Final answer:
To solve for the shaft diameter, use the formulas for tension in the belt and power transmitted by the belt to calculate. Then use the formula for shaft diameter.
Step-by-step explanation:
To solve for the shaft diameter, we need to consider the relationship between the power transmitted by the belt and the tension in the belt. The power transmitted by the belt is given by P = (T₁ - T₂) * v, where T₁ and T₂ are the tensions in the belt and v is the velocity of the belt. The tension in the belt can be determined using the formula T = F * μ, where F is the force applied to the belt and μ is the coefficient of friction between the belt and the pulley. Once we have the tension in the belt, we can determine the shaft diameter using the formula D = (2P)/(πN), where D is the shaft diameter, P is the power transmitted by the belt, and N is the rotational speed of the pulley.
Let's go through the steps:
Calculate the tension in the belt using the formula T = F * μ.
Calculate the power transmitted by the belt using the formula P = (T₁ - T₂) * v.
Calculate the shaft diameter using the formula D = (2P)/(πN).