Elevator question?

Question

Can someone help me with this question?

Suppose that the mass of an elevator and passengers were 1500 kg and the frictional force was 9000 N (wheels on tracks). Use g = 10 N/kg

Can you describe what the force diagram looks like?

What is the acceleration?

Suppose that a 50 kg woman is standing on a bathroom scale is in the elevator car. What would the scale read? Can you describe what the force diagram would look like?

Answer 1

The only forces acting would be weight (down) and friction (opposite the motion).

The force diagram would be different depending on whether the elevator is going up or going down. I will be assuming the elevator is going down. You can do the calculations if the elevator is going up.


If the elevator is going down, then the frictional force will act up.

So......

Fr - W = ma

9000 - 15000 = (1500)a
a = -4 m/s²

The acceleration is negative because the elevator is going down. In fact, it is accelerating down.



What are the forces acting on the woman?

Normal force (up)
Weight (down)

The scale will read the Normal force. Normal force and apparent weight mean the same exact thing.

N - W = ma
N = ma + mg
N = m(a + g)
N = 50(-4 + 10)
N = 300 N


Notice that this is less than her normal weight of 500 N. This makes sense... as the elevator accelerates downward, she should feel lighter.

Answer 2

According to the info given, the elevator is falling with only friction to restrain it. In that case, the force diagram would show 1500*10 N down and 9000 N up → net f = 6000 N down.

a = F/m = 6000/1500 = 4 m/s² down

The force diagram for the scale would show 50(10-4) = 300 N net force pressing on the scale.