# Calculating Kinetic & Potential Energy of Rama's Impact

• Mecia22
In summary, the equation for calculating the energy of an object before it hits the earth, using its mass and velocity, is E= EK + ΔEP, where EK is the kinetic energy and ΔEP is the change in potential energy. It is important to determine the altitude at the point where the velocity is known in order to accurately calculate the energy on impact.
Mecia22

## Homework Statement

-- This is out of Rendezvous With Rama by Arthur C. Clarke
You know it is 907184 kg and is going 50,000 m/s
So how much energy does it have right before it hits the earth?

## Homework Equations

Do I use Fg= Gm1m2/r^2 ?
Ek=1/2mv^2?
I have ΔE=1/2mv^2 written down as an equation to use as well.

## The Attempt at a Solution

I think I'm supposed to calculate the potential energy at 2 different spots and find the ΔE, but I'm not sure.

E=Gm1m2/r+1/2mv^2 would that work?

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At any particular point it has both KE and PE. As it descends, PE decreases and KE increases by the same amount. At the point you describe the KE is given by Ek=1/2mv^2, but to know what the energy will be when it strikes Earth you also need to know how much PE it will lose in the remaining descent. So you need the altitude at the point where the speed is known.

haruspex said:
At any particular point it has both KE and PE. As it descends, PE decreases and KE increases by the same amount. At the point you describe the KE is given by Ek=1/2mv^2, but to know what the energy will be when it strikes Earth you also need to know how much PE it will lose in the remaining descent. So you need the altitude at the point where the speed is known.

Okay, so then the equation would be E=EK+EP?

Depends what you mean by EP there. Write the equation in terms of four entities: Eki = KE at known initial point, Epi = PE at known initial point, Ekf = KE on collision, Epf = PE on collision.

Yikes... you're confusing me.
I guess what I'm asking is what steps would I do to get to my final equation?Would it be Efinal=Ekinetic+change of Epotential ?

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Mecia22 said:
Yikes... you're confusing me.
I guess what I'm asking is what steps would I do to get to my final equation?

Would it be Efinal=Ekinetic+change of Epotential ?

Yes, provided (i) Efinal means the KE on impact, and (ii) you get the sign right on the change in potential.

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is calculated as one-half of the object's mass multiplied by the square of its velocity.

## What is potential energy?

Potential energy is the energy an object possesses due to its position or state. It is calculated based on the object's mass, height, and the force acting on it.

## How do I calculate the kinetic energy of Rama's impact?

To calculate the kinetic energy of Rama's impact, you will need to know the mass of Rama and the speed at which he is moving. Then, use the formula KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity.

## How do I calculate the potential energy of Rama's impact?

To calculate the potential energy of Rama's impact, you will need to know the mass of Rama, the height at which he is positioned, and the force acting on him. Then, use the formula PE = m * g * h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.

## Can the kinetic and potential energy of Rama's impact be equal?

Yes, it is possible for the kinetic and potential energy of Rama's impact to be equal. This can happen if Rama has reached his maximum potential energy and is moving at a constant velocity, resulting in equal amounts of kinetic and potential energy.

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