When a ball at rest is dropped, can it rebound to a greater height than its original height?

Answer 1

Usually, no.

A ball has a gravitational potential energy given by #mgh#, where #m# is mass, #g# is the acceleration due to gravity, and #h# is the height.

When the ball falls, some of its gravitational potential energy is converted to other forms of energy, such as kinetic energy and rotational energy.

When it rebounds, these other forms of energy is converted back to gravitational potential energy.

During this process, some of its energy is lost from friction, heat, sound, etc. This means that it cannot be rebound back to its original height.

However, this only means that its final gravitational potential energy #mgh# is lower than original. Usually, this corresponds to a loss in height #h#. But if the ball gained energy during falling and rebounding (such as if the ball ejects some of its matter towards the ground, a force is applied to the ball during falling or rebound, etc.), its rebound height might be greater than its original height.

But, usually, the ball will not be rebound to a height greater than its original height.

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Answer 2

Yes, theoretically, a ball dropped from rest can rebound to a greater height than its original height if external factors such as air resistance and energy loss are negligible. This situation can occur if the ball experiences a perfectly elastic collision with the surface, converting its kinetic energy into potential energy, resulting in a rebound to a greater height. However, in real-world scenarios, energy loss due to factors like air resistance and surface imperfections typically causes the rebound height to be lower than the original height.

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Answer 3

No, a ball at rest that is dropped cannot rebound to a greater height than its original height. According to the law of conservation of energy, the total mechanical energy of the ball (the sum of its kinetic energy and potential energy) remains constant if no external forces, such as air resistance, are acting on it. When the ball is dropped, it initially has potential energy due to its position above the ground. As it falls, this potential energy is converted into kinetic energy. At the bottom of its fall, the ball has maximum kinetic energy and minimum potential energy.

When the ball rebounds, it does so due to the elastic properties of the material it is made of. However, the rebound height will always be less than or equal to the original height from which it was dropped. This is because some of the energy is lost as heat and sound during the collision and rebound process. This loss of energy is known as energy dissipation, and it prevents the ball from reaching a greater height than its original height after rebounding. Therefore, in an ideal scenario without external influences, a ball dropped from rest can never rebound to a height greater than the height from which it was dropped.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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