If the radius of curvature of the bump is 52 m, find the apparent weight of a 62-kg person in your car as you pass over the top of the bump. Express your answer using two significant figures.

The answer is below

Explanation:

Driving in your car with a constant speed of 12m/s, you encounter a bump in the road that has a circular cross-section, as indicated in the figure . If the radius of curvature of the bump is 52 m, find the apparent weight of a 62-kg person in your car as you pass over the top of the bump.  

Solution:

Centripetal force is the net force acting on a body which makes it move along a curved path. This force is always towards the center of curvature.

As the car passes over the bump, the centripetal acceleration acts downward towards the circle center.

The sum of all vertical forces is equal to zero, hence:

F - mg + ma = 0

where F is the apparent weight of the person, m is the mass of the person, ma = centripetal force = mv²/r

Given that:

m = 62 kg, v = velocity = 12 m/s, r = radius of curvature of bump = 52 m, g = acceleration due to gravity = 10 m/s. Therefore:

F - mg + ma = 0

F - mg + mv²/r = 0

F = mg - mv²/r

F = m(g - v²/r)

Substituting:

F = 62(10 - 12²/54)

F = 456.67 N

The apparent weight of a 62-kg person as the top of the bump is passed = 456.67 N

But the weight of the person = mg = 62* 10 = 620 N

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