Mathematics for Machine Technology
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 62, Problem 27A
To determine

The weight of the steel bearing washer.

Expert Solution & Answer
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Answer to Problem 27A

The weight of the steel bearing washer is 4.62lb.

Explanation of Solution

Given information:

The number of rib is 4 and the weighs of steel is 0.283

poundpercubicinch.

Write the expression of volume of the rib.

VR=12lbh ......... (I)

Here, the length of the rib is l, the width of the rib is b and the height of the rib is h.

Write the expression of the total volume of rib.

VTR=nVR ......... (II)

Here, the number of rib is n.

Write the expression of volume of the larger cylinder.

VLC=π4(D12d12)t1 ......... (III)

Here, the thickness of the large cylinder is t1, the internal diameter of the large cylinder is d1 and the external diameter of the large cylinder is D1.

Write the expression of volume of the smaller cylinder.

VSC=π4(D22d22)t2 ......... (IV)

Here, the thickness of the small cylinder is t2, the internal diameter of the small cylinder is d2 and the external diameter of the small cylinder is D2.

Write the expression of the steel bearing washer.

W=Vw .......... (V)

Here, the weighs is w.

Write the expression of the total volume.

V=VTR+VLC+VSC

Substitute VTR+VLC+VSC for V in Equation (V).

W=(VTR+VLC+VSC)w ......... (VI)

Calculation:

Substitute 1.625in for l, 0.75in for b and 0.375in for h in Equation (I).

VR=12(1.625in)(0.75in)(0.375in)=12(1.625in)(0.28 in2)=0.23in3

Substitute 4 for n and 0.23in3 for VR in Equation (II).

VTR=(4)(0.23 in3)=0.92in3

Substitute 6.375in for D1, 1.625in for d1 and 0.375in for t1 in Equation (III).

VLC=π4{( 6.375in)2( 1.625in)2}(0.375in)=π4(0.375in){(40.64 in 2)(2.64 in 2)}=π4(0.375in)(38 in2)=11.19in3

Substitute 3.125in for D2, 1.625in for d2 and 0.75in for t2 in Equation (IV).

VSC=π4{( 3.125in)2( 1.625in)2}(0.75in)=π4(0.75in){(9.77 in 2)(2.64 in 2)}=π4(0.75in)(7.13 in2)=4.2in2

Substitute 0.92in3 for VTR, 4.2in2 for VSC, 11.19in3 for VLC and 0.283

poundpercubicinch for w in Equation (VI).

W={(0.92 in 3)+(11.19 in 3)+(4.2 in 2)}(0.283poundpercubicinch)={(0.92 in 3)+(11.19 in 3)+(4.2 in 2)}(0.283lb/ in 3)=(0.283lb/ in 3)(16.31 in3)=4.62lb

Conclusion:

The weight of the steel bearing washer is 4.62lb.

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