2014年AP力学简答题真题+答案+PDF下载
Mech. 1.
In an experiment, a student wishes to use a spring to accelerate a cart along a horizontal, level track. The spring is attached to the left end of the track, as shown in the figure above, and produces a nonlinear restoring force of magnitude Fs=As2 + Bs, where s is the distance the spring is compressed, in meters. A measuring tape, marked in centimeters, is attached to the side of the track. The student places five photogates on the track at the locations shown.
(a) Derive an expression for the potential energy U as a function of the compression s. Express your answer in terms of A, B, s, and fundamental constants, as appropriate.
In a preliminary experiment, the student pushes the cart of mass 0.30 kg into the spring, compressing the spring 0.040 m. For this spring,A = 200 N/m2 and B = 150 N/m. The cart is released from rest. Assume friction and air resistance are negligible only during the short time interval when the spring is accelerating the cart.
(b) Calculate the following:
i. The speed of the cart immediately after it loses contact with the spring
ii. The impulse given to the cart by the spring
In a second experiment, the student collects data using the photogates. Each photogate measures the speed of the cart as it passes through the gate. The student calculates a spring compression that should give the cart a speed of 0.320 m/s after the cart loses contact with the spring. The student runs the experiment by pushing the cart into the spring, compressing the spring the calculated distance, and releasing the cart. The speeds are measured with a precision of ±0.002 m/s. The positions are measured with a precision of ±0.005 m.
(c) On the axes below, plot the data points for the speed u of the cart as a function of position x. Clearly scale and label all axes, as appropriate.
(d) i. Compare the speed of the cart measured by photogate 1 to the predicted value of the speed of the cart just after it loses contact with the spring. List a physical source of error that could account for the difference.
ii. From the measured speed values of the cart as it rolls down the track, give a physical explanation for any trend you observe.
Mech. 2.
A small block of mass m starts from rest at the top of a frictionless ramp, which is at a height h above a horizontal tabletop, as shown in the side view above. The block slides down the smooth ramp and reaches point P with a speed u0 . After the block reaches point P at the bottom of the ramp, it slides on the tabletop guided by a circular vertical wall with radius R, as shown in the top view. The tabletop has negligible friction, and the coefficient of kinetic friction between the block and the circular wall is m .
(a) Derive an expression for the height of the ramp h. Express your answer in terms of u0 , m, and fundamental constants, as appropriate.
A short time after passing point P, the block is in contact with the wall and moves with a speed of u .
(b) i. Is the vertical component of the net force on the block upward, downward, or zero?
____ Upward ____ Downward ____ Zero
Justify your answer.
ii. On the figure below, draw an arrow starting on the block to indicate the direction of the horizontal component of the net force on the moving block when it is at the position shown.
Express your answers to the following in terms of u0 , u , m, R, m , and fundamental constants, as appropriate.
(c) Determine an expression for the magnitude of the normal force N exerted on the block by the circular wall as a function of u .
(d) Derive an expression for the magnitude of the tangential acceleration of the block at the instant the block has attained a speed of u .
(e) Derive an expression for u(t) , the speed of the block as a function of time t after passing point P on the track.
2014年AP力学简答题真题余下省略！
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