Conservation Laws
Graph Analysis
Angular Stuff
100
A 0.5 kg pendulum bob is raised to 1.0 m above the floor, as shown in the figure above. The bob is then released from rest. When the bob is 0.2 m above the floor, its speed is most nearly
4 m/s
100
Two identical cars, car 1 and car 2, are moving in opposite directions on a straight road. The position of each car as a function of time is represented in the graph. What is the speed of the center of mass of the two-car system?
Zero
100
A meterstick with a uniformly distributed mass of 0.5 kg is supported by a pivot placed at the 0.25 m mark from the left, as shown. At the left end, a small object of mass 1.0 kg is placed at the zero mark, and a second small object of mass 0.5 kg is placed at the 0.5 m mark. The meterstick is supported so that it remains horizontal, and then it is released from rest. One second after it is released, what is the change in the angular momentum of the meterstick?
Zero
200
A box of mass m is initially at rest at the top of a ramp that is at an angle θ with the horizontal. The block is at a height h and length L from the bottom of the ramp. The block is released and slides down the ramp. The coefficient of kinetic friction between the block and the ramp is µ .
What is the kinetic energy of the box at the bottom of the ramp?
mgh - µmgL cos θ
200
A 2kg box is pushed from rest across a horizontal surface where friction between the box and the surface is negligible. Students record the applied force at several equally spaced positions while pushing the box and create the graph shown. The change in momentum of the box is most nearly
12 kg m/s
200
The figure above represents a stick of uniform density that is attached to a pivot at the right end and has equally spaced marks along its length. Any one of the four forces shown can be exerted on the stick as indicated. Which force will create the largest rate of change in the stick’s angular momentum?
The 60N Force
300
Two blocks are on a horizontal, frictionless surface. Block A is moving with an initial velocity of v0 toward block B, which is stationary, as shown above. The two blocks collide, stick together, and move off with a velocity of v0/2 . Which block, if either, has the greater mass?
neither block has greater mass
300
During an experiment a student records the net horizontal force exerted on an object moving in a straight line along a horizontal frictionless track. The graph above shows the force as a function of time. Of the following, which is the best approximation of the magnitude of the change in momentum of the object between 0 s and 4 s?
30 kg m/s
300
Three identical forces of magnitude F0 are applied to a meterstick that rests on a horizontal table, as shown in the diagram. At what location on the meterstick would a fourth force, also of magnitude F0, need to be applied in order to establish static equilibrium?
B
400
At time t = 0 two figure skaters are moving together over ice with negligible friction, as shown above. Skater 1, represented by the large black dot, is twice as massive as skater 2, represented by the gray dot. At t = 2 s the skaters push off of one another. The location of skater 1 is shown at t = 4 s . At t = 4 s , skater 2 is located at which of the labeled points?
Point D
400
Question
Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is τX. Similarly, the average value for Object Y is τY. The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. What is τY in terms of τX ?
τY = 2τX
400
A regular hexagon of uniform density is initially at rest and free to rotate about an axis at its center. Three forces have equal magnitude and are able to be applied in the direction and at the point shown in the figure. Which of these forces, if applied individually and for the same time interval, will produce the greatest increase in the hexagon’s angular speed?
F(A)
500
An apple is released from rest 250 m above the ground. Due to the combined forces of air resistance and gravity, it has a speed of 40 m s when it reaches the ground. What percentage of the initial mechanical energy of the apple-Earth system was dissipated due to air resistance? Take the potential energy of the apple-Earth system to be zero when the apple reaches the ground.
68%
500
A 2.0kg disk is able to move on a straight, level track with negligible friction. With the disk initially at rest, a horizontal force is applied to the disk. The force is measured as a function of the disk’s displacement, and the data are shown in the graph. When the disk’s displacement is 2.0m2.0m, the speed of the disk is most nearly
4 m/s
500
A disk with radius of 0.5 m is free to rotate around its center without friction. A string wrapped around the disk is pulled, as shown above, exerting a 2 N force tangent to the edge of the disk for 1 s. If the disk starts from rest, what is its angular speed after 1 s?
Cannot be determined