How does the angle of a ramp affect the total work done when you pull a cart up the ramp?

Question

How does the angle of a ramp affect the total work done when you pull a cart up the ramp?

If the ramp is 90 degrees... W=Fd, where d is the height of the ramp.
If the ramp is 0 degrees (or flat)... W=fd, where d is the length of the ramp.
Does that mean that the ramp angle is, the more efficient it is, and the less work is done?

Then what if the angle of the ramp was 45 degrees... Would "d" be the height of the ramp, the horizontal distance of the ramp, or the actual length of the ramp?

Thank you!

Answer 1

No, no, no!



Work = force * distance IN THE DIRECTION OF THE FORCE.



The force in this case is gravity, which always acts straight downwards. You are good when the ramp angle is 90 degrees, but when the ramp angle is zero degrees, you are not doing any work at all, however far you pull the cart.



[ we are assuming that this is a frictionless ramp. Work done against friction is a different story.]



What matters is the vertical distance through which the cart moves. At any angle between 0 and 90 the cart is easier to pull [force is smaller], but you need to pull it further to achieve a given vertical height, so the work done still ends up as (force * vertical height).



When you use a ramp, you are just trading distance for force. It's a form of 'mechanical advantage' if you have met the term.



Hope that helps.

Answer 2

w=f(cos(theta))(d) you cant have a ramp of 90 degrees or else there's no gravity pushing the object onto the ramp and the ramp isn't doing anything

In a perfect model the angle still effects the work done because gravity affect's the object differently different amounts of the objects total gravity are pushing the gravity to the ramp

Answer 3

In a perfect model the angle of the ramp doesn't affect the work done.



In a practical model it does because there will be friction loses to take into account



LB gave a fuller answer. but it amounts to the same thing

Answer 4

With a low angle, a smaller force is applied over a greater distance to achieve the same amount of work that you would get using a greater force over a shorter distance. If you increase the angle, or steepen the ramp, a greater force is applied over over a shorter distance.

Answer 5

rigidity = mass x acceleration artwork finished = rigidity x distance so which you double the mass, you double the rigidity required to get the comparable acceleration. with the objective to take the comparable course up the ramp might want double the flexibility. you could double verify this with gravitational ability ability: Gravitational ability ability = mass * acceleration by way of gravity * height = mgh g and h are the comparable, in case you double mass, you double the flexibility required.