Question

For this problem, imagine that you are on a ship that is oscillating up and down on a rough sea. Assume for simplicity that this is simple harmonic motion (in the vertical direction) with amplitude 5 cm and frequency 2 Hz. There is a box on the floor with mass m = 1kg. (a)Assuming the box remains in contact with the floor throughout, find the maximum and minimum values of the normal force exerted on it by the floor over an oscillation cycle. (b)How large would the amplitude of the oscillations have to become for the box to lose contact with the floor, assuming the frequency remains constant? (Hint: what is the value of the normal force at the moment the box loses contact with the floor?)

Answer 1

The net force on the box is:

mg - R - F = 0

this is zero since the box is in contact with the ground and hence is in equilibrium.

F is due to the SHM

where a is the acceleration whose maximum value will be:

[A = amplitude of the motion]

and minimum value will be:

so, the normal force R will be minimum when F = +ve and maximum when F = -ve

=>

and

when the box looses contact, the normal force becomes zero since there is no contact to provide that force.

Therefore,

=>

this should be the amplitude for the same frequency for the box to loose contact from the ground.