A gear motor can develop 2 hp when it turns at 450rpm. If the motor turns a solid shaft with a diameter of 1 in., determine the maximum shear stress developed in the shaft. (30 pts)

Maximum shear stress is;

τ_max = 1427.12 psi

Explanation:

We are given;

Power = 2 HP = 2 * 746 Watts = 1492 W

Angular speed; ω = 450 rev/min = 450 * 2π/60 rad/s = 47.124 rad/s

Diameter; d = 1 in

We know that; power = shear stress * angular speed

So,

P = τω

τ = P/ω

τ = 1492/47.124

τ = 31.66 N. m

Converting this to lb. in, we have;

τ = 280.2146 lb. in

Maximum shear stress is given by the formula;

τ_max = (τ•d/2) / J

J is polar moment of inertia given by the formula; J = πd⁴/32

So,

τ_max = (τ•d/2) / (πd⁴/32)

This reduces to;

τ_max = (16τ) / (πd³)

Plugging in values;

τ_max = (16 * 280.2146) / ((π*1³)

τ_max = 1427.12 psi