Order of Magnitude: Earth's Acceleration Towards You

  • Thread starter Thread starter dizco29
  • Start date Start date
  • Tags Tags
    Magnitude
AI Thread Summary
The discussion revolves around calculating the Earth's acceleration towards a person jumping off a chair and the distance it moves during that time. The participant is trying to apply Newton's second law (F=ma) to determine the Earth's acceleration, realizing that the forces exerted by both the person and the Earth are equal. They are encouraged to use the Earth's mass and the person's acceleration due to gravity (approximately 9.8 m/s²) to find the Earth's acceleration. The conversation emphasizes understanding the interaction between the two bodies and visualizing the scenario from an external inertial frame. Ultimately, the key point is that both the person and the Earth accelerate towards each other, albeit at different magnitudes.
dizco29
Messages
32
Reaction score
0
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!
 
Physics news on Phys.org
dizco29 said:
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.
 
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?
 
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.
 
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?
 
MechaMZ said:
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?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top