Concept explainers
(a)
Whether the magnitude of the force is
(a)
Explanation of Solution
Given:
The force acting on 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 force.
Substitute
Take the dot product between the force and
Conclusion:
Thus, the magnitude of the force is
(b)
The work done by the force on the particle.
(b)
Explanation of Solution
Given:
The particle is moving around a circle of radius
Formula Used:
Write the expression for the work done by a force on a particle.
Here,
Calculation:
Write the expression for the instantaneous position of the particle on the circumference of the circle.
Here,
Rearrange the expression for force.
Substitute
Substitute
Conclusion:
Thus, the magnitude of the work done by the force on the particle is
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Chapter 6 Solutions
Physics for Scientists and Engineers, Vol. 3
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