Basic Frictional Forces/Gravity Question

[Seinfeld4]

Homework Statement

An elevator containing three passengers (with a mass of 72kg, 84kg, and 35kg, respectively) has a combined mass of 1030kg. The cable attached to the elevator exerts an upward force of 12 000N, but friction opposing the motion of the elevator is 1400N.

a) Calculate the net acceleration of the elevator and its passengers.

I started by calculating F(net).

F(net) = 12 000N - (Ff + Fg)
F(net) = 12 000N - (1400N + (1030kg * 9.80m/s^2))
F(net) = 506N

Now, to calculate net acceleration:

a(net) = F(net) / m
a(net) = 506N / 1030kg
a(net) = 0.49m/s^2

Is that correct? That seems realistic for an elevator (I think).

b) Calculate the force normal acting on the 35kg passenger.

Fn = mg - ma
Fn = (35kg)(9.80m/s^2) - (35kg)(0.49m/s^2)
Fn = 325.85N

Am I doing this properly so far?

c) What velocity will the elevator have 12 seconds after the passengers have entered the elevator?

v = a * t
v = 0.49m/s^2 * 12s
v = 5.88m/s

Can anybody verify if this is correct? It would be much appreciated!

 

[SteamKing]

You are standing in an elevator when the door closes and the elevator starts to go up. Do you feel heavier or lighter when the elevator car starts to move?

You are in an elevator at the top of a building when the elevator cable suddenly snaps and the elevator starts to fall. When the fall starts, do you feel heavier or lighter?

 

[Seinfeld4]

So...I didn't do it properly then?

I know that you feel heavier when the elevator begins to ascend, and you feel lighter when the elevator begins to descend.

Since the elevator is ascending in this case, should Fn = mg + ma?

Fn = mg + ma
Fn = (35kg)(9.80m/s^2) + (35kg)(0.49m/s^2)
Fn = 360.15N

Is this what you're trying to get at? Sorry, I'm a little lost!

 

[Chi Meson]

That is correct. You are not exactly adding "+a" with "-g." In a classical physics explanations (as opposed to the more correct General Relativity explanation) you can think that the normal force has to do two things--1: balance the weight of the person, then 2: supply additional net force to cause the person's acceleration. This means the normal force, when accelerating up, will be m(g+a) {these values are the magnitudes of the vector quantities}, and when accelerating down (which includes coming to a stop when the elevator arrives at the top ) it's m(g-a) .

 

[Seinfeld4]

Makes sense, thanks a lot!

So I did part a) and c) properly then?

 

[Chi Meson]

It appears so. I don't have my calculator, but the process is correct.