Help finding the change in potential energy in this problem

In summary, the task involves calculating the change in potential energy in a given scenario, which typically requires knowing the initial and final positions of an object and using the formula for gravitational potential energy. By determining the height difference and applying the appropriate mass and gravitational constant, one can find the change in potential energy.
  • #1
AJII
4
0
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!
 
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  • #2
AJII said:
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.
 
  • #3
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.
 
  • #4
AJII said:
Fnet = T - mg = 0
Right. And what is the relationship between T and the motion of the puck?
 
  • #5
Thank you for replying again, and I think that the Tension corresponds to the rotational speed of the puck
 
  • #6
AJII said:
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?
 
  • #7
sorry, i meant tension is the centripetal force of the puck so:
T = mac
 
  • #8
AJII said:
sorry, i meant tension is the centripetal force of the puck so:
T = mac
Right, but you know something about the centripetal acceleration.
 
  • #9
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?
 
  • #10
AJII said:
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.
 

FAQ: Help finding the change in potential energy in this problem

What is potential energy?

Potential energy is the energy stored in an object due to its position or configuration. In the context of gravitational potential energy, it is the energy an object possesses because of its height above the ground, which can be calculated using the formula PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the height above a reference point.

How do I calculate the change in potential energy?

The change in potential energy can be calculated by finding the difference between the final potential energy and the initial potential energy. This can be expressed mathematically as ΔPE = PE_final - PE_initial, where ΔPE is the change in potential energy.

What factors affect potential energy?

The primary factors that affect potential energy are the mass of the object, the height of the object above a reference point, and the acceleration due to gravity. Increasing the mass or the height of the object will increase its potential energy, while changes in gravity will affect the potential energy for a given height and mass.

Can potential energy be negative?

Yes, potential energy can be negative depending on the chosen reference point. For example, if the reference point is set at a certain height, any object below that height will have negative potential energy. However, it is often more useful to consider potential energy relative to a defined zero point.

What is the significance of potential energy in physics?

Potential energy is significant in physics because it helps to explain the conservation of energy in a system. It allows us to understand how energy is stored and transformed, particularly in mechanical systems where potential energy can be converted to kinetic energy and vice versa, illustrating the principle of energy conservation.

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