How Do You Calculate Elevator Cable Tension for Maximum Acceleration?

[yandereni]

1. The problem statement, all variables and given/known data
An elevator(4850kg) is to be designed so that the maximum acceleration is 0.068m/s². What are the minumum and maximum forces the motor must exert on the supporting cable?

2. Homework Equations
Force = mass(acceleration)
Force_vertical = Ftens + Fgrav

The Attempt at a Solution

Force_vertical = Ftens + Fgrav
Force = 4850kg(0.068m/s²)
= 329.8N

Force_vertical = 329.8N - 47530N
= -47200N

I'm not so sure about both answers but i think the first solution is kinda right?

thanks in Advance!

 

[Cake]

Not quite. Think about what is happening. It also has to account for the force of gravity. So the minimum amount of force needed would be to support the force of gravity, and the maximum would be to not only support the force of gravity, but to accelerate the elevator upward at 0.068m/s2. So How would you express those forces with mathematics?

 

[haruspex]

Force_vertical = F_tens + F_grav

Please define what Force_vertical represents.

Force = 4850kg(0.068m/s²)

Which of the forces in the first equation corresponds to "Force" in this equation?

 

[yandereni]

Please define what Force_vertical represents.

Force_vertical means forces on the y-axis

Which of the forces in the first equation corresponds to "Force" in this equation?

Ftens is the one that corresponds to "Force"

 

[haruspex]

Forcevertical means forces on the y-axis

No, there are two applied forces (plural) on the y axis, and you have those on the right hand side of the equation. Force_vertical is one force. The word I'm looking for is 'net' force, or 'resultant' force.

F_tens is the one that corresponds to "Force"

Then that's where you are wrong. In the standard equation F=ma, what does F represent? Yes, I know it's a force, but exactly what force?