AP Physics C Mechanics: 3.1 Work-Energy Theorem – Exam Style questions with Answer- MCQ

Question

For a particular nonlinear spring, the relationship between the magnitude of the applied force F and the resultant displacement x from equilibrium is given by the equation \(F = kx^2\). What is the amount of work done by stretching the spring a distance \x_o\)?

(A)\(kx^3_0\)

(B)\(\frac{1}{3}kx_0\)

(C)\(\frac{1}{2}kx^2_{0}\)

(D)\(\frac{1}{3}kx^2_{0}\)

(E)\(\frac{1}{2}kx^3_0\)

Answer/Explanation

 

Question


 A small block of mass m = 2.0 kg is pushed from the initial point \(x_i , z_i)\) = (0 m, 0 m) upward to the final point \((x_f, z_f)\) = (3 m, 3 m) along the path indicated. Path 1 is a portion of the parabola \(z=x^2\), and Path 2 is a quarter circle whose equation is \((x-1)^2 + (z-3)^2 = 4\). How much work is done by gravity during this displacement?
(A) -6oJ
(B) -Bo J
(C) -90 J
(D)-100 J
(E) -120 J

Answer/Explanation

Ans: A

Since gravity is a conservative force, the actual path taken is
irrelevant. If the block rises a vertical distance of z = 3 m,
then the work done by gravity is

Question

                          

In the lab setup above, block 1 is being pulled across a smooth surface by a light string connected across a pulley to a falling block 2. The pulley has negligible mass and friction. Students measure the mass of each block, the distance from A to B, and the speeds of the block on the surface at points A and B. Which of the following hypotheses can be tested with this setup?

A As block 1 moves from point A to point B , the work done by the tension on block 1 is equal to the kinetic energy of block 1 at point B .

B As block 1 moves from point A to point B , the work done by the tension on block 1 is equal to the kinetic energy of the two-block system when block 1 is at point B .

C As block 1 moves from point A to point B , the work done by gravity on block 2 is equal to the kinetic energy of block 1 at point B .

D As block 1 moves from point A to point B , the work done by gravity on block 2 is equal to the change in the kinetic energy of the two-block system.

E As block 1 moves from point A to point B, the work done by the tension on block 2 is equal to the kinetic energy of block 2 when block 1 has reached point B .

Answer/Explanation

Ans:D

 

Question

                                   

In an experiment, a variable, position-dependent force F(x) is exerted on a block of mass 1.0kg that is moving on a horizontal surface. The frictional force between the block and the surface has a constant magnitude of Ff. In addition to the final velocity of the block, which of the following information would students need to test the hypothesis that the work done by the net force on the block is equal to the change in kinetic energy of the block as the block moves from x=0 to x=5m ?

A The function F(x) for 0<x<5 and the value of \(F_f\).

B The function a(t) for the time interval of travel and the value of \(F_f\).

C The function F(x) for 0<x<5, the block’s initial velocity, and the value of \(F_f\).

D The function a(t) for the time interval of travel, the time it takes the block to move 5  m, and the value of \(F_f\).

E The block’s initial velocity, the time it takes the block to move 5  m , and the value of \(F_f\).

Answer/Explanation

Ans:C

 

Question

Students use a stretched elastic band to launch carts of known mass horizontally on a track. The elastic bands exert a force F, which is nonlinear as a function of the distance x that the band is stretched. A meterstick is used to measure x, and a motion detector is used to measure the resulting maximum speed of the carts. This procedure is repeated to gather data for several different values of x. Which of the following graphs, if linear, supports the hypothesis that F is a function of \(x^2\) ?
A A graph of the cart’s maximum speed as a function of x

B A graph of the cart’s maximum speed as a function of \(x^2\)

C A graph of the cart’s maximum speed squared as a function of x

D A graph of the cart’s maximum speed squared as a function of \(x^2\)

E A graph of the cart’s maximum speed squared as a function of \(x^3\)

Answer/Explanation

Ans: E

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