Work on an object moving in a circle.

In summary, the problem involves two people, A and B, riding on a spinning ferris wheel with mass m_A and m_B respectively. The total work done on A and B as they move from the bottom to the top and vice versa is equal to the sum of the work done by all the forces on the bodies. This can be calculated using the Work-Energy Theorem, W=\Delta K, or by conservation of mechanical energy, \Delta U + \Delta K = 0. The work done on B by the ferris wheel is equal to 2m_B*g*R, where R is the radius of the ferris wheel. The work done on A is equal to zero due to the constant velocity
  • #1
jj8890
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[SOLVED] Work on an object moving in a circle.

Homework Statement


I have a question for a test review that has two people, a with a certain mass, let's say m_A and m_B riding on a spinning ferris wheel with a certain radius, let's say R, in carts opposite to one another. One (A) is originally at the bottom of the ferris wheel while the other (B) is at the top of the ferris wheel. As the wheel turns, B comes to the bottom while A arrives at the top. Neglect air resistance. I need to find the magnitude of the total work done on A and B moving from the bottom to top and top to bottom respectively.
I don't want to give the numbers because I want to work it out myself. I just need help figuring out how to set up the problem. I would appreciate any help.


Homework Equations


The total work is the sum of the work done by all of the forces on the body, W total = F_net · ds.

The Attempt at a Solution


I was thinking that the W_total on student A from bottom to top would be found by 2(Ma-Mb)gR but I am not sure that this looks right.

Wouldn't the Work done on student B by Ferris wheel is be 0 because the direction of motion is always perpendicular to force?
 
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  • #2
I have been trying to work it out and now I think that it is switched, the total work done on student A=0 because it says that the velocity is constant, and the masses certainly aren't changing and the change in kinetic energy equals change in total work so since there is not change in mass or velocity W_total must be zero. In order to clarify, it asks for the total work done on A (which would be zero) but only the work done on B, is there a difference? Would the work done on B also be 0, how would I go about this?
 
  • #3
Have you by chance studied the Work-Energy Theorem yet? [tex]W=\Delta K[/tex] or Conservation of Mechanical Energy? Or have you only learned that W= F*displacement ?
 
  • #4
yes we have used W=deltaK... W=K_2-K_1 but how would I use this to find the work done on B? I know that K=1/2mv^2 but since the speed is not changing how would I work this out? That is why I was wondering if it would be the same...zero
 
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  • #5
I wish I was not so tired right now, else I could think this through. Regardless of constant velocity, if an object moves through a vertical displacement, there is work done by gravity (I'm fairly confident that is a true statement).

Now. If you know that by W-E theorem [itex]W=\Delta K[/itex] and by conservation of mechanical energy [itex]\Delta U+\Delta K=0[/tex] What does that say about W?
 
  • #6
Well, obviously deltaK=-deltaU so W=-DeltaU or -U_2 +U_1 but where would i go from there? Or am I totally on the wrong path?
 
  • #7
Well, if the radius was R and the mass of the person was m_B, would the work done on B by the ferris wheel be 2m_B*g*R because person B moves 2 times the radius...or would I have to include the mass of person A in there somewhere?
 
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  • #8
The above was right..thanks
 

Related to Work on an object moving in a circle.

1. What is the centripetal force in circular motion?

The centripetal force in circular motion is the force that acts towards the center of the circle, keeping an object moving in a circular path.

2. How does the speed of an object affect its motion in a circle?

The speed of an object affects its motion in a circle by determining the magnitude of the centripetal force required to keep it moving in a circular path. Higher speeds require a greater centripetal force.

3. What is the relationship between the radius of a circle and the centripetal force?

The relationship between the radius of a circle and the centripetal force is inverse. As the radius increases, the centripetal force required to maintain the circular motion decreases.

4. How is the direction of the centripetal force related to the motion in a circle?

The direction of the centripetal force is always perpendicular to the velocity of the object, pointing towards the center of the circle. This ensures that the object stays on its circular path.

5. What is the difference between centripetal force and centrifugal force?

Centripetal force is the inward force that keeps an object moving in a circle, while centrifugal force is the outward force that appears to act on an object moving in a circle due to its inertia. Centrifugal force is not a true force, but rather a perceived force.

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