# Intro Physics question f = ma problem

## Homework Statement

1) An elevator cable can withstand a maximum tension of 19,500N before breaking. The elevator has a mass of 490 kg and a maximum acceleration of 2.24 m/s2. Engineering safety standards require that the cable tension never exceed two-thirds of the breaking tension. How may 65-kg people can the elevator safely accommodate?

F = ma

## The Attempt at a Solution

F = ma

F = (2/3)*(19,500 N)
F = 13,000 N

Then:

n = { [(13,000 N) / (2.24 m/s^2)] - 490 kg } / 65 kg
n = 81.7

n = 81 people

ehild
Homework Helper
Do not forget gravity. The cable exerts the upward tension T and gravity exerts the downward force mg. The resultant of these forces accelerate the elevator upward.

ehild

n = { [(13,000 N) / (2.24 m/s^2)] - 490 kg } / 65 kg
In addition to what ehild said, don't forget that the entire elevator, people plus car, are accelerating.

This is what I've gotten so far.

Since "require that the cable tension never exceed two-thirds of the breaking tension" :
F = ma
F = (2/3)*(19500)
F = 13000

Max Acceleration = 2.24 m/s^2
Acceleration due to gravity = 9.81 m/s^2
Acceleration = 2.24 + 9.81 = 12.05 m/s^2

So,

F = ma
13000 = ((490kg)+(65kgx))(12.05m/s^2)
x = 9.059 people

Rounded it to 9 people.

ehild
Homework Helper
This is what I've gotten so far.

Since "require that the cable tension never exceed two-thirds of the breaking tension" :
F = ma
F = (2/3)*(19500)
F = 13000

Max Acceleration = 2.24 m/s^2
Acceleration due to gravity = 9.81 m/s^2
Acceleration = 2.24 + 9.81 = 12.05 m/s^2

So,

F = ma
13000 = ((490kg)+(65kgx))(12.05m/s^2)
x = 9.059 people

Rounded it to 9 people.
Your "F" is the tension in the cable.

The elevator is accelerated by the sum of both forces: tension and gravity. The net force on the elevator is T-mg upward. So ma=T-mg.

Rearranging the equation, it becomes the same you used. T=m(a+g). The result is correct.

ehild

• xforeverlove21
Oh that makes sense now ehild.

Thanks a lot guys, the help is much appreciated.

ehild
Homework Helper
Oh that makes sense now ehild.

Thanks a lot guys, the help is much appreciated.
You are welcome ehild