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Answer :
Motorcycle has a constant speed of 25.0 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of the motorcycle and driver is 342 kg. The normal force acting on the motorcycle at the top of the hill is approximately 11,370 N.
The centripetal force and the normal force acting on the motorcycle as it passes over the top of the hill, we need to consider the forces acting on the motorcycle at that point.
1. Centripetal Force:
The centripetal force (Fc) is the force directed towards the center of the circular path and keeps the motorcycle moving in a curved trajectory. It can be calculated using the following formula:
Fc = (m * v^2) / r
Where:
m is the mass of the motorcycle and driver (342 kg),
v is the constant speed of the motorcycle (25.0 m/s),
r is the radius of curvature of the hill (126 m).
Substituting the given values into the formula:
Fc = (342 kg * (25.0 m/s)^2) / 126 m
Calculating the value:
Fc ≈ 17,180 N
Therefore, the centripetal force acting on the motorcycle is approximately 17,180 N.
2. Normal Force:
The normal force (N) is the force exerted by the surface of the hill perpendicular to the surface. At the top of the hill, the normal force will be different from the weight of the motorcycle and driver due to the centripetal force.
To calculate the normal force, we can use the following equation:
N = mg + Fc
Where:
m is the mass of the motorcycle and driver (342 kg),
g is the acceleration due to gravity (9.8 m/s^2),
Fc is the centripetal force (17,180 N).
Substituting the given values into the equation:
N = (342 kg * 9.8 m/s^2) + 17,180 N
Calculating the value:
N ≈ 11,370 N
To learn more about normal force refer here:
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