1. Calculate the centripetal force exerted on a vehicle of mass m = 1450 kg that

Question

1. Calculate the centripetal force exerted on a vehicle of mass m = 1450 kg that is moving at a speed of 16 m/s around a curve of radius R = 430 m.

2.erhaps the biggest thrill to be had at an amusement park is on a roller coaster with a vertical loop in it , where passengers feel almost weightless at the top of the loop. Suppose the vertical loop has a radius of 4.78 m. What is the apparent weight (Wap) of a rider on the roller coaster at the bottom of the loop? (Assume that friction between roller coaster and rails can be neglected. Give your answer in terms of m and g.)

Explanation / Answer

1. Centripetal force = mv^2/R = (1450*16^2)/430 = 863.255

2. at top since the rider feels weightless

net fforce = 0

so mv^2/R = mg

Now at bottom both are in same direction

so Wap = 2mg= 2mv^2/R //Answer

3. Since the time period T is equal

So angular velocity w is also equal for both skaters. i.e. w1=w2

Now v= wr

So ratio v1/v2 = w1r1/w2r2 , where r1=r2/3

sp v1/v2= 1/3

Force = mw1^2r1/mvv2^2r2 = 1/3 //Answer

4. for no sliding to take place

mv^2/r = mu.m.g

so v= (mu.g.r)^1/2 = (0.9.9.8.40)^1/2 =18.78 m/s Answer

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