# Ball Up Incline: Total Energy & Height Q&A

• mikefitz
In summary, the total energy of the sphere is equal to the sum of its rotational and translational kinetic energy, and the height of the ball after it has traveled up the incline is determined using the equation mgh.
mikefitz
http://img207.imageshack.us/img207/5524/untitledll1.png

what I'm looking for is 1. the total energy of the sphere, and 2. the height of the ball after it has traveled up the incline.

i have some questions however. First, i understand that total energy = KE+PE. looking at the solution, KE=1/2mv^2. why does PE=1/1*Iw^2? this is the first time I've ever seen PE defined as such an equation.

in the second part of the solution, they use mgh - why isn't mgh used in the first solution? thanks

Last edited by a moderator:
mikefitz said:
i have some questions however. First, i understand that total energy = KE+PE. looking at the solution, KE=1/2mv^2. why does PE=1/1*Iw^2? this is the first time I've ever seen PE defined as such an equation.

The term 'PE=1/1*Iw^2' you were referring to was supposed to be the rotational kinetic energy of the sphere, which equals 1/2 I w^2, so I assume it was a mistype. You're right - total energy is defined as the sum of potential and kinetic energy - but, since you have a rolling sphere, the kinetic energy is the sum of rotational and translational kinetic energy.

The total energy of the sphere is the sum of its kinetic energy (KE) and potential energy (PE). In this case, the KE is given by 1/2mv^2, where m is the mass of the sphere and v is its velocity. The potential energy, on the other hand, is given by 1/2*I*w^2, where I is the moment of inertia and w is the angular velocity of the sphere. This equation is used because the sphere is rolling without slipping, so its energy is a combination of translational and rotational energy.

In the second part of the solution, the height (h) is used in the potential energy equation (mgh) because the sphere has reached a certain height after traveling up the incline. This height is used to calculate the change in potential energy, which is then equal to the change in kinetic energy (since KE+PE is constant). In the first part of the solution, the sphere is at the bottom of the incline and has not yet traveled up, so the height is not used in the potential energy equation.

## 1. What is the total energy of a ball rolling up an incline?

The total energy of a ball rolling up an incline is the sum of its kinetic energy and potential energy. Kinetic energy is the energy of motion, while potential energy is the energy that an object has due to its position or state.

## 2. How does the height of the incline affect the total energy of the ball?

The height of the incline affects the total energy of the ball by changing the potential energy component of the total energy. As the ball rolls up the incline, it gains potential energy due to its increased height, which adds to the total energy.

## 3. Is the total energy of the ball constant throughout its motion?

Yes, according to the law of conservation of energy, the total energy of a system remains constant. This means that the total energy of the ball rolling up an incline will remain constant, as long as no external forces act on it.

## 4. How does friction affect the total energy of the ball?

Friction can decrease the total energy of the ball by converting some of its kinetic energy into heat. This means that the ball will have less total energy as it rolls up the incline compared to a frictionless scenario.

## 5. Can the ball have more potential energy than kinetic energy while rolling up an incline?

Yes, it is possible for the ball to have more potential energy than kinetic energy while rolling up an incline. This can happen if the incline is steep enough that the ball slows down significantly due to gravity, increasing its potential energy.

• Introductory Physics Homework Help
Replies
10
Views
800
• Introductory Physics Homework Help
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
975
• Introductory Physics Homework Help
Replies
4
Views
405
• Introductory Physics Homework Help
Replies
13
Views
3K
• Introductory Physics Homework Help
Replies
44
Views
4K
• Introductory Physics Homework Help
Replies
13
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
584