Order of Magnitude: Earth's Acceleration Towards You

[dizco29]

Hello all,

Need some help with this question:

You stand on the seat of a chair and hop off.

a) During the time you are in flight down the floor, the Earth is lurching up toward you with an acceleration of what order of magnitude? In your solution explain your logic. Model the Earth as a perfectly solid object.

b) The eath moves up through a distance of what order of magnitude?



what I did for part (a):

I figured that the order of magnitude would be in the opposite direction when the falling mass hits the earth. I also figured I could use this equation:

F=ma

SO I think I have to solve for acceleration. I know the mass of the sun (5.98 x 10^24). But I'm missing force and acceleration (is acceleration the gravity in this case?)

a little stuck at this point.



what I did for part (b):

I used the same equation but to no avail. Can anyone help explain this to me? thanks!

 

[Doc Al]

what I did for part (a):

I figured that the order of magnitude would be in the opposite direction when the falling mass hits the earth. I also figured I could use this equation:

F=ma

SO I think I have to solve for acceleration. I know the mass of the sun (5.98 x 10^24). But I'm missing force and acceleration (is acceleration the gravity in this case?)

You have the right idea to use F = ma to find the Earth's acceleration. Since you're finding the earth's acceleration, use the earth's mass. Hint: The force that the Earth pulls on you must equal the force that you pull on the earth. What's that force equal?

what I did for part (b):

I used the same equation but to no avail. Can anyone help explain this to me?

First figure out part (a) so you can compare the acceleration of you (what is your acceleration, by the way?) with the acceleration of the earth. Then you can figure out--roughly, to an order of magnitude--how far the Earth moves during the time it takes you to hit the ground.

 

[dizco29]

hey Doc, thanks for the hint.

If I understand, can I use the mass of the Earth and multiply it with acceleration to five me force? so if I take 5.98x10^24 and multiply it with 9.8, it'll give me 5.86 x 10^25. Is this the appraoch I should be taking?

 

[Doc Al]

The force that you and the Earth exert on each other is the same, so:
$$m_{you}a_{you} = m_{earth}a_{earth}$$

Of course, $$a_{you} = g$$.

 

[MechaMZ]

I can't visualize the scenario for part b. why my moving distance is the height of chair yet there will be a movement for Earth towards me?

 

[Doc Al]

I can't visualize the scenario for part b. why my moving distance is the height of chair yet there will be a movement for Earth towards me?

View things from an inertial frame outside of earth. You and the Earth exert a force on each other, so both of you accelerate: You down towards earth, the Earth up towards you. Your acceleration is about 9.8 m/s^2. What's the Earth's acceleration?