This is a picture of a little hill along a road, just a little rise in the pavem

Question

This is a picture of a little hill along a road, just a little rise in the pavement. If you don't drive so very slowly, you feel a little lighter, a little "lifted" in your seat as you go over the top of it. (If you drive too fast, you spend a moment in the air!) First, without doing any calculations, explain why you feel lifted in your seat. Now we're going to come up with an estimate of how much lighter you feel. Suppose the hill is approximately shaped like an arc of a circle that has a radius of 20m. Find the magnitude of the force the seat exerts upward on you, as the moment you're at the top of the bump, expressed as a percentage of your weight. (You're driving about 20mph.)

Explanation / Answer

a)

This happens beacuse of centrifugal force, which appears to act on a body moving in a circular path and is directed away from the centre around which the body is moving, the center being the centre of the bump/hill modeled as an arc.

The magnitude of this force is m*v2 / r , where m = mass of object (traveller, vehicle etc.), v is speed, and r is the radius of arc. Since, this is directed away from the centre, it's vrtical component acts against gravity and makes you feel 'light' or and if speed be large enough even may lift you from your seat.

b)

v= 20 m/h = 8.94 m/s, r = 20 m

at the top, the centrifugal force is directed upwards while gravity acts vertically downwards,

so magnitude of net force experienced as a percentage of weight= normal applied by seat to you = m*g-m*v2 / r

Expressed as percentage of weight:

[(m*g-m*v2 / r )/(m*g)] * 100%

= [(g-(v2 / r ))/(g)] * 100% = 59.2 %

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