How Much Charge Is Needed to Levitate a Car Using Static Electricity?

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Homework Statement

Imagine that space invaders could deposit extra electrons in equal amounts on the Earth and on your car, which has a mass of 1200kg. Note that the rubber tires would provide some insulation. How much charge Q would need to be placed on your car (same amount on earth) in order to levitate it (overcome gravity)? (Hint: Assume the separation distance is the radius of the Earth- and that the Earth's charge is sprea uniformly so it acts as if it were located at the Earth's center.)

Homework Equations

Fg =Gm₁m₂/ d²

and possily: F= kq₁q₂/d²

The Attempt at a Solution

So i think you would first find the force of gravity between the Earth and the car, however from there I am not sure how you would determine the charge from that in order to lift the car. Could someone please help me with this part?

 

[Dick]

Equate G*m1*m2/d^2=k*q1*q2/d^2. m1 is mass of the earth, m2 is mass of the car and the problem told you q1=q2=Q.

 

[toasted]

Equate G*m1*m2/d^2=k*q1*q2/d^2. m1 is mass of the earth, m2 is mass of the car and the problem told you q1=q2=Q.

I tried the technique that you said and I got the charge to be 5.3x 10⁷C, but according to my teacher i was suppose to get 7.3 x 10³C. Could you try to clarify why i got this answer? When you try it what answer do you get?

 

[Dick]

I get the same thing your teacher got. Maybe you'd better show your work.

 

[Dick]

I tried the technique that you said and I got the charge to be 5.3x 10⁷C, but according to my teacher i was suppose to get 7.3 x 10³C. Could you try to clarify why i got this answer? When you try it what answer do you get?

I think your number is 5.3*10^7 coulombs^2=Q^2. You have to take a square root to get Q.

 

[toasted]

I think your number is 5.3*10^7 coulombs^2=Q^2. You have to take a square root to get Q.

O I forgot that I had q² on top! thank you so much for your help, and explaining it through!