Concept explainers
(a)
To Show: The magnitude of the force is inversely proportional to
(a)
Explanation of Solution
Given:
The mass of the particle is
Formula used:
The vector notation of vector
Write the expression for magnitude of any vector.
Here,
Calculation:
Write the expression for the magnitude of the given force.
Substitute
From the above expression it can be concluded that force is inversely proportional to square of radius.
Take the dot product between the force and
Substitute
The direction is in the opposite to
Conclusion:
Thus, the magnitude of the force is inversely proportional to
(b)
The work done by the force.
(b)
Explanation of Solution
Given:
The value of
The particle moves in
Formula used:
Write the expression of work done by a particle.
Here,
Calculation:
The particle is moving along
Substitute
Substitute
Conclusion:
Thus, the work done by the force is
(c)
The work done by the force on the particle.
(c)
Explanation of Solution
Given:
The particle moving around a circle of radius
Calculation:
Write the expression for the instantaneous position of the particle on the circumference of the circle.
Write the expression for the work done by the force.
Substitute
Substitute
Conclusion:
Thus, the work done by the force on the particle moving around a circle is
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Chapter 6 Solutions
Physics For Scientists And Engineers
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