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Solved: Two identical balls, A and B, are each attached to
Chapter 9, Problem 17DQ(choose chapter or problem)
Two identical balls, A and B, are each attached to very light string, and each string is wrapped around the rim of a frictionless pulley of mass M. The only difference is that the pulley for ball A is a solid disk, while the one for ball B is a hollow disk, like part (e) in Table 9.2. If both balls are released from rest and fall the same distance, which one will have more kinetic energy, or will they have the same kinetic energy? Explain your reasoning.
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QUESTION:
Two identical balls, A and B, are each attached to very light string, and each string is wrapped around the rim of a frictionless pulley of mass M. The only difference is that the pulley for ball A is a solid disk, while the one for ball B is a hollow disk, like part (e) in Table 9.2. If both balls are released from rest and fall the same distance, which one will have more kinetic energy, or will they have the same kinetic energy? Explain your reasoning.
ANSWER:Solution 17DQ
Step 1 of 4:
The rotational kinetic energy of the pulley is given by,
Where is angular speed and I is moment of inertia.
But in the given problem, we need to calculate the kinetic energy for solid disk and hollow disk when they are used as pulley for the identical mass and released. As they are attached to identical balls,mass remains same(m) and hence the angular speed of rotation of pulleys().