Abox is sitting stationary on a ramp that is 42° to the horizontal. the box has a gravitational force of 112.1 n. what is the minimum amount of force that can be applied to the box to get the box to move? 70 n 75 n 80 n 83 n

We should draw a Free Body Diagram of the box here. As the box is sitting on a ramp 42 degrees to the horizontal. It experiences only one force that is the gravitational force (mg) downwards whose value is given to be 112.1 N.

Now if we take components of this force.

We get one component as mg sin (Theta) Sliding Downwards from the ramp slope.

We get another component as mg cos (Theta) into the ramp.

Now to move the box we must apply a force opposite to the mg sin (Theta) component as that is the only movable plane.

So the minimum force will be equal to mg sin (Theta)

= 112.1 * Sin( 42 degrees)

= 75 N approximately ( Answer is B)  

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