1. Ideal Mechanical Advantage (IMA): 9
Explanation:
For a wheel and axle system like the steering wheel, the IMA is given by:
where
is the radius of the wheel
is the radius of the axle
For the steering wheel of the problem, we see that and
, so the IMA is
2. Efficiency: 88.9%
Explanation:
The efficiency of a system is defined as the ratio between the AMA (actual mechanical advantage) and the IMA:
In this problem, AMA=8 and IMA=9, so the efficiency is
Answer:
K_{f} / K₀ =1.12
Explanation:
This problem must work using the conservation of angular momentum (L), so that the moment is conserved in the system all the forces must be internal and therefore the torque is internal and the moment is conserved.
Initial moment. With arms outstretched
L₀ = I₀ w₀
the wo value is 5.0 rad / s
final moment. After he shrugs his arms
= I_{f} w_{f}
indicate that the moment of inertia decreases by 11%
I_{f} = I₀ - 0.11 I₀ = 0.89 I₀
L_{f} = L₀
I_{f} w_{f} = I₀ w₀
w_{f} = I₀ /I_{f} w₀
let's calculate
w_{f} = I₀ / 0.89 I₀ 5.0
w_{f} = 5.62 rad / s
Having these values we can calculate the change in kinetic energy
/ K₀ = ½ I_{f} w_{f}² (½ I₀ w₀²)
K_{f} / K₀ = 0.89 I₀ / I₀ (5.62 / 5)²
K_{f} / K₀ =1.12