Step-by-step explanation:
a) Sum of the forces on the seat in the radial direction:
∑F = ma
F = m v² / r
We know the mass m and radius r. We need to find the velocity v. We know it takes 10 s to make one revolution, so:
v = 2πr / t
v = 2π(10 m) / (10 s)
v = 2π m/s
Finding the force:
F = (50 kg) (2π m/s)² / (10 m)
F = 200 N
b) If the beam breaks, the seat's inertia keeps it moving tangent to the circle.
c) The instant that the beam breaks, the seat's velocity is the same as its tangential velocity:
v = 2π m/s = 6.28 m/s
d) (i) The work done by friction equals the change in kinetic energy:
W = ΔKE
W = ½ mv² − ½ mv₀²
W = ½ m (v² − v₀²)
W = ½ (50 kg) ((0 m/s)² − (5 m/s)²)
W = -625 J
(ii) Power = work / time
P = W / t
P = -625 J / 5 s
P = -125 W