Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Textbook Question
Chapter 63, Problem 1A

A rectangular strip of steel 2 ft 4 in. long, 1 ft 6 in. wide, and 5 8 in. thick has four holes drilled through the strip, each with a diameter of 1 1 2 in. If steel weighs 0.264 lb/cubic inch, what is the weight of this strip? Round the answer to the nearest pound.

Expert Solution & Answer
Check Mark
To determine

The weight of the rectangular strip of steel.

Answer to Problem 1A

Weight of the rectangular strip W = 82lb.

Explanation of Solution

Given:

Length l=2ft4in.

Breadth b=1ft6in.

Thickness t=58in.

Diameter of hole d=112in.

Specific volume of the steel strip ν=0.264lbin.3

Concept used:

The weight of the steel strip is

  W=νV

Here, W is the weight, v is the specific volume and V is the total volume.

Calculation:

The total volume of the steel strip is calculated by the formula

  V=Vr4Vc _______ (1)

Here, V is the total volume of the steel strip, Vr is the volume of rectangular strip and Vc is the volume of circular holes.

Now, the volume of the rectangular strip Vris calculated as

  Vr=lbt

Here, l is the length, b is the breadth and t is the thickness of rectangle.

By substituting the values we get

  Vr=(2ft4in.)(1ft6in.)(58in.)Vr=(2×12+4in.)(1×12+6in.)(58in.)Vr=28×18×58in.Vr=315in.3

Again, the volume of the circular holes Vc is calculated as

  Vc=πr2t

Here, r is the radius and t is the thickness of rectangle.

By substituting the values we get

  Vc=3.14( 1 1 2 2in.)2(58in.)Vc=3.14( 3 4in.)2(58in.)Vc=3.14×916×58in.Vc=1.104in.3

Now, substituting the value of volume of rectangular strip and volume of circular holes in equation (1) we get

  V=3154(1.104)V=3154.416V=310.584in.3

The weight of the steel strip is

  W=νV

Here, W is the weight, v is the specific volume and V is the total volume.

By substituting the values we get

  W=0.264×310.584W=81.99W=82lb

Conclusion:

The weight of the steel strip is W = 82lb.

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