Physics quiz question: energy changes of barrel rolled up a ramp

Physics 205A Quiz 5, fall semester 2019
Cuesta College, San Luis Obispo, CA

A Physics 205A student uses a ramp and a trailer to deliver an empty barrel. Ignore friction and drag; the barrel rolls without slipping. As the barrel is rolled up the ramp with constant speed, its __________ increases.
(A) gravitational potential energy.
(B) translational kinetic energy.
(C) rotational kinetic energy.
(D) (Two of the above choices.)
(E) (All of the above choices.)
(F) (None of the above choices.)

Correct answer (highlight to unhide): (A)

The energy transfer-balance equation is given by:

W_nc = ∆KE_tr + ∆KE_rot ∆PE_grav + ∆PE_elas,

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

Just looking at the three 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 constant, v₀ and v_f have the same magnitude, then KE_tr is constant (∆KE_tr = 0).

Similarly for the change in rotational kinetic energy:

∆KE_rot = (1/2)·I·(ω_f² – ω₀²),

and since the angular speed is constant, ω₀ and ω_f have the same magnitude, then KE_rot is constant (∆KE_rot = 0).

Then for the change in gravitational potential energy:

∆PE_grav = m·g·(y_f – y₀),

since y_f is greater than y₀, then PE_grav increases (∆PE_grav is positive).

(In order for the equality to hold for the energy transfer-balance equation, the student must then be doing positive work on the barrel in order to increase its gravitational potential energy.)

Sections 70854, 70855
Exam code: quiz05Gu1L
(A) : 41 students
(B) : 1 student
(C) : 0 students
(D) : 7 students
(E) : 3 students
(F) : 0 students

Success level: 79%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53