Physics quiz question: energy changes of hill-sliding student

Physics 205A Quiz 5, fall semester 2018
Cuesta College, San Luis Obispo, CA

A Physics 205A student on a cardboard sheet slides down a grassy slope starting from rest, and has a final speed of 0.80 m/s. Consider the Physics 205A student and cardboard sheet as a single 75 kg object. Friction is not negligible. Ignore drag.

For this process, the decrease in the Physics 205A student and cardboard sheet's gravitational potential energy is __________ the increase in translational kinetic energy.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

The energy transfer-balance equation is given by:

W_nc = ∆KE_tr + ∆PE_grav + ∆PE_elas,

where ∆PE_elas = 0, as there is no spring involved in this process.

Just looking at the two remaining terms on the right-hand side of the energy transfer-balance equation, for the change in translational kinetic energy:

∆KE_tr = (1/2)·m·(v_f² – v₀²),

and since the speed is increasing, v_f is faster than v₀, and so KE_tr is increasing (∆KE_tr is positive).

Also for the change in gravitational potential energy:

∆PE_grav = m·g·(y_f – y₀),

and since y_f is lower than y₀, then PE_grav decreases (∆PE_grav is negative).

On the left-hand side of the energy transfer-balance equation, the work done by kinetic friction against the student and cardboard sheet is negative, as the kinetic friction force points up along the slope, while the displacement points down along the slope, such that:

W_nc = ∆KE_tr + ∆PE_grav,

with the ± signs as noted for each term:

(–) = (+) + (–),

and so the decrease in gravitational potential energy (negative change) must be greater than the increase in translational kinetic energy (positive change) on the right-hand side of the energy transfer-balance equation to be equal to the negative non-conservative work done by kinetic friction.

(Note that the normal force does no work on the student and cardboard sheet, as this force is perpendicular to the displacement, which points down the slope. Also we do not need to calculate the work done by the weight force on the student and cardboard sheet in this energy transfer-balance equation, as this is a conservative force that is already included in the gravitational potential energy term on the right-hand side of the equation.)

Sections 70854, 70855
Exam code: quiz04W3rK
(A) : 11 students
(B) : 24 students
(C) : 11 students
(D) : 5 students

Success level: 22%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.43