# Block moving on a circular track-Work energy Circular Motion problem

1. ### Tanya Sharma

1. The problem statement, all variables and given/known data

A block of mass 1 Kg initially at rest at point B is being pulled by a constant force F= 100N along a smooth circular track of radius 10 m . Find the velocity of the block when it reaches point P making an angle 60 with the vertical.

2. Relevant equations

3. The attempt at a solution

KE1+PE1+W[F]=KE2+PE2

Now KE1=PE1=0 assuming reference level to be at B.
KE2=1/2(mv[2]
PE2=mgl(1-cos60°)
W[F]=?

How do we calculate work done by force F? My understanding says that angle between constant force and displacement changes continuously as the block moves along the track.Please help me.Thanks...

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2. ### azizlwl

975
F is a conservative force.

3. ### Tanya Sharma

No... F is force applied by some external agent.

4. ### Tanya Sharma

The block is pulled via a light inextensible string by external force F.

### Staff: Mentor

Yes, the angle continually changes but luckily the force is constant. What's the displacement in the direction of that constant force?

6. ### Tanya Sharma

Thanks Doc Al ...I have thought about displacement in the direction of constant force but not able to comprehend ...Sorry......please explain

7. ### Tanya Sharma

I feel the direction of force is continuously changing as the block moves.

### Staff: Mentor

So it's not a constant force? Did you misstate something in the problem statement?

9. ### ehild

12,387
Tanya, is the magnitude of the force constant and acting along the track or is it really a constant horizontal force? The drawing suggest a constant horizontal force.

ehild

10. ### Tanya Sharma

The block is being pulled by a light inextensible string which passes over a small frictionless massless pulley . The string is pulled by a constant horizontal force of magnitude 100 N .

11. ### Tanya Sharma

What i meant by change of direction of force is that the magnitude of tension in the string pulling the block will remain constant but the direction of this tension force changes.Whereas the displacement of the block is always tangential to the circular track.

### Staff: Mentor

Good. So the direction of that force F is kept horizontal. (Makes things easier.)

### Staff: Mentor

Does the tension do any work on the block?

As far as the work done by that constant force F, go back to my earlier question: What's the displacement in the direction of that constant force?

14. ### Tanya Sharma

Please correct me if i am wrong...the constant force is being applied on the string which in turn pulls the block.So , now external force on the block is the tension .Now since the string is massless the force applied on the string = Tension in the string. But the angle between this tension force and the displacement of the block changes continuously isnt it ??

Doc Al ...We have to relate displacement of the block with the tension not the constant horizontal force... isnt it ?

### Staff: Mentor

Yes, you are correct. I guess I wasn't paying close enough attention to your diagram. (I was thinking of something else. ) Nonetheless, there's a much easier way to solve this and my suggestion stands as is.
Ask yourself: How much work is done on the system by that constant force? That's all you need to know.

16. ### Tanya Sharma

Displacement in the direction of constant force should be 10sin60° .Work done accordingly is 100 × 10(√3/2) ??? is this the work done ??

### Staff: Mentor

Exactly. Whatever is exerting that constant force is doing work on the system.

Edit: My mistake! Please use the displacement of the applied force--how much the string moves--not the displacement of the block.

Last edited: Sep 2, 2012
18. ### ehild

12,387
If the work is equal to the product of the force acting on the rope and the displacement of the body in the direction of that force, what is the work done on the block in the picture by the force F when it raises with height h? Is it zero because the force and displacement enclose 90°angle?

ehild

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19. ### Tanya Sharma

echild... sir... please help me with the problem...What you have asked ...according to Doc Al... that should be zero...But i feel positive work is done when the block is raised because force acting on block is tension not F.Yes F=T. But It is T which is acting on the block not F.... Please help with my problem...

20. ### ehild

12,387
The tension acts along a chord which makes angle β with the tangent of the circle. The work during displacement ds along the arc is Tds cos(β). β=(\pi/3-φ)/2. The total work of the rope is $$W=\int_0^{\pi/3}{TR\cos(\pi/6-0.5 \phi)d\phi}$$

There is an easier approach: The rope is pulled by the horizontal constant force F. The end of the rope moves horizontally along a distance L, the work done by the pulling force is FL. The rope is inextensible, so L is equal to the length of the chord between the initial and final position of the block.

ehild

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