A level physics question on gravitational fields

Calculate the change in the kinetic energy of the satellite when it moves from its 850 km orbit to one at a height of 700 km above the Earth’s surface. Make it clear whether the change in kinetic energy is an increase or decrease. The mass of the satellite is 2100kg

I tried to calculate the velocities of at the two distances and then calculate change in KE and then I tried to calculate change in V and then use the formula W=m*change in V but it didn't work. The mark scheme says to equate the centripetal force equation and the force between 2 masses. They got Ek= GMm/2 *(1/r1 -1/r2). I have no idea how they got that.

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TypicalNerd

18

Original post by Willow96

Calculate the change in the kinetic energy of the satellite when it moves from its 850 km orbit to one at a height of 700 km above the Earth’s surface. Make it clear whether the change in kinetic energy is an increase or decrease. The mass of the satellite is 2100kg

I tried to calculate the velocities of at the two distances and then calculate change in KE and then I tried to calculate change in V and then use the formula W=m*change in V but it didn't work. The mark scheme says to equate the centripetal force equation and the force between 2 masses. They got Ek= GMm/2 *(1/r1 -1/r2). I have no idea how they got that.

After you equate F = GmM/r^2 and F = mv^2/r and simply the result, what is the result and what happens if you substitute it into the kinetic energy equation?

Original post by Willow96

Calculate the change in the kinetic energy of the satellite when it moves from its 850 km orbit to one at a height of 700 km above the Earth’s surface. Make it clear whether the change in kinetic energy is an increase or decrease. The mass of the satellite is 2100kg

I tried to calculate the velocities of at the two distances and then calculate change in KE and then I tried to calculate change in V and then use the formula W=m*change in V but it didn't work. The mark scheme says to equate the centripetal force equation and the force between 2 masses. They got Ek= GMm/2 *(1/r1 -1/r2). I have no idea how they got that.

First of all, I was puzzled by what you had done.

I tried to calculate the velocities of at the two distances and then calculate change in KE …

Isn’t this is what the question wants: calculate the change in the kinetic energy?

Why would you do the following?

…and then I tried to calculate change in V and then use the formula W=m*change in V ...

The mark scheme says to equate the centripetal force equation and the force between 2 masses. They got Ek= GMm/2*(1/r1 -1/r2). I have no idea how they got that.

The mark scheme is essentially doing what you have done for this: "I tried to calculate the velocities of at the two distances and then calculate the change in KE".
The first step of equating gravitational force with centripetal force is to find KE in terms of the G, r and the masses. Using the found KE, we can compute the change in KE in terms of G, r and the masses.

A level physics question on gravitational fields

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