1. A steel wire of length L connects a hook on the ceiling to a bowling ball, Wi

Question

1. A steel wire of length L connects a hook on the ceiling to a bowling ball, With the steel wire kept taut, the bowling ball is lifted to a height h above the floor, and then released. The bowling ball swings back and forth in the motion of a pendulum. After the bowling ball is released, what is the maximum height above the floor that it reaches? Assume that friction does not affect its motion.

a) 1.33h

b) L

c) h/2

d) h

2.A steel wire of length L connects a hook on the ceiling to a bowling ball, With the steel wire kept taut, the bowling ball is lifted to a height habove the floor, and then released. The bowling ball swings back and forth in the motion of a pendulum. When is the energy of the bowling ball transformed from gravitational potential energy to kinetic energy? ( same picture as #1)

a) when the height of the bowling ball is increasing

b) when the height of the bowling ball is decreasing

c) when the bowling ball is at height h above the floor, but not lower

d) continuously until the pendulum stops moving

2.A steel wire of length L connects a hook on the ceiling to a bowling ball, With the steel wire kept taut, the bowling ball is lifted to a height habove the floor, and then released. The bowling ball swings back and forth in the motion of a pendulum. When is the energy of the bowling ball transformed from gravitational potential energy to kinetic energy? ( same picture as #1)

a) when the height of the bowling ball is increasing

b) when the height of the bowling ball is decreasing

c) when the bowling ball is at height h above the floor, but not lower

d) continuously until the pendulum stops moving

Explanation / Answer

1.

Since there is no friction force, there is no dissiaption of energy and energy reamains coserved. At the time of the release the height was h above the floor.

Initial energy = mgh, kinetic energy is zero initially when the ball is released.

When the ball swings to the other side and reaches maximum height H above the floor, its speed again becomes zero. So energy at that point is mgH

Since energy is conserved, we have

mgh = mgH

or H = h

so the masimum height reached is h.

So, the correct option is d)

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2.

Total mechanical energy is the sum of the kinetic+potential energy. In absence of dissipative forces, like friction, the mechanical energy remains constant which means the decrease in potential energy would have to be compensated with corresponding increase in kinetic enerrgy and vice versa to keep the mechanical energy constant.

So, if the gravitational potential energy is being transformed into kinetic energy then the potential energy must decrease which happens when the height of the ball decreases.

So, the correct option is b)

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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....

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