A frictionless pulley has the shape of a uniform solid disk of mass 5.00 k g and
ID: 2296669 • Letter: A
Question
A frictionless pulley has the shape of a uniform solid disk of mass 5.00kg and radius 13.0cm . A 1.10kg stone is attached to a very light wire that is wrapped around the rim of the pulley(Figure 1) , and the stone is released from rest. As it falls down, the wire unwinds without stretching or slipping, causing the pulley to rotate. How far must the stone fall so that the pulley has 6.20J of kinetic energy?
-How far must the stone fall so that the pulley has 6.20J of kinetic energy?
A frictionless pulley has the shape of a uniform solid disk of mass 5.00kg and radius 13.0cm . A 1.10kg stone is attached to a very light wire that is wrapped around the rim of the pulley(Figure 1) , and the stone is released from rest. As it falls down, the wire unwinds without stretching or slipping, causing the pulley to rotate. How far must the stone fall so that the pulley has 6.20J of kinetic energy?
-How far must the stone fall so that the pulley has 6.20J of kinetic energy?
Explanation / Answer
1/2*I*w^2=6.2 j
I=1/2*m*r^2=0.5*5*0.13^2 = 0.04225
w^2=6.2/0.021125=293.49112426
w=17.1315826549 rad/s
now conservation of energy
m*g*h=(6.2j+1/2*m*v^2) (but v=wr)
1.1*9.8*h=(6.2+0.5*1.1*293.5*0.13^2)
h=8.9280825/10.78=0.828208 m==>answer