# Solve Energy Word Problem: Find Height Swinging Rope w/ 3.5 m/s Vel

• Thenewbie
In summary, the conversation discusses a student trying to find the maximum height they can swing by grabbing a hanging rope at an initial velocity of 3.5 m/s. They mention using the formula PEi + KEi = PEf + KEf and discuss the law of conservation of mechanical energy. The solution is found by considering the kinetic and potential energy at the point of grabbing the rope and at its maximum height. The student expresses gratitude for the guidance in understanding the material better.
Thenewbie

## Homework Statement

A student is running at a speed of 3.5 m/s and grabs a long rope that is hanging vertically from the ceiling. How high can the student swing?

## Homework Equations

For what we're learning right now, we should be using:
PEi + KEi = PEf + KEf

## The Attempt at a Solution

I don't even know where to start. What possible formula can help me find this answer with only the initial velocity?

PS. The answer is provided, but I am trying to figure out just HOW to do this. Thanks to somebody who can explain or guide in the right path...

hmm that's strange when we did the law of conservation of mechanical energy there was never a question with only one variable given. I am pretty sure that question is impossible unless they expect you somewhere to assume a variable. Check that its not apart of a bigger question or a series of questions that references the other variables that you require.

I'd consider using conservation of energy.

At the point he grabs the rope, he has all kinetic energy and no potential energy. By the time the rope reaches its maximum height, it has no kinetic energy and all potential energy.

It's at least a mental starting point for you to try, as long as you know the expressions for kinetic and potential energy.

whybother said:
I'd consider using conservation of energy.

At the point he grabs the rope, he has all kinetic energy and no potential energy. By the time the rope reaches its maximum height, it has no kinetic energy and all potential energy.

It's at least a mental starting point for you to try, as long as you know the expressions for kinetic and potential energy.

AHH! Thank you thank you! I just got the answer, wow, don't know why I didn't see it before. Our teacher went through this material really fast, so I'm still trying understand it all a little better.

Thanks for all your help!

## What is the formula for solving this energy word problem?

The formula for solving this energy word problem is: Height = (Velocity)^2 / (2 * Acceleration due to gravity).

## What is the unit of measurement for the velocity in this problem?

The unit of measurement for the velocity in this problem is meters per second (m/s).

## What is the value of acceleration due to gravity in this problem?

The value of acceleration due to gravity is 9.8 m/s^2.

## What is the height of the swinging rope if the velocity is 3.5 m/s?

If the velocity is 3.5 m/s, the height of the swinging rope can be calculated as: Height = (3.5)^2 / (2 * 9.8) = 0.632 meters.

## How does changing the velocity affect the height of the swinging rope?

Increasing the velocity will result in a higher height for the swinging rope, while decreasing the velocity will result in a lower height. This is because the height is directly proportional to the square of the velocity in this formula.

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