Review. There are (one can say) three coequal theories of motion for a single particle: Newton’s second law, stating that the total force on the particle causes its acceleration; the work–kinetic energy theorem, stating that the total work on the particle causes its change in kinetic energy; and the impulse–momentum theorem, stating that the total impulse on the panicle causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A 3.00-kg object has velocity
(a)
The final velocity of the object.
Answer to Problem 51AP
The final velocity of the object is
Explanation of Solution
The mass of the object is
Write the expression of impulse momentum equation.
Here,
Conclusion:
Substitute
Thus, the final velocity of the object is
(b)
The acceleration of the object.
Answer to Problem 51AP
The acceleration of the object is
Explanation of Solution
Write the expression to calculate the acceleration of the object.
Here,
Substitute
Thus, the acceleration of the object is
Conclusion:
Therefore, the acceleration of the object is
(c)
The acceleration of the object.
Answer to Problem 51AP
The acceleration of the object is
Explanation of Solution
Write the expression to calculate the acceleration of the object.
Substitute
Thus, the acceleration of the object is
Conclusion:
Therefore, the acceleration of the object is
(d)
The vector displacement of the object.
Answer to Problem 51AP
The vector displacement of the object is
Explanation of Solution
Write the expression to calculate the vector displacement of the object.
Here,
Substitute
Thus, the vector displacement of the object is
Conclusion:
Therefore, the vector displacement of the object is
(e)
The work done on the object.
Answer to Problem 51AP
The work done on the object is
Explanation of Solution
Write the expression to calculate the work done on the object.
Here,
Substitute
Thus, the work done on the object is
Conclusion:
Therefore, the work done on the object is
(f)
The final kinetic energy of the object.
Answer to Problem 51AP
The final kinetic energy of the object is
Explanation of Solution
Write the expression to calculate the final kinetic energy of the object.
Substitute
Thus, the final kinetic energy of the object is
Conclusion:
Therefore, the final kinetic energy of the object is
(g)
The final kinetic energy of the object.
Answer to Problem 51AP
The final kinetic energy of the object is
Explanation of Solution
Write the expression to calculate the final kinetic energy of the object.
Substitute
Thus, the final kinetic energy of the object is
Conclusion:
Therefore, the final kinetic energy of the object is
(h)
The result of comparison of the answers in part (b), (c) and (f), (g).
Answer to Problem 51AP
The value of acceleration in part (b), (c) and kinetic energy in part (f), (g) are same.
Explanation of Solution
Write the expression to calculate the acceleration of the object.
Write the expression to calculate the acceleration of the object.
According to the second law of motion,
Substitute
The equation (2) and (8) are same therefore, the value of acceleration in part (b) and (c) are same.
Write the expression to calculate the work done on the object,
Substitute
The equation (10) and (6) are same.
Thus, the value of kinetic energy in part (f) and (g) are same.
Conclusion:
Therefore, the value of acceleration in part (b), (c) and kinetic energy in part (f), (g) are same.
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Chapter 9 Solutions
Physics for Scientists and Engineers
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