# Energy During Motion and Bounce of a Ball

• new hand
In summary, the discussion is focused on the behavior of a ball that is thrown upwards with an initial velocity. It is observed that the velocity of the ball after bouncing back is smaller than the initial velocity, and this is due to the external force of air resistance. While energy is always conserved, the mechanical energy of the ball (kinetic energy + potential energy) is not constant due to energy loss through air resistance and inelastic collisions with the ground. The total energy of the system, which includes heat energy, remains the same if heat does not escape the system. Therefore, the statement "the energy of the ball and the air is conserved" is not entirely accurate.
new hand
Here are the questions:

If a ball is thrown upwards with a initial velocity (u) from the hand, the ball throws to the highest point and after bouncing the floor, it bounces back to its initial position. In this case, it is said that air resistance is not negligible. Okay, I am confused by the followings:

1. The velocity after bouncing back is less than or larger than the initial velocity?
2. Is the energy of the ball and conserved?
3. Is there any net force acting on the ball when it is at its highest point?

THX everyone!

new hand said:
1. The velocity after bouncing back is less than or larger than the initial velocity?
2. Is the energy of the ball and conserved?
3. Is there any net force acting on the ball when it is at its highest point?
If I understood your question correctly,
1-What do you think? Should it be less or larger? Try doing this experiment in your home.
2-Energy is always conserved. That's the law of conservation of energy
3- Why does it fall down?

However, energy is only conserved only if there is no external force on the ball. However, the force exerted by the air resistance is the external force is not conserved. Besides, if the velocity after bouncing back is smaller, the energy is not conserved also. So, is this right or not?

new hand said:
However, energy is only conserved only if there is no external force on the ball. However, the force exerted by the air resistance is the external force is not conserved. Besides, if the velocity after bouncing back is smaller, the energy is not conserved also. So, is this right or not?

Use correct terms. The ball will have kinetic energy while moving.
If you are throwing it straight up, then the ball's kinetic energy will decrease as it raise up. It's kinetic energy is being converted to gravitational potential energy.
This is happening because there is an external force. What do you think it is?
Edit:{ Yes, the air resistance will also act like friction and will help your ball to lose energy as heat}
If the ball hits some place and if the collision is inelestic, then the kinetic energy of the ball will not be conserved. It will change to heat energy so the ball will move slower.
However, the total energy of the system will stay the same if heat does not escape the system.
Eventually, all the energy you gave to the ball will be wasted as hat energy and the ball will stop moving.

Last edited:
new hand said:
However, energy is only conserved only if there is no external force on the ball. However, the force exerted by the air resistance is the external force is not conserved. Besides, if the velocity after bouncing back is smaller, the energy is not conserved also. So, is this right or not?
You're right, but adjacent's comment might be due to your choice of words. Instead of saying that the energy of the ball is not conserved, it might be better to say that it is not constant, that the ball loses energy to the environment, both through air resistance and due to the fact that the collision with the gound is not purely elastic.

So,
for (2), the energy is not conserved.
for (3), there is net force acting on the ball

this??

new hand said:
So,
for (2), the energy is not conserved.
for (3), there is net force acting on the ball

this??
Yes.It is correct. but I prefer "kinetic energy is not conserved" in (2)

THX la~~~~ everyone!

How about total energy, because total energy refers to PE and KE
KE changes then the total energy changes.
would it be better??

new hand said:
How about total energy, because total energy refers to PE and KE
KE changes then the total energy changes.
would it be better??

Total energy is the total energy of the system. It also includes heat. So the total energy of the system remains the same. However, we can say that the mechanical energy(KE+PE) of the ball is changing

Total energy is the total energy of the system.
But if you consider the system to be the ball, and not the ball plus the air, then air resistence will transfer some energy to the air. Likewise, if you consider a realistic collision with the ground, it will be inelastic and some energy will be transferred to the ground.

DrClaude said:
But if you consider the system to be the ball, and not the ball plus the air, then air resistence will transfer some energy to the air. Likewise, if you consider a realistic collision with the ground, it will be inelastic and some energy will be transferred to the ground.

Oh, I forgot to mention that I referred the whole place to be the system in my previous posts.
It should be evident from this:
However, the total energy of the system will stay the same if heat does not escape the system.

how about I change the statement like this:

Are the energy of the ball and the air conserved?
Is this correct or not?

