Finding Forces and Work in a Pulley System

[gunni91]

Homework Statement

Need some serious help with this one :O

A box with a weight WA hangs in pulleys ,(see figure 1). Find the force to pull A up with constant speed and calculate the work which the tractive force F produces ( with the movement of s) and also the work and tractive force T1 produce .
Pulleys and strings are frictionless and both without mass!.

Homework Equations

The Attempt at a Solution

 

[ehild]

What have you tried so far?

ehild

 

[ErwinMoses]

Homework Statement

Need some serious help with this one :O

A box with a weight WA hangs in pulleys ,(see figure 1). Find the force to pull A up with constant speed and calculate the work which the tractive force F produces ( with the movement of s) and also the work and tractive force T1 produce .
Pulleys and strings are frictionless and both without mass!.

Homework Equations

The Attempt at a Solution

taikng tensions ,T₁=4F
and taking constrained motion,
acc. of pulling end=4 times acc. of w_A
differentiating that we get s=4s₁
therefore work done by F=Fs
work done by T₁=T₁s₁=4F x s/4=Fs

correct me if i m wrong,i just tried.

 

[ehild]

The result is correct. Balance of forces gives that W_A=T1=4F. The question is the force needed to move the load with constant speed, so write out that F=W_A/4.
The mass moves with constant speed so there is no acceleration. The constraints apply for the displacements and changes of length of the pieces of the ropes, but not for the non-existent accelerations. You can say that moving the end of the left rope by s will cause the other two pieces shorten by s/2 so the middle pulley raises by s/2. In the same way, raising the end of the right rope by s/2 lifts the right pulley by s/4.

ehild

 

[ErwinMoses]

thank you echild.

 

[ErwinMoses]

sorry didn't see the name
properly,very sorry.thanks ehild!

 

[ehild]

sorry didn't see the name
properly,very sorry.thanks ehild!

You are welcome

ehild