Work done to bring the Earth to rest

In summary, the problem asks for the work needed to halt an object moving at a constant velocity, not to stop it from moving in a circular direction.
  • #1
walking
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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.
 
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  • #2
The word centripetal is not a force but a direction. The force in this case is gravity.
 
  • #3
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.
 
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  • #4
walking said:
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?
 
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  • #5
walking said:
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.
 
  • #6
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)!
 
  • #7
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.
 

1. What is "work done to bring the Earth to rest"?

Work done to bring the Earth to rest is a theoretical concept in physics that explores the amount of energy required to stop the Earth's rotation and bring it to a state of rest. It is often used as an example to illustrate the principles of work and energy.

2. How much work would it take to stop the Earth's rotation?

The exact amount of work needed to stop the Earth's rotation is difficult to calculate, as it would depend on various factors such as the Earth's mass, velocity, and the method used to stop it. However, it is estimated that it would require an immense amount of energy, likely beyond our current technological capabilities.

3. Is it possible to stop the Earth's rotation?

In theory, it is possible to stop the Earth's rotation by applying a strong enough force in the opposite direction of its rotation. However, this would have catastrophic consequences for our planet and is not a feasible or advisable course of action.

4. What would happen if the Earth suddenly stopped rotating?

If the Earth were to suddenly stop rotating, it would have disastrous effects on the planet and all life on it. The change in rotational speed would cause extreme weather patterns, changes in the length of day and night, and potentially even a shift in the Earth's axis. This would have devastating consequences for the environment and all living organisms.

5. Why is it important to understand the concept of "work done to bring the Earth to rest"?

Studying the concept of work done to bring the Earth to rest helps us better understand the principles of work and energy, and how they apply to large-scale systems like our planet. It also highlights the immense amount of energy and effort required to change the Earth's natural state, emphasizing the importance of preserving and protecting our planet's delicate balance.

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