# Work Done by F on a Ball: Path or Displacement?

• wolovemm
In summary, the work done by F on the ball depends on the component of the displacement in the direction of the force. This can be understood through the concept of scalar or dot product of two vectors, where the work done is the product of the magnitude of the force and the displacement. This is also known as the conversion of kinetic energy into gravitational potential energy.
wolovemm

the question is what is the work done by F on the ball
so this is what i did
since F is constant we can apply

and now here's my question, does the work done in this case depends on the path (curve) or the displacement (straight line)?

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so I'm trying to find the work done by F on the ball

and this is what i got

where
sqrt(2LH) is the displacement from the bottom to the position with height H.

So, I'm just wondering if this is correct or I'm missing something

Last edited:
wolovemm said:
and now here's my question, does the work done in this case depends on the path (curve) or the displacement (straight line)?
It depends on the component of the displacement in the direction of the force. (Read up on the meaning of the scalar/dot product of two vectors.)

it depenson dsplacement...kinectic converted into gravitational

## 1. What is meant by "work done by F on a ball: path or displacement?"

The work done by F on a ball refers to the amount of energy transferred to the ball by a force, causing it to move. The term "path or displacement" refers to the different ways in which the ball can move, either along a specific path or from one point to another (displacement).

## 2. How is work done by F on a ball calculated?

The work done by F on a ball can be calculated by multiplying the force applied to the ball by the distance over which the force is applied. This is represented by the equation W = F * d, where W is work, F is force, and d is distance.

## 3. Does the path or displacement of the ball affect the amount of work done by F?

Yes, the path or displacement of the ball can affect the amount of work done by F. If the force is applied in the same direction as the ball's movement (parallel to the displacement), then the work done will be equal to the force multiplied by the displacement. However, if the force is applied at an angle to the displacement, the work done will be less than the force multiplied by the displacement.

## 4. How does the work done by F on a ball affect the ball's kinetic energy?

The work done by F on a ball increases the ball's kinetic energy, which is the energy it has due to its motion. This is because work is a measure of energy, and the work done by F transfers energy to the ball, increasing its speed and therefore its kinetic energy.

## 5. Does the work done by F on a ball depend on the mass of the ball?

Yes, the work done by F on a ball does depend on the mass of the ball. This is because the amount of energy transferred to the ball by a force is directly proportional to the mass of the object it is acting on. Therefore, a greater mass will require more work to be done on it to achieve the same change in motion as a smaller mass.

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