A frictionless pulley has the shape of a uniform solid disk of mass 2.70 kg and
ID: 1645238 • Letter: A
Question
A frictionless pulley has the shape of a uniform solid disk of mass 2.70 kg and radius 20.0 cm. A 1.00 kg stone is attached to a very light wire that is wrapped around the rim of the pulley (Figure 1), and the system is released from rest. You may want to review For related problem solving tips and strategies, you may want to view a Video Tutor Solution of An unwinding cable ii. How far must the stone fall so that the pulley has 3.10 J of kinetic energy What percent of the total kinetic energy does the pulley have?Explanation / Answer
PART A
As the stone falls the loss in PE equals the increase in KE of the stone,
1*g*d = 0.5*1*v^2
The increase in rotational KE of the pulley, P = 0.5*I*v^2/r^2
where, I is the moment of inertia
I = 0.5*2.7*r^2
P = 0.5*0.5*2.7*v^2
By, energy equation
1*g*d = 0.5*1*v^2 + 0.25*2.7*v^2
Given, K.E = 3.1 J
0.25*2.7*v^2 = 3.1
v = sqrt(3.1/(0.25*2.7)) = 2.14
1*g*d = 1.15*4.6
d = 1.15*4.6/9.8 = 0.54 m
PART B
Kp/Ktot = (0.25*2.7*v^2/(0.5*1*v^2+0.25*2.7*v^2))*100%
Kp/Ktot = (0.25*2.7/(0.5+0.25*2.7))*100
= 57.4