Translational Kinetic Energy AP Physics C Mechanics MCQ – Exam Style Questions etc.
Translational Kinetic Energy AP Physics C Mechanics MCQ
Unit 3: Work, Energy, and Power
Weightage : 15-25%
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
W = -mgz = -(2.0 kg)(10 N/kg)(3 m) = -60 J
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
Using the function F(x) and the value of \(F_f\), the work done by the net force in moving the block from x=0 to x=5m can be calculated. Using the mass and initial and final velocities, the change in kinetic energy can be calculated; thus, the hypothesis that the work done is equal to the change in kinetic energy can be testedQuestion
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
Work is related to kinetic energy by the equation \(W=ΔK\) . The work done by the elastic band is calculated by integrating the function relating force and stretch. If \(W=∫Fdx=∫kx^2dx=\frac{1}{3}kx^3\) , then setting this W equal to kinetic energy yields \(\frac{1}{3}kx^3=\frac{1}{2}mv^2\). Since k and m are constants, if \(v^2\) as a function of \(x^3\) is a straight line, that would support the hypothesis that F is a function of \(x^2\).
Answer/Explanation
Ans:C
Forces exerted perpendicular to velocity vectors do not change the speed of the object; thus, they do no work on the object since work is the dot product of force and displacement.