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)

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.