Work, energy, power tennis ball problem

In summary, the force applied to a tennis ball is described by the function F(x) = 2x + 5, with the force in Newtons and the position in meters. To find the work done by the force as the ball moves from -2.5 m to 2.4 m, we need to integrate F(x) from -2.5 to 2.4, which results in 48.02 J. The error in the previous attempt was not integrating the function.
  • #1
ferrariistheking
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Homework Statement


A force applied to a tennis ball is described by the function

F(x) = 2x + 5, with the force in Newtons and the position in meters.

How much work does the force do on a tennis ball as it moves from -2.5 m to a new position of 2.4 m?

Homework Equations


F(x)= 2x+5
force x distance= work

The Attempt at a Solution


I found the distance from -2.5m to 2.4m which is 4.9m.

Then I plugged -2.5m into x for the function which is 0.

I then plugged in 2.4m into the function which is 9.8.

With 9.8, I multiplied it by 4.9 m getting 48.02 which is incorrect

Can anybody find my error? Thanks!
 
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  • #2
You need to integrate F(x) from x=-2.5 to x=2.4.
 
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  • #3
andrewkirk said:
You need to integrate F(x) from x=-2.5 to x=2.4.
ohhhh I see. Thanks for the help once again.
 

1. What is the work-energy theorem?

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This means that when a force is applied to an object, causing it to move, the work done by that force will result in a change in the object's speed or direction.

2. How is work calculated in a tennis ball problem?

In a tennis ball problem, work is calculated by multiplying the force applied to the ball by the distance the ball travels. This can be represented by the formula: W = F * d, where W is work, F is force, and d is distance.

3. What is the relationship between work and power?

Work and power are related because power is the rate at which work is done. This means that the more power an object has, the faster it can do work. Power is calculated by dividing work by time, or P = W/t.

4. How does the mass of a tennis ball affect its energy?

The mass of a tennis ball does not directly affect its energy. However, the mass of an object does affect the amount of work needed to change its kinetic energy. In a tennis ball problem, a lighter ball will require less work to achieve the same change in energy as a heavier ball.

5. What is the conservation of energy principle?

The conservation of energy principle states that energy cannot be created or destroyed, only transferred or transformed. This means that in a tennis ball problem, the total energy of the ball at the beginning and end of the problem should be the same, even if the ball's kinetic energy has changed.

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