Help finding the change in potential energy in this problem

[AJII]

Homework Statement

A 0.200-kg puck on a frictionless, horizontal table is connected by a string through a hole in the table to a hanging 1.20-kg block.
(a) With what speed must the puck rotate in a circle of radius 0.500 m if the block is to remain hanging at rest?
Answer: 5.42 m/s
(b) Someone pulls the block down by a certain amount so that, at the end of the pull (at which point the block again hangs at rest), the puck is rotating at one fourth of the speed found in (a). By how much has the potential energy of the block changed?

Relevant Equations

Net force equation and potential energy due to gravity equation.

Hi guys, I was able to get the answer for part A. but I am having trouble finding the answer for part B.

From my understanding, in order to get the answer for part B:
first, we need to determine the force that the puck exerts with its new speed which is 1/4 of the original speed obtained from part A.
Then we use this force to find out the values of the forces on the hanging block with the pulling force. I think that we have to use the change in the tension forces somehow but I am not sure how to use it to find the change in potential energy for the problem.

Would really appreciate your help!

 

[haruspex]

find out the values of the forces on the hanging block

What are those forces? What equation can you write? Remember "at which point the block again hangs at rest". Assume the person is no longer pulling on it.

 

[AJII]

Hi, thank you for replying.

I believe the forces on the block are the tension force from the string and gravitational force; hence, these two forces would be opposing each other as the block hangs at rest. Since it hangs at rest the net force would be equal to zero.

Equation i would write for the block as the system would be:
Fnet = T - mg = 0

I know that the change of Potential energy for the block is equal to mg(delta)h, where (delta)h is the change in height of the block, but I am not sure how to obtain the change in height.

 

[haruspex]

Fnet = T - mg = 0

Right. And what is the relationship between T and the motion of the puck?

 

[AJII]

Thank you for replying again, and I think that the Tension corresponds to the rotational speed of the puck

 

[haruspex]

Thank you for replying again, and I think that the Tension corresponds to the rotational speed of the puck

ok, but what is the equation?

 

[AJII]

sorry, i meant tension is the centripetal force of the puck so:
T = ma_c

 

[haruspex]

sorry, i meant tension is the centripetal force of the puck so:
T = ma_c

Right, but you know something about the centripetal acceleration.

 

[kuruman]

If the end of the string were attached to a fixed post instead of going through a hole, what equation would you write down relating the tension and the acceleration?

 

[jbriggs444]

Homework Statement: A 0.200-kg puck on a frictionless, horizontal table is connected by a string through a hole in the table to a hanging 1.20-kg block.
[...]
(b) Someone pulls the block down by a certain amount so that, at the end of the pull (at which point the block again hangs at rest), the puck is rotating at one fourth of the speed found in (a). By how much has the potential energy of the block changed?

It is perhaps worth noting that someone must also have reached in and slowed the puck down.