# Deriving a formula for Kinetic Energy

• Vince716
In summary, the conversation is about a problem involving the conservation of mechanical energy and determining the horizontal range of a ball released from a certain height. There are some ambiguities in the problem statement, such as the definition of 'h' and the type of energy being referred to. The person asking the question is also asked if they have learned about moment of inertia and rotational kinetic energy.
Vince716
Homework Statement
A ball is rolled off the top of a ramp, onto the ground. Derive the following formula for kinetic energy by any means possible:
Relevant Equations
Ek=gmR^2/4h
I have no idea how to do this. I've tried conservation of mechanical energy and it didn't work.
Ek = Kinetic Energy
R = horizontal range of the ball
h = height from which the ball is released

Forum policy requires you to provide your own attempt. If you can’t solve it, what have you thought about? What concepts do you believe are relevant?

There are some ambiguities in the problem statement.
Is h the height of the ramp from bottom to top, the height of the bottom of the ramp from the ground, or the sum of the two?
Is the energy in question the KE as it leaves the ramp, the KE as it hits the ground, or the difference of the two?

In addition to what @Orodruin and @haruspex have said, may I ask: have you learned about moment of inertia and rotational kinetic energy yet?

If the answer is ‘no’ (which I suspect is the case), then I think you have stated the question (very) wrongly!

(Edit: If you have learned about rotational kinetic energy, is 'Ek' the translational or total kinetic enery?)

Check you have posted the original question, word-for-word, and include any diagram supplied.

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is a scalar quantity and is dependent on the mass and velocity of the object.

## What is the formula for kinetic energy?

The formula for kinetic energy is KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

## How is the formula for kinetic energy derived?

The formula for kinetic energy is derived from the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. By applying this theorem to an object with a constant velocity, the formula for kinetic energy can be derived.

## What is the relationship between kinetic energy and mass/velocity?

The kinetic energy of an object is directly proportional to its mass and the square of its velocity. This means that an object with a larger mass or a higher velocity will have a greater kinetic energy.

## What are the units of kinetic energy?

The SI unit for kinetic energy is joules (J). However, it can also be expressed in other units such as foot-pounds (ft-lb) or kilocalories (kcal).

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