Answer:
a) F₁ = 483 N, b) F₂ = 176 N and c) F₁ / W = 2.2 , F₂ / W = 0.82
Explanation:
To find force we use Newton's second law, where acceleration is centripetal
F = m a
The centripetal acceleration is
a = v² / r
The relationship between linear and angular velocity is
v = w r
Substituting Newton's law
F = m (w r)² / r
F = m w² r
Let's calculate for each case
a) Let's reduce the units to the SI system
w = 40.0 rev / min (2pi rad / rev) (1min / 60s)
w = 4,189 rad/s
F₁ = 22.0 4.189² 1.25
F₁ = 482.6 N
F₁ = 483 N
b) w = 3.00 rev / min = 0.314 rad / s
F₂ = 22.0 0.314 2 8.00
F₂ = 176 N
c) the child's weight is
W = m g
W = 22.0 9.8
W = 215.6 N
To make this comparison we can divide the two quantities
F₁ / W = 483 / 215.6
F₁ / W = 2.2
F₂ / W = 176 / 215.6
F₂ / W = 0.82
