# A prospector uses a hand-powered winch (see figure) to raise a bucket of ore in his mine shaft. The axle of the winch is a steel rod of diameter d = 0.625 in. Also, the distance from the center of the axle to the center of the lifting rope is b = 4.0 in, If the weight of the loaded bucket is W = 100 lb, what is the maximum shear stress in the axle due to torsion? If the maximum bucket load is 125 lb and the allowable shear stress in the axle is 9250 psi, what is the minimum permissible axle diameter?

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 3, Problem 3.3.5P
Textbook Problem
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## A prospector uses a hand-powered winch (see figure) to raise a bucket of ore in his mine shaft. The axle of the winch is a steel rod of diameter d = 0.625 in. Also, the distance from the center of the axle to the center of the lifting rope is b = 4.0 in, If the weight of the loaded bucket is W = 100 lb, what is the maximum shear stress in the axle due to torsion? If the maximum bucket load is 125 lb and the allowable shear stress in the axle is 9250 psi, what is the minimum permissible axle diameter?

(a)

To determine

The maximum shear stress in the axle.

### Explanation of Solution

Given information:

The diameter of steel rod is 0.625in , distance from the center of the lifting rope is 4in and the weight of the loaded bucket is 100lb .

Write the expression for torque.

T=Wb ....... (I)

Here, torque is T , weight is W and the distance from the center of lifting rope is b .

Write the expression for maximum shear stress.

τallow=16Tπd3....... (II)

Here, allowable shear stress is τallow and the diameter is d .

Calculation:

Substitute 100lb for W and 4in for b in Equation (I).

T=(100lb)×4in=400lbin

Substitute 400lbin for T and 0

(b)

To determine

The minimum permissible diameter.

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