Concept explainers
As described in example box 6.2, a 120-kg crate is accelerated by a net force of 96 N applied for 4 s.
- a. What is the acceleration of the crate from Newton’s second law?
- b. If it starts from rest, how far does it travel in the time of 4 s? (See section 2.5 in chapter 2.)
- c. How much work is done by the 96-N net force?
- d. What is the velocity of the crate at the end of 4 s?
- e. What is the kinetic energy of the crate at this time? How does this value compare to the work computed in part c?
(a)
The acceleration of the crate from Newton’s second law.
Answer to Problem 2SP
The acceleration of the crate from Newton’s second law is
Explanation of Solution
Given info: The mass of the crate is
Write the expression for the force according to Newton’s second law.
Here,
Solve for
Substitute
Conclusion:
Therefore, the acceleration of the crate from Newton’s second law is
(b)
The distance travelled by the crate in
Answer to Problem 2SP
The distance travelled by the crate in
Explanation of Solution
Given info: The acceleration is
Write the expression for the displacement from the fundamental equations of motion.
Here,
Since the crate is accelerated from rest, the initial velocity is zero. Thus the expression for
Substitute
Conclusion:
Therefore, the distance travelled by the crate in
(c)
The work done by the
Answer to Problem 2SP
The work done by the
Explanation of Solution
Given info: The force is
Write the expression for the work done by a horizontally applied force.
Here,
Substitute
Conclusion:
Therefore, the work done by the
(d)
The velocity of the crate by the end of
Answer to Problem 2SP
The velocity of the crate by the end of
Explanation of Solution
Given info: The acceleration is
Write the expression for the final velocity from the fundamental equations of motion.
Since the initial velocity is zero, the equation for
Substitute
Conclusion:
Therefore, the velocity of the crate by the end of
(e)
The kinetic energy of the crate at the time
Answer to Problem 2SP
The kinetic energy of the crate at the time
Explanation of Solution
Given info: The mass of the crate is
Write the expression for the kinetic energy of an object.
Here,
Substitute
The kinetic energy of the crate by the end of the time
Conclusion:
Therefore, the kinetic energy of the crate at the time
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Chapter 6 Solutions
Physics of Everyday Phenomena
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