Question

A 57-kg woman holds a 6-kg package as she stands within an elevator which briefly accelerates upward at a rate of 0.15g. Determine the force R which the elevator floor exerts on her feet and the lifting force L which she exerts on the package during the acceleration interval. If the elevator support cables suddenly and completely fail, what values would R and L acquire

Answer 1

R = 710.7N

L = 67.689 N

During gravity fall L = R = 0 N

Step-by-step explanation:

So the acceleration that the elevator is acting on the woman (and the package) in order to result in a net acceleration of 0.15g is

g + 0.15g = 1.15g

The force R that the elevator exerts on her feet would be product of acceleration and total mass (Newton's 2nd law):

a(m + M) = 1.15g(57 + 6) = 1.15*9.81*63 = 710.7N

The force L that she exerts on the package would be:

am = 1.15g *6 = 1.15*9.81*6 = 67.689N

When the system is falling, all have a net acceleration of g. So the acceleration that the elevator exerts on the woman (and the package) is 0, and so are the forces L and R.