Work done to bring the Earth to rest

[walking]

I know how to solve this using work energy theorem but how can one solve it starting from the fact that net force is centripetal? My attempt was "this means we only need an "anticentripetal" force of same magnitude, but centripetal force does 0 work hence new force also 0 work to counter it". This is wrong but I don't see why.

 

[kuruman]

The word centripetal is not a force but a direction. The force in this case is gravity.

 

[Halc]

An anticentripetal force applied to Earth would indeed do no work (at first), but it would also merely cause Earth to cease its acceleration, so its path becomes straight instead of curved. It wouldn't in any way bring Earth to rest as the problem statement asks.

 

[haruspex]

starting from the fact that net force is centripetal

I don't understand. Who is saying you could start from that fact to answer the question?
A block sliding horizontally on a frictionless surface has no net force on it. How can you use that fact to find the work needed to halt it?

 

[Lnewqban]

View attachment 279537

I know how to solve this using work energy theorem but how can one solve it starting from the fact that net force is centripetal? My attempt was "this means we only need an "anticentripetal" force of same magnitude, but centripetal force does 0 work hence new force also 0 work to counter it". This is wrong but I don't see why.

As you have limited internet time, I would recommend to consider the trajectory of the planet like it was linear and its movement as of constant velocity.
That would not be different than a problem of calculating the work required to stop a car from certain speed.

 

[walking]

Thanks everyone, I understand where I went wrong now - I was trying to stop an object moving in circular motion by stopping its circular motion, but this doesn't stop the object (by NI)!

 

[PeroK]

It's all very well calculating a number like this, but how would it be possible to bring the Earth to rest? Unless we have some sort of mechanism in mind, it seems like a pointless calculation.