2013年AP力学简答题真题+答案+PDF下载
Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions,which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part.
Mech 1.
A student places a 0.40 kg glider on an air track of negligible friction and holds it so that it touches an uncompressed ideal spring, as shown in Figure 1 above. The student then pushes the glider back to compress the spring by 0.25 m, as shown in Figure 2. At time t = 0, the student releases the glider, and a motion sensor begins recording the velocity of the reflector at the front of the glider as a function of time. The data points are shown in the table below. At time t = 0.79 s, the glider loses contact with the spring.
(a) On the axes below, plot the data points for velocity V as a function of time t for the glider, and draw a smooth curve that best fits the data. Be sure to label an appropriate scale on the vertical axis.
(b) The student wishes to use the data to plot position x as a function of time t for the glider.
i. Describe a method the student could use to do this.
ii. On the axes below, sketch the position x as a function of time t for the glider. Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate.
(c) Calculate the time at which the glider makes contact with the bumper at the far right.
(d) Calculate the force constant of the spring.
(e) The experiment is run again, but this time the glider is attached to the spring rather than simply being pushed against it.
- i. Determine the amplitude of the resulting periodic motion.
- ii. Calculate the period of oscillation of the resulting periodic motion.
Mech 2.
A box of mass m initially at rest is acted upon by a constant applied force of magnitude FA , as shown in the figure above. The friction between the box and the horizontal surface can be assumed to be negligible, but the box is subject to a drag force of magnitude ku where u is the speed of the box and k is a positive constant.Express all your answers in terms of the given quantities and fundamental constants, as appropriate.
(a) The dot below represents the box. Draw and label the forces (not components) that act on the box.
(b) Write, but do not solve, a differential equation that could be used to determine the speed u of the box as a function of time t. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).
(c) Determine the magnitude of the terminal velocity of the box.
(d) Use the differential equation from part (b) to derive the equation for the speed u of the box as a function of time t. Assume that u = 0 at time t = 0.
(e) On the axes below, sketch a graph of the speed u of the box as a function of time t. Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate.
。。。。。。余下真题省略！
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