How Many People Can an Elevator Hold Without Breaking the Cable?

[Voltrical]

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?

Homework Equations

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]

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

 

[tms]

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.

 

[Voltrical]

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]

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

 

[Voltrical]

Oh that makes sense now ehild.

Thanks a lot guys, the help is much appreciated.

 

[ehild]

Oh that makes sense now ehild.

Thanks a lot guys, the help is much appreciated.

You are welcome

ehild