Work Done by Constant and Variable Forces: Practice Problem & Solution
Assertion (A): The kinetic energy of a particle continuously increases with time if the resultant force on the particle must be at an angle less than \(90^{\circ}\) to the velocity at all instants. Reason (R): The work done by the external forces on a system equals to change in total energy.
Solution Explained:
To solve this problem, we apply the core principles of Work Done by Constant and Variable Forces. Understanding the underlying formula is key to arriving at the correct answer below:
Assertion (A) is true.
Kinetic energy \(K\) increases if the net work done \(W_{\text{net}}\) is positive. Since \(W_{\text{net}} = \int \vec{F} \cdot d\vec{s}\) and \(d\vec{s}\) is in the direction of \(vec{v}\) , \(W_{\text{net}} > 0\) implies \(vec{F} \cdot \vec{v} > 0\). This means the angle between \(vec{F}\) and \(vec{v}\) must be less than \(90^{circ}\).
Reason (R) is also true, interpreting "total energy" as kinetic energy in the context of \(W_{\text{net}} = \Delta K\) for a particle or total mechanical energy for a system with external work. Reason (R) provides the fundamental principle behind Assertion (A). Therefore, both are true and R explains A.
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