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(a)
Whether the statement is true or false.
(a)
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Explanation of Solution
Introduction:
The work energy theorem states that the net or total work done on a particle is equal to the change in its kinetic energy.
According to the work energy theorem, the net or total work done on a particle is equal to the change in its kinetic energy.
Write the expression for the work-energy theorem.
Here,
Conclusion:
Thus, for non-zero work done, the initial and final speeds mustdiffer i.e. there must be a change in speed of the particle. Hence, the given statement is true.
(b)
Whether the statement is true or false.
(b)
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Explanation of Solution
According to the work energy theorem, the net or total work done on a particle is equal to the change in its kinetic energy.
Write the expression for the work-energy theorem.
Here,
Introduction:The work energy theorem states that the net or total work done on a particle is equal to the change in its kinetic energy.
Conclusion:Thus, for non-zero work done, the initial and final velocities must differ i.e. there must be a change in velocity of the particle. Hence, the given statement is true.
(c)
Whether the statement is true or false.
(c)
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Explanation of Solution
Introduction:
The work energy theorem states that the net or total work done on a particle is equal to the change in its kinetic energy.
According to the work energy theorem, the net or total work done on a particle is equal to the change in its kinetic energy.
Write the expression for the work-energy theorem.
Here,
For a particle moving in straight line, i.e. its direction of motion is not changing, if its speed changes with time then, the net work done on it will be non-zero while if its speed is constant then, the net work done on it will be zero.
Conclusion:
Thus, for a particle moving in straight line, i.e. its direction of motion is not changing, and its speed changing with time then, the net work done on it will be non-zero. Hence, the given statement is true.
(d)
Whether the statement is true or false.
(d)
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Explanation of Solution
Introduction:
The work energy theorem states that the net or total work done on a particle is equal to the change in its kinetic energy.
According to the work energy theorem, the net or total work done on a particle is equal to the change in its kinetic energy.
Write the expression for the work-energy theorem.
Here,
For a particle at rest, the speed is zero throughout and thus, work done on it will be zero.
Conclusion:
Thus, for a particle at constant rest, the initial and final velocities of the particle are same and thus work done is zero.
(e)
Whether the statement is true or false.
(e)
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Explanation of Solution
Introduction:
The work done on a particle is given by the dot product of force acting on it and its displacement.
For a particle experiencing a force in a particular direction and having a displacement, the work done on it is given by the dot product of force acting on it and its displacement.
If the angle between force and displacement is
Conclusion:
Thus, if a force is always perpendicular to the velocity of particle, the angle betweenforce and displacement is
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Chapter 6 Solutions
Physics for Scientists and Engineers
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