A motorcycle has a constant speed of 24.3 m/s as it passes over the top of a hill whose radius of curvature is 182 m. The mass of the motorcycle and driver is 391 kg. Find the magnitude of (a) the centripetal force and (b) the normal force that acts on the cycle.

(a) F = 1268.6 N = 1.27 KN

(b) Fn = 5100.4 N = 5.1 KN

Explanation:

(a)

The centripetal force is given as:

F = mv²/r

where,

F = Centripetal Force = ?

m = mass of the bike and man = 391 kg

v = constant speed = 24.3 m/s

r = radius of curvature = 182 m

Therefore,

F = (391 kg) (24.3 m/s) ²/182 m

F = 1268.6 N = 1.27 KN

(b)

At the top, there are two forces acting on the body, which are centripetal force and the weight, both acting downwards. So, the normal reaction must be equal to the sum of these forces:

Fn = F + W

Fn = F + mg

Fn = 1268.6 N + (391 kg) (9.8 m/s²)

Fn = 1268.6 N + 3831.8 N

Fn = 5100.4 N = 5.1 KN