Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN: 9781305084766
Author: Saeed Moaveni
Publisher: Cengage Learning
Question
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Chapter 7, Problem 15P
To determine

Calculate the average pressure at the bottom of the women’s high-heeled dress shoe and a women’s athletic walking shoe.

Expert Solution & Answer
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Answer to Problem 15P

The average pressure at the bottom of the women’s high-heeled dress shoe is 2.17psi_.

The average pressure at the bottom of the women’s athletic walking shoe is 1.67psi_.

Explanation of Solution

Given information:

Weight of the women is W=120lb

Calculation:

The weight of the women is carried by both shoes. Hence, the weight (Force) acting on each shoe is as follows:

F=W2=1202=60lb

Sketch the profile of high-heeled dress shoe in inches as shown in Figure 1.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List), Chapter 7, Problem 15P , additional homework tip  1

Refer to Figure 1.

The profile of contact area is divided into two equal parts and each part is divided into 8 trapezoids of equal heights.

Consider the area of top portion as A1 and the bottom portion as A2.

Apply trapezoidal rule as shown below.

A=h[12y0+y1+y2++yn2+yn1+12yn] (1)

Calculate the area of top portion (A1) using Equation (1) as shown below.

A1=1×[12(0)+1.12+1.37+1.25+1.75+2.12+2.12+2+1.87+12(0)]=13.6in.2

Calculate the area of bottom portion (A2) using Equation (1) as shown below.

A2=1×[12(0)+1.5+1.62+1.75+2.12+2.12+2+1.62+1.25+12(0)]=13.9814in.2

Calculate the total area of high-heeled dress shoe as shown below.

A=A1+A2

Substitute 13.6in.2 for A1 and 14in.2 for A2.

A=13.6+14=27.6in.2

Calculate the average pressure at the bottom of high-heeled dress shoe as shown below.

Pressure=Force(F)Area(A) (2)

Substitute 60lb for F and 27.6in.2 for A in Equation (2).

Pressure=6027.6=2.17psi

Hence, the average pressure at the bottom of the women’s high-heeled dress shoe is 2.17psi_.

Sketch the profile of athletic walking shoe in inches as shown in Figure 2.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List), Chapter 7, Problem 15P , additional homework tip  2

Refer to Figure 2.

The profile of contact area is divided into two equal parts and each part is divided into 12 trapezoids of equal heights.

Consider the area of top portion as A1 and the bottom portion as A2.

Calculate the area of top portion (A1) using Equation (1) as shown below.

A1=1×[12(0)+1.12+1.37+1.25+1+0.87+1.12+1.75+2.12+2.12+2+1.87+12(0)]=16.5616.6in.2

Calculate the area of bottom portion (A2) using Equation (1) as shown below.

A2=1×[12(0)+1.5+1.62+1.75+1.62+1.75+2+2.12+2.12+2+1.62+1.25+12(0)]=19.3519.4in.2

Calculate the total area of athletic walking shoe as shown below.

A=A1+A2

Substitute 16.6in.2 for A1 and 19.4in.2 for A2.

A=16.6+19.4=36in.2

Calculate the average pressure at the bottom of athletic walking shoe as shown below.

Substitute 60lb for F and 36in.2 for A in Equation (2).

Pressure=6036=1.67psi

Therefore, the average pressure at the bottom of the women’s athletic walking shoe is 1.67psi_.

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