Oh, I forgot to mention that I referred the whole place to be the system in my previous posts.
It should be evident from this:

However, the total energy of the system will stay the same if heat does not escape the system.

Even then, I would argue that the ball is loosing energy to the air through the process of air resistence itself, independetly of subsequent heat transfers.

new hand said:
how about I change the statement like this:

Are the energy of the ball and the air conserved?
Is this correct or not?

The question should be rephrased as " Are the total energy of the ball and the air conserved?" Are you OK with it?

Anyway, if we say that heat does not escape the system(First let's define the system.Let the system include the ball, the air, the walls, the roof, floor and everything related to the ball), then total mechanical energy of the ball will not be conserved, as some energy is wasted as heat.We can also say that the total energy of the air is not conserved because some of the heat(Which was generated because of air resistance) in air may get absorbed by the walls, floor etc.

Edit:
DrClaude said:
Even then, I would argue that the ball is loosing energy to the air through the process of air resistence itself, independetly of subsequent heat transfers.
So if we define the system as I defined above, still the total energy of the system will not be constant?

is the new posed statement right?

ok ok

The question should be rephrased as " Are the total energy of the ball and the air conserved?" Are you OK with it?

Anyway, if we say that heat does not escape the system(First let's define the system.Let the system include the ball, the air, the walls, the roof, floor and everything related to the ball), then total mechanical energy of the ball will not be conserved, as some energy is wasted as heat.We can also say that the total energy of the air is not conserved because some of the heat(Which was generated because of air resistance) in air may get absorbed by the walls, floor etc.

Edit:

So if we define the system as I defined above, still the total energy of the system will not be constant?
If you include enough things in the "system", eventually you will get a "system" for which the energy is conserved.

For the kind of problem in the OP, one would usually consider the ball to be the system. Since there is air resistance, the mechanical energy of the system (kinetic energy + gravitational potential energy) is not conserved. Some of the energy is converted to heat energy.

Your contention was that the total energy of the ball was conserved. My argument is that this is not the case, as the air resistance also heats up the air (and not just through the fact that the ball gets warmer). The friction with the air does not only convert the ball's mechanical energy to thermal energy, it also transfers some of the ball's energy to the air.

To make things more complicated (and realistic), one could also then consider the collision of the ball with the ground.

DrClaude said:
Your contention was that the total energy of the ball was conserved.
I never said that. I said that the mechanical energy of the ball will not be conserved.
I guess I should change my "conserved" to "not constant" as you said before.

DrClaude said:
The friction with the air does not only convert the ball's mechanical energy to thermal energy, it also transfers some of the ball's energy to the air.
What energy are you talking about here?

new hand said:

2. Is the energy of the ball and conserved?

2-Energy is always conserved. That's the law of conservation of energy

This might be the origin of our misunderstanding. The OP is not correctly worded, and I took it as "Is the energy of the ball conserved?"

However, the total energy of the system will stay the same if heat does not escape the system.
For me, the system was the ball, and therefore I this to mean that the total energy of the ball was conserved (no transfer of energy to the environment).

What energy are you talking about here?
The ball's energy is kinetic energy, gravitational energy, and heat energy of the ball.

## 1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is calculated by multiplying half the object's mass by its velocity squared.

## 2. How does the height of a ball affect its potential energy?

The higher a ball is held above the ground, the greater its potential energy. Potential energy is the energy an object possesses due to its position or height above the ground.

## 3. Why does a ball bounce when it is dropped?

When a ball is dropped, it gains kinetic energy as it falls. When it hits the ground, this kinetic energy is converted into elastic potential energy as the ball compresses. This potential energy then causes the ball to bounce back up.

## 4. How does air resistance affect the bounce of a ball?

Air resistance can decrease the height of a ball's bounce. As the ball falls, air resistance slows it down, decreasing its kinetic energy and therefore the height it can bounce back up to.

## 5. What is the relationship between a ball's bounce and the surface it bounces on?

The surface a ball bounces on can affect the height of its bounce. A harder surface, like concrete, will cause the ball to bounce higher compared to a softer surface, like grass, which will absorb some of the ball's energy and result in a lower bounce.

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