Question

An object slides down a very smooth ramp, with negligible friction. It slides with constant acceleration a under the action of two forces: the supporting force n exerted by the ramp, and the force m g due to gravity exerted by the earth. What can you say about how the magnitude of n compares to the magnitude of m g?
1. n is less than m g.
2. Their magnitudes are equal, as is almost always true on the earth’s surface.
3. None of these
4. n is greater than m g.

Answer 1

Answer:

In statics condition and if is a body is over plane surface N = mg

In all cases which a body is on a ramp force N will be smaller than mg, and depending on the level of the ramp (bigger the ramp smaller force N)

Explanation:

See annex (Figure 1)

We can see with the help of force diagram the relation between  N force  and mg

Lets look first the body on the ramp assuming there is not movement

The  sum of forces alog y axis = 0

mg* cos∠ BAC = N (normal force)

So N is always a fuction of mg and of the cosine of the inclination angle, and the cosine of angle varies from value 1 when the angle is 0 (look the case where the block is on the surface without inclination N = mg ).

And as the inclination increase the value of cosine will become smaller and so will N force which is directly proportional of cosine of the inclination angle

Therefore we can say that force N is always minor than mg unless in extreme case where the block is over the surface in which case N takes its maximum value N = mg