Final answer:
The question involves an engineering problem to design a solid steel shaft to transmit 16 hp at 1200 rpm with a limit on shearing stress. By using the power and speed given, the first step involves computing the torque. Then, using the formula for shear stress and the allowable shearing stress, we calculate the minimum shaft diameter.
Step-by-step explanation:
The student's question pertains to the design of a solid steel shaft that is intended to transmit a certain amount of power at a given speed. We are given the power (16 horsepower) and the rotational speed (1200 revolutions per minute) along with the material's allowable shearing stress (5.4 ksi). To design the shaft, we will need to use formulas that relate torque, power, and rotational speed, and then use the shear stress to calculate the required shaft diameter.
First, let's convert the power to watts and the torque to newton meters. The formula to find power in watts (P) when given horsepower (hp) is P = hp × 746. The formula to find torque (Τ) when power (P) and angular speed in radians per second (ω) is given is Τ = P / ω. We must convert rpm to rad/s using ω = rpm × (2π / 60).
After we have computed the torque, we can use it to determine the minimum shaft diameter using the allowable shearing stress and the formula for shear stress (τ), which is τ = T×c/J, where c is the outer radius of the shaft, and J is the polar moment of inertia.
By combining these steps, we can calculate the necessary dimensions of the steel shaft while considering the shaft's mechanical strength and ensuring that it doesn't exceed the allowed shearing stress.