Question

I have a conceptual/ theoretic question. Let's say you have a box on a ramp which is at first parallel to the ground but then you raise the track to an angle α with the horizontal and the cart's acceleration is zero with the scale parallel to the track, what is the amount of force you are applying?

I drew a free body diagram and got mgsinalpha.

The question then asks what will be the applied force if you increased the angle between the direction of the pull and the surface of the track to be β while the cart has zero acceleration and the track angle α as before. There can be multiple answers.

1)0 N Larger amount of force compared to when the pull was parallel to the track

2)(m · g · sin(α) · cos(β)

3)(m · g · cos(α+β) ) N

4) m*g sin (alpha) / cos (beta)

5)(m · g · sin(α+β) )

6)(m · g)

7) N  Smaller amount of force compared to when the pull was parallel to the track

I tried to solve this by drawing a free body diagram. I seperated the applied force for the angle beta into x and y components. So mg cos beta and mg sin beta. However, I am unsure of how to get the total applied foce. I thought it would be ((mgsin(beta))^2 + (mgcos(beta)+mgsin(alpha))^2)^(1/2)

Obviously I am way off though so an explanation will be helpful.

Answer 1

Ans - (4) m*g sin (alpha) / cos (beta)

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