Work Done by Constