Constant force but angle is increased, what happens to work

In summary, as the angle theta increases in the work formula, the work decreases. This is due to the behavior of the cosine function, which initially decreases and then increases as the angle increases from 0 to 180 degrees (or 0 to π radians). This is why, when the calculator is in degree mode, the cosine values decrease as the angle increases, but when in radian mode, the cosine values go from -1 to 1.
  • #1
Frankenstein19
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Homework Statement


A box is dragged a distance d across the floor by a force F which makes an angle theta with the horizontal. If the magnitude of the force is held constant but the angle theta is increased, does the work remain the same, increase, decrease, or first increase and then decrease?

Homework Equations

The Attempt at a Solution


Ok so I know what the graph of cosine looks like, which initially (well if we start from zero, anyway) goes down and then up and then down and so on. But I don't have an option that says that. The correct answer is that it decreases. If I make a table on my calculator with it being in degree mode, I can see that cosine gets smaller and smaller as the angle increases, however, when it's in radian mode it goes from -1 to 1. I don't understand why work decreases as the angle is increased.
 
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  • #2
Frankenstein19 said:
If I make a table on my calculator with it being in degree mode, I can see that cosine gets smaller and smaller as the angle increases, however, when it's in radian mode it goes from -1 to 1. I don't understand why work decreases as the angle is increased.
I don't understand how you are getting the cosine to increase from -1 to 1 as the angle θ in the work formula increases. Note that θ always lies between 0 and 180 degrees; that is, between 0 and ##\pi## radians. So, what happens to the cosine function as θ goes from 0 radians to ##\pi## radians?
 

FAQ: Constant force but angle is increased, what happens to work

1. What is work?

Work is defined as the product of the force applied to an object and the distance over which the force is applied. It is measured in joules (J).

2. How is work affected by a constant force?

A constant force applied to an object will result in a constant work output, meaning that the amount of work done will be consistent regardless of the magnitude of the force.

3. How does increasing the angle affect work?

Increasing the angle between the direction of the force and the direction of motion of the object will decrease the amount of work done. This is because only the component of the force in the direction of motion is responsible for doing work.

4. Does the amount of force affect the work done?

Yes, the amount of force applied to an object affects the work done. The greater the force, the greater the work output.

5. What happens to work if the angle is increased but the force remains constant?

If the force remains constant but the angle is increased, the work done will decrease. This is because the component of the force in the direction of motion will decrease, resulting in a lower work output.

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