Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 7.10, Problem 44SEP
To determine

The raising height of the pendulum for achieving the fracture of the specimen.

Expert Solution & Answer
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Answer to Problem 44SEP

The raising height of the pendulum for achieving the fracture of the specimen is 0.305m

Explanation of Solution

Write the expression of height of the hammer when it reached 120° from its initial position is,

    h1=l+lsin30°                                                                            (I).

Here, raised height is h1 and length of arm is l.

Write the expression for potential energy stored in the hammer is,

    P.E1=m×g×h1                                                                         (II).

Here, potential energy stored in the hammer is P.E1,the, mass of the hammer is m, acceleration due to gravity is g and the height of impact is h1.

Write the expression of remaining energy after fracture of the specimen is,

    E=P.E1E1                                                                        (III)

Here, remaining energy stored in the hammer is E, potential energy stored in the hammer is P.E1 is and energy required for fracture is E1.

Write the expression of energy used for lifting is,

    E=m×g×h2h2=Em×g                                                                               (IV)

Here, mass of hammer is m, remaining energy is E, acceleration due to gravity is g is and lifting height or impact height is h2.

Conclusion:

Below figure represent the new position of the hammer when hammer is raised to 120°,

Foundations of Materials Science and Engineering, Chapter 7.10, Problem 44SEP

Figure-(1)

From Figure-(1), when the hammer is rotated to an angle of 120°, then the arm will become horizontal. From this height in which hammer raised h1 height of length of the arm l is found.

Substitute, 120cm for l in Equation (I).

    h=(120cm)+(120cm)sin30°=180cm(1m100cm)=1.8m

Substitute, 15kg for m, 9.81m/s2 for g and height 1.8m for h1 in Equation (II).

    P.E1=15(kg)×9.81(m/s2)×1.8(m)=(246.87kgm2/s2)[1N1kgm/s2][1J1Nm]=246.87J

Substitute, 246.87J for P.E1 and 220J for E1 in Equation (III).

    E=264.87J220J=44.87J

This remaining energy is used for lifting of hammer.

Substitute, 44.87Joule for E, 15kg for m and 9.81m/s2 for g in Equation (IV).

    h2=44.87J15(kg)×9.81(m/s2)=(44.87J)[1Nm1J][1kgm/s21N](15kgm/s2)×9.81(m/s2)=0.305m

Thus, the raising height of the pendulum for achieving the fracture of the specimen is 0.305m

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