Determining the factors impacting the amount of Work done

[BiggestAfrica]

Homework Statement

Suppose you are moving an oven onto the back of a truck which is 1.5m above the ground.

1. Would pushing the oven up a ramp 4m long require more force than pushing the oven up a ramp 10m long?

2. Would pushing the oven up a ramp 4m long require more work than pushing the oven up a ramp 10m long?

Relevant Equations

W = FdcosѲ

Apologies for my fairly undescriptive title, I'm having trouble coming up with a better one.

I'm simply trying to verify whether my understanding of this problem is correct.

1. Pushing the oven up a ramp 4m long would require more force (my reasoning here is based on the results of a lab which I'm confident about, which suggested that there is an inverse relationship between length of ramp and applied force)

2. Both scenarios would require the same amount of work to be done, as both the distance and angle are changing

 

[haruspex]

Pushing the oven up a ramp 4m long would require more force

Yes.

Both scenarios would require the same amount of work to be done, as both the distance and angle are changing

Yes, the same if no friction. (Any thoughts on how friction might change that?)
But the reason you give only says they could be the same. Can you offer an argument that says (friction aside) they would be the same?

 

[BiggestAfrica]

Yes.

Yes, the same if no friction. (Any thoughts on how friction might change that?)
But the reason you give only says they could be the same. Can you offer an argument that says (friction aside) they would be the same?

I'm completely unsure about friction... I initially thought that they would be the same due to the distance increasing while the angle decreased, until I recalled that Ѳ is the angle between force applied and displacement vector. Now I think it's possibly due to the cosine aspect of the equation being negligible (cos0 = 1), but I'm not entirely confident in that reasoning.

 

[haruspex]

I'm completely unsure about friction... I initially thought that they would be the same due to the distance increasing while the angle decreased, until I recalled that Ѳ is the angle between force applied and displacement vector. Now I think it's possibly due to the cosine aspect of the equation being negligible (cos0 = 1), but I'm not entirely confident in that reasoning.

Since your original question did not mention friction, I would guess you are supposed to assume there is none. I only asked to see if you had any thoughts on that.

You would need to think about the magnitude of the normal force. It is complicated by the issue of the angle at which the force is applied. When there is friction, you can do better than applying the force parallel to the ramp. So you would first have to decide which case you wanted to consider, parallel to the ramp or optimal angle.