The heels on a pair of women’s shoes have radii of 0.46 cm at the bottom. If 30%

Question

The heels on a pair of women’s shoes have
radii of 0.46 cm at the bottom.
If 30% of the weight of a woman weighing
510 N is supported by each heel, find the stress
on each heel.

A tugboat tows a ship using a steel cable. The
maximal strain the cable may sustain without
breaking is 0.034 . Suppose the drag exerted
on the towed ship by the water is 2.8 × 106 N
and the tugboat is using the thinnest steel cable
that would do the job (no safety margin).
What is the diameter of this cable? The
Young’s modulus of steel is 2 × 1011 Pa.

Explanation / Answer

1) 0.3*510 = 153N

Stress = F/A = 153/(3.14*0.0046^2) = 2.303 MPa

2) Y = Stress/Strain
=> Stress = (2x10^11)*0.034 = 6.8x10^9
=> 6.8x10^9 = 2.8x10^6/(3.14*d^2/4) => d = 0.005725 m
Therefore, diameter = 0.5725 cm or 0.005725 m

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