Download 1-4 Work and Energy Sol

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Physics 213
Problem 4
Work and Energy
Week 1
The Work Energy Equation shown in the Discussion Notes,
Won =Δ(KE),
holds only for translational motion of a simple object. More generally, work done on an object can
also cause a change in rotational or vibrational energies of the object.
1) Consider the case of a board of length L = 2 m and mass m = 3 kg initially at rest on ice. A rope
pulls with constant force F = 10 N at one end. Here are some snapshots of the motion:
F
D=7m
F
F
F
L=2m
dcm = 6 m
Notice that the force acts through a distance of D = 7 meters but the center of mass of the board
travels only dcm = 6 meters. Mark true (T) or false (F) for the statements below and give short
justifications of your answers.
a) Won = FD
b) Won = Fdcm
c) acm = F/m
d) acm < F/m
e) Fdcm = ½ mvcm2
f) Won = Δ(KEcm)+ Δ(KErot)
True, work = force times distance the agent acts.
False, because the object has internal (rotation) energy.
True !!!, Newton’s second law.
False. acm = F/m, always.
True (see problem 2a). It’s just F = macm.
True. Conservation of energy.
2) Determine the rotational energy KErot of the board at the time of the last snapshot above
using conservation of energy. (No moment of inertia or angular velocity required here.)
Using equation f) above: Δ(KErot) = Won - Δ(KEcm) = FD – Fdcm = (10 N)(1 m) = 10 J