How Do You Calculate the Velocity of a Counterweight Relative to an Elevator?

[deveny7]

Homework Statement

In the sketch at right, the winch W draws the cable at a constant rate of 2 m/s.
Calculate the velocity of the counterweight C relative to the elevator E.

Homework Equations

(S_a-S_c)+(S_b-S_c)+S_b=I₂

The Attempt at a Solution

I must be using the wrong equation because I am getting really strange answers.

 

[NascentOxygen]

I must be using the wrong equation because I am getting really strange answers.

Perhaps, perhaps not, we're unable to say either way since you haven't included your working for us to see what equation/s you are using.

Q: How fast is the elevator rising?

 

[deveny7]

I used 4Vw +Vc = 0. Which means the elevator would rise at 8m/s but that can't be right.

 

[CWatters]

Think about it in terms of the amount of rope wound in. If the winch winds in 2m the elevator goes up 1m. So the elevator moves up at half the speed of the winch eg 1m/s

Then look at the elevator and counter weight. If the elevator were raised say 1 meter how far does the counterweight move relative to the platform? How far does it move relative to the elevator?

 

[Nickie]

I would first clarify the given information and assumptions. Is the elevator moving or stationary? Is the counterweight moving or stationary? Is the cable being drawn in a straight line or at an angle? Are there any external forces acting on the elevator or counterweight? These factors can affect the equations and solutions.

Assuming the elevator and counterweight are both initially stationary and the cable is being drawn straight up, we can use the equation Vc = Ve + Vw, where Vc is the velocity of the counterweight, Ve is the velocity of the elevator, and Vw is the velocity of the winch. Since the winch is drawing the cable at a constant rate of 2 m/s, Vw = 2 m/s. If we assume the elevator is also moving at a constant rate of 2 m/s, then Ve = 2 m/s. Therefore, the velocity of the counterweight relative to the elevator is Vc = 2 m/s + 2 m/s = 4 m/s. This assumes no external forces are acting on the system.

If we want to take into account external forces, we can use the equation F = ma, where F is the net force acting on the object, m is the mass of the object, and a is the acceleration. We can also use the equation F = mg, where g is the acceleration due to gravity. In this case, if we assume the elevator and counterweight have the same mass, then the net force acting on the system is 0, since the force of gravity on the elevator is cancelled by the force of the counterweight. Therefore, the acceleration of the system is also 0, and the velocity of the counterweight relative to the elevator would also be 0. Again, this is assuming no external forces are acting on the system.

In conclusion, the velocity of the counterweight relative to the elevator depends on the given information and assumptions. Clarifying these factors can help determine the appropriate equations and solutions.