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A motorcycle has a constant speed of 23.7 m/s as it passes over the top of a hill with a radius of curvature of 139 m. The mass of the motorcycle and driver is 302 kg.

Find the magnitude of:

(a) the centripetal force

(b) the normal force that acts on the motorcycle.

Answer :

Final answer:

The magnitude of the centripetal force acting on the motorcycle is about 1229 N, directed towards the center of the hill's curvature. The normal force exerted by the surface on the motorcycle is also approximately 1229 N, but it is directed upwards from the contact point.

Explanation:

To solve this problem, we need to use the concepts of centripetal force and normal force. The centripetal force is the force that keeps an object moving along a circular path. It is calculated using the formula: Fc = mv²/r, where m is the mass, v is the speed, and r is the radius of the path.

a) Centripetal Force:
Using the provided values, we can substitute into the formula: Fc = 302 kg * (23.7 m/s)² / 139 m. Crunching the numbers, we find the centripetal force to be about 1229 N, directed towards the center of the hill's curvature.

b) Normal Force:
The normal force is the force exerted by a surface that supports the weight of an object resting on it. In this case, when the motorcycle is at the top of the hill, the normal force and weight must add up to supply the required centripetal force, so they are equal in magnitude but opposite in direction. Therefore, the normal force is equal to the centripetal force, which is approximately 1229 N, directed upwards from the contact point between the motorcycle and ground.

Learn more about Centripetal and Normal Forces here:

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