Efficiency and Energy to move a box on a conveyor belt

[UnknownQuestioner]

Homework Statement

Please refer to the attached picture.

Relevant Equations

This is where I am stuck at, I can’t seem to figure out the formulas to use and the combination of using them.

 

[etotheipi]

What force acts on the box? I assume the conveyor belt is horizontal.

 

[UnknownQuestioner]

Gravity? Not sure

 

[etotheipi]

If the box is being accelerated by the belt, the belt's got to be exerting a force on it. You know the mass of the box (from the weight) and the acceleration, so can you get the force the belt exerts on the box?

 

[UnknownQuestioner]

 

[etotheipi]

Yeah, but you can just use components here. Just say $F=ma$. What is the force?

 

[UnknownQuestioner]

Would that be 350 x 2.78 to get 973 N as the force?

 

[etotheipi]

Would that be 350 x 2.78 to get 973 N as the force?

What's the mass of the box?

 

[UnknownQuestioner]

Oops, that would be 35.7 kg. Then 35.7 x 2.78 to get 99.2 N

 

[haruspex]

Oops, that would be 35.7 kg. Then 35.7 x 2.78 to get 99.2 N

So how much work is done on the box in moving it the 100m?

 

[UnknownQuestioner]

So how much work is done on the box in moving it the 100m?

I used f=ma to get 99.2N then I used W=fd to get 9920J. This energy is the output, so output/0.25=input. To get a final answer of 3.97 x 10^4 J This is correct?

 

[haruspex]

I used f=ma to get 99.2N then I used W=fd to get 9920J. This energy is the output, so output/0.25=input. To get a final answer of 3.97 x 10^4 J This is correct?

Looks good.