AP® Physics C
1997 Free respon Questions
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1997M1. A nonlinear spring is compresd horizontally. The spring exerts a force that obeys the equation F(x) = Ax½, where x is the distance from equilibrium that the spring is compresd and A is a constant. A physics student records data on the force exerted by the spring as it is compresd and plots the two graphs below, which include the data and the student's best-fit curves.
a. From one or both of the given graphs, determine A. Be sure to show your work and specify the
units.
b. i. Determine an expression for the work done in compressing the spring a distance x.
ii. Explain in a few ntences how you could u one or both of the graphs to estimate a numerical answer to part (b)i for a given value of x.
c. The spring is mounted horizontally on a countertop that is 1.3 m high so that its equilibrium position
is just at the edge of the countertop. The spring is compresd so that it stores 0.2 J of energy and is then ud to launch a ball of mass 0.10 kg horizontally from the countertop. Neglecting friction,
determine the horizontal distance d from the edge of the countertop to the point where the hall strikes the floor
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1997M2. An open-top railroad car (initially empty and of mass M o) rolls with negligible friction along 文体部是干什么的
秩序什么然
a straight horizontal track and pass under the spout of a sand conveyor. When the car is under the conveyor, sand is dispend from the conveyor in a narrow stream at a steady rate ∆M/∆t = C and falls vertically from an average height h above the floor of the railroad car. The car has initial speed v o and sand is filling it from time t = 0 to t = T. Express your answers to the following in terms of the given quantities and g.
a. Determine the mass M of the car plus the sand that it catches as a function of time t for 0 < t < T.
b. Determine the speed v of the car as a function of time t for 0 < t < T.可爱颂歌曲>广播电视工程
c. i. Determine the initial kinetic energy K i of the empty car.
ii. Determine the final kinetic energy K f of the car and its load.理查德杰弗森
iii. Is kinetic energy conrved? Explain why or why not.
d. Determine expressions for the normal force exerted on the car by the tracks at the following times.
i. Before t = 0
ii. For 0 < t < T
iii. After t = T
1997M3. A solid cylinder with mass M, radius R, and rotational inertia ½MR2 rolls without slipping down the inclined plane shown above. The cylinder starts from rest at a height H. The inclined plane makes an angle θ with the horizontal. Express all solutions in terms of M, R, H, θ, and g.
a. Determine the translational speed of the cylinder when it reaches the bottom of the in clined plane.
b. On the figure below, draw and label the forces acting on the cylinder as it rolls down the inclined
plane Your arrow should begin at the point of application of each force.
c. Show that the acceleration of the center of mass of the cylinder while it is rolling down the inclined
plane is (2/3)g sinθ.
d. Determine the minimum coefficient of friction between the cylinder and the inclined plane that is
required for the cylinder to roll without slipping.
e. The coefficient of friction μ is now made less than the value determined in part (d), so that the
cylinder both rotates and slips.
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i. Indicate whether the translational speed of the cylinder at the bottom of the inclined plane is greater
中干than, less than, or equal to the translational speed calculated in part (a). Justify your answer.
ii. Indicate whether the total kinetic energy of the cylinder at the bottom of the inclined plane is greater than, less than, or equal to the total kinetic energy for the previous ca of rolling without slipping. Justify your answer.
1997E1. A technician us the circuit shown above to test prototypes of a new battery design. The switch is clod, and the technician records the current for a period of time. The curve that best fits the results is shown in the graph below.
The equation for this curve is I = I o e-k t where t is the time elapd from the instant the switch is clod and I o and k are constants.
a. i.
o
across the resistor
immediately after the switch is clod.
ii. Would the open circuit voltage of the fresh battery have been less than, greater than, or equal to the value in part i ? Justify your answer.
b. Determine the value of k from this best-fit curve. Show your work and be sure to include units in
your answer.
c. Determine the following in terms of R, I o, k, and t.
i. The power delivered to the resistor at time t = 0
ii. The power delivered to the resistor as a function of time t
iii. The total energy delivered to the resistor from t = 0 until the current is reduced to zero
