Which of the steps of the procedure should the student revise to determine the effect of mass on oscillation period? Justify your selection.
Step 3, because the student must specify whether the new vertical position should be above or below the system’s equilibrium position.
Step 5, because the meterstick should be used to measure total displacement of the system from its lowest vertical position to its highest vertical position.
Step 6, because the stopwatch should be used only to measure the time it takes for the system to make 1 complete oscillation.
Step 7, because the experiment should not be repeated for different vertical displacements and block masses.
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