# Force exerted on Earth by accelerating ball

• Entr0py
In summary, when a ball is bounced from the ground, the Earth exerts a force on the ball to reverse its velocity. This is due to the force of gravity between the Earth and the ball. When the ball hits the ground, it exerts a force on the ground (normal force) and the ground exerts an equal and opposite force on the ball. This force causes the ball to change its velocity in the upward direction, resulting in acceleration. The Earth also experiences a small acceleration, but it is not noticeable due to its large mass. This is the reason why we perceive the ball to accelerate upwards.
Entr0py

## Homework Statement

When a ball is bounced from the ground, the Earth exerts the force necessary to reverse its velocity. Is there a simultaneous force exerted on the earth? If there is one, why don't we perceive any acceleration of the earth?

## Homework Equations

Newton's second law: net F=ma, F and a being vectors
Newton's third law: all forces act in pairs, equal and opposite

## The Attempt at a Solution

So when the ball is say released from my hand it heads toward the ground. Now the ball's velocity is changing and therefore is accelerating. Its speed is increasing but its direction is in the downward direction. Now the acceleration of the ball is due to the force of attraction of earth. That makes sense to me. However, when the ball hits the ground, its exerts a force on the ground (normal force') and the ground exerts an upward force (normal force). The ball has another force acting on it, its weight and it exerts a force (weight') on the earth. But I'm confused which force causes the ball to bounce back in the opposite direction, causing it to accelerate it upwards. I know that the Earth does accelerate but its effect is trivial since mass of Earth is large relative to the ball.

In which direction is the net acceleration during the bounce? The answer to this question should give you a hint as to what is the force responsible.

Orodruin said:
In which direction is the net acceleration during the bounce? The answer to this question should give you a hint as to what is the force responsible.
The net acceleration is downwards because of gravity and then upwards due to normal force. So is this the contact force from the ground (earth) that causes the ball to change its velocity in upward direction? That's what I'm thinking

Yes.

Orodruin said:
Yes.
This makes sense to me now. And when the ball and ground come in contact, the ground DOES accelerate but is very hard to notice due to Earth's mass. The reason I see the ball accelerate upward is because its mass is lighter with respect to the ground (the earth).

## 1. What is the formula for calculating the force exerted on Earth by an accelerating ball?

The formula for calculating force is F = ma, where F represents force, m represents mass, and a represents acceleration. Therefore, the force exerted on Earth by an accelerating ball can be calculated by multiplying the mass of the ball by its acceleration.

## 2. How does the mass and acceleration of the ball affect the force exerted on Earth?

The force exerted on Earth by an accelerating ball is directly proportional to its mass and acceleration. This means that as the mass or acceleration of the ball increases, the force exerted on Earth will also increase.

## 3. Is the force exerted on Earth by an accelerating ball constant?

No, the force exerted on Earth by an accelerating ball is not constant. As the ball accelerates, the force exerted on Earth will change accordingly. Once the ball reaches a state of constant velocity, the force exerted on Earth will also become constant.

## 4. How does the direction of the ball's acceleration affect the force exerted on Earth?

The direction of the ball's acceleration does not affect the force exerted on Earth. The force exerted on Earth will always be in the opposite direction of the ball's acceleration, as described by Newton's third law of motion.

## 5. Can the force exerted on Earth by an accelerating ball be negative?

Yes, the force exerted on Earth by an accelerating ball can be negative. This would occur if the direction of the force is opposite to the direction of the acceleration. For example, if a ball is slowing down, the force exerted on Earth would be negative.

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