Concept explainers
A Charpy V-notch specimen is tested by the impact-testing machine in Figure 7.9. In the test, the 10 kg hammer of arm-length 110 cm (measured from the fulcrum to the point of impact) is raised to 80° and then released. (a) What is the potential energy stored in the mass at this point? (b) After fracture of the specimen, the hammer swings to 45°. What is the potential energy at this point? (c) How much energy was expended in the fracture of the specimen? Hint: potential energy = mass × g × height.
Figure 7.9
Schematic drawing of a standard impact-testing apparatus.
(a)
The potential energy stored in the mass at the point of impact when the hammer raised to
Answer to Problem 43SEP
The potential energy stored in the mass at the point of impact is
Explanation of Solution
Write the expression for Potential energy stored in the hammer is,
Here, mass of hammer is
Conclusion:
Below figure represent the new position of the hammer when hammer is raised to
From Figure-1, when the hammer is rotated to an angle of
Substitute
Thus, the potential energy stored in the mass at the point of impact is
(b)
The potential energy at the point of impact when the hammer swing to
Answer to Problem 43SEP
The potential energy stored in the mass at the point of impact is
Explanation of Solution
Write the expression height of impact when hammer is raised
Here, height of impact is
Write the expression for Potential energy stored in the hammer is,
Here, mass of hammer is
Conclusion:
Below figure represent the new position of the hammer when hammer is swing to
From Figure-2, when the hammer is swing to an angle of
Substitute
Substitute
Thus, the potential energy stored in the mass at the point of impact is
(c)
The amount of energy expended in the fracture of the specimen.
Answer to Problem 43SEP
The amount of energy expended in the fracture of the specimen is
Explanation of Solution
Write the expression of energy expended in the fracture of the specimen is,
Conclusion:
Substitute
The amount of energy expended in the fracture of the specimen is
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