Circular motion problem (A2 level)

AI Thread Summary
The discussion revolves around a circular motion problem involving a girl at the equator. The user successfully calculated the angular speed and resultant force but struggled with the reading on weighing scales. The key point clarified is that the centripetal force acts downward, meaning the scale reading should reflect the weight minus the centripetal force, not an addition. The final calculation showed the scale would read 586.57N, which is less than her weight due to the Earth's rotation. This understanding highlights the relationship between gravitational force and centripetal force in circular motion.
breen155
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Hey, I am having a problem understanding something to do with circular motion, its the last part of a question.

Homework Statement


part 1 - Calculate the angular speed of a girl standing at the equator, i used angular speed = 2pi/(60x60x24) = 7.3x10^-5 rad/s

part 2 - The radius of the Earth is 6400km and the girl has a mass of 60kg, calculate the resultant force on the girl necessary for this circular motion. I used
F=mass x radius x angular speed ^2 and got 2.03N

Part 3 - (The problem part) If the girl was standing on weighing scales calibrated in Newtons, what reading would she get?
I used reading = mg + resultant Force which got me an answer of 590.6N (taking g = 9.81) However the mark scheme stated that i had to take away the resultant force rather than add it, I was just wondering why this was the case? I thought that the force of the girl would be towards the centre of the Earth and therefore must be added rather than taken away :confused:

Thanks in advance
 
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breen155 said:
I thought that the force of the girl would be towards the centre of the Earth and therefore must be added rather than taken away :confused:
The net force on the girl is towards the center of the earth. What individual forces act on the girl?

Hint: If the Earth didn't rotate, the forces on the girl would add to zero: The upward normal force (which is what the scale reads) and the downward gravitational force (mg) would be equal. How does that change when you consider the Earth's rotation?
 
well the forces acting downwards are her weight and the centripetal force? and upwards is the contact force between her and the scales?
 
breen155 said:
well the forces acting downwards are her weight
Right.
and the centripetal force?
The "centripetal force" is just the name we give to the net force, not a separate force in itself. The net force is downward, though.
and upwards is the contact force between her and the scales?
Right.

So the two actual forces on her are her weight and the contact force. They must add up to equal the net centripetal force. (Set up that equation.)
 
so is it Force = weight (mg) - contact force?
 
breen155 said:
so is it Force = weight (mg) - contact force?
Right! (By "Force" I assume you mean "centripetal force".)

So solve for the contact force. Is it more or less than her weight?
 
so its (9.81 x 60)-2.03 = 586.57N
 
breen155 said:
so its (9.81 x 60)-2.03 = 586.57N
Good!
 
:) oh i get it now, thanks for all the help :)
 
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