Answer:
48 rev
Explanation:
a) we can calculate the distance covered by the tube using the formula:
θ = (ω + ωo)t/2
where ω is the final angular speed, θ is the distance covered, t is the time taken, ωo is the initial angular speed.
Firstly, we calculate the distance covered from 0 to 9 s then from 9s to 24 s.
within 9s, the tub runs from rest (0) to 4 rev/s, hence:
t = 9s, wo = 0, w = 4 rev/s = (4 * 2π) rad/s = 8π rad/s. Hence:
θ = (ω + ωo)t/2 = (0 + 8π)9 / 2 = 36π rad
θ = 36π rad = (36π)/2π rev = 18 rev
Also, within 15 s, the tub runs from 4 rev/s to rest, hence:
t = 15 s, wo = 4 rev/s = 8π rad/s, w = 0 rad/s. Hence:
θ = (ω + ωo)t/2 = (8π + 0)15 / 2 = 60π rad
θ = 60π rad = (60π)/2π rev = 30 rev
Therefore the total revolutions by the tube during 24 s interval = 30 rev + 18 rev = 48 rev
