Gravitational Potential Energy of a rope

In summary, the problem involves Bruce standing on a bank beside a pond and swinging out into the water using a 10m long rope attached to a nearby tree at an angle of 35 degrees with the vertical. The solution involves using the equation for change in gravitational potential energy and setting the initial velocity as 0. The website used to submit the homework was not accepting the answer, but the mistake was most likely a computational error.
  • #1
FailingPHYS
3
0
The problem states that: "Bruce stands on a bank beside a pond, grasps the end of a 10.0m long rope attached to a nearby tree and swings out to drop into the water. If the rope starts at an angle of 35 degrees with the vertical, what is Bruce's speed at the bottom of the swing?
Variables:
angle of the rope with the vertical: 35 degrees
Length of rope: 10m


I'm trying to use the equation for the change in gravitational potential energy, where the Work due to gravity = -mg(yf-yi) which is equal to Kf-Ki, and therefore -mg(yf-yi)= -1/2mvi^2+-1/2mvf^2. With the initial velocity as 0 and the masses canceling out the solution should be Vf=[tex]\sqrt{}[/tex]2g(yf-yi).



I am apparently either setting up the question wrong, or going about it wrong all together. I'm pretty much stumped as to what I'm doing wrong and how to fix it. If someone could point me in the right direction I'd be ecstatic...
 
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  • #2
There is nothing wrong with your setup. Why do you think that there is?
 
  • #3
I thought I was doing it right, but the website we use to submit our homework wasn't accepting the answer I got from the formula. Thanks.
 
  • #4
FailingPHYS said:
I thought I was doing it right, but the website we use to submit our homework wasn't accepting the answer I got from the formula. Thanks.

You must be making a computational error. If you post your calculations, we can find your mistake.
 
  • #5
That's okay. I think I know what happened. I probably rounded off to the wrong number is all. A similar thing happened in another homework assignment after I posted the question. Thankfully I caught that one before I ran out of chances to answer the question.
 

1. What is gravitational potential energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is the energy that is stored in an object as a result of its vertical position or height.

2. How is gravitational potential energy calculated?

The equation for gravitational potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground.

3. How is gravitational potential energy related to a rope?

A rope can have gravitational potential energy if it is hanging or suspended above the ground. The amount of potential energy it has will depend on its height above the ground and the mass of the rope.

4. Can gravitational potential energy be converted into other forms of energy?

Yes, gravitational potential energy can be converted into other forms of energy, such as kinetic energy, when an object falls due to gravity. This conversion of energy is known as potential energy to kinetic energy conversion.

5. How does the length of a rope affect its gravitational potential energy?

The length of a rope does not affect its gravitational potential energy. The height above the ground is the determining factor for gravitational potential energy, not the length of the rope itself.

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