Answer :
Final answer:
The magnitudes of the centripetal and normal forces acting on the motorcycle and driver as they pass over the hill are 1695 N and 1656.6 N, respectively.
Explanation:
To solve the problem, we need to find two things: (a) the centripetal force and (b) the normal force acting on the motorcycle and driver as they pass over the hill. Given are the constant speed of the motorcycle (25.0 m/s), the radius of curvature of the hill (126 m), and the combined mass of the motorcycle and the driver (342 kg).
Centripetal Force (a)
The formula for calculating centripetal force (Fc) is:
Fc = m*v2/r, where
m = mass of the motorcycle and driver (342 kg),
v = speed of the motorcycle (25.0 m/s), and
r = radius of curvature of the hill (126 m).
Thus, Fc = 342 kg * (25.0 m/s)2 / 126 m = 1695 N (rounded to three significant figures).
Normal Force (b)
At the top of the hill, the normal force (FN) plus the centripetal force equals the gravitational force (Fg) exerted on the system. Therefore, FN = Fg - Fc, where Fg is calculated as the mass multiplied by the acceleration due to gravity (g = 9.8 m/s2).
Fg = 342 kg * 9.8 m/s2 = 3351.6 N.
Therefore, FN = 3351.6 N - 1695 N = 1656.6 N (rounded to three significant figures).
The centripetal force on the motorcycle at the top of the hill is 1696.42 N and the normal force is 1723.57 N.
The speed of the motorcycle is 25 m/s and the mass of the motorcycle is 342 kg and the radius of curvature of the hill is 126m.
(a) The centripetal force on any curvature is given by,
F =MV²/R
Where,
F is the centripetal force,
M is the mass of the motorcycle,
R is the radius of curvature of the hill,
V is the speed at which it is travelling.
Putting all the values,
F = 342 x 25 x 25/126
F = 1696.42 N.
The centripetal force is 1696.42 N.
(b) At the top of the hill, the centripetal force and the normal force will be away from the ground and in opposite direction of the weight of the motorcycle,
N = W- F
W is the weight,
F is centripetal force and N is the normal force.
Putting values,
N = 3420 - 1696.42
N = 1723.57N.
The normal force is 1723.57 N.
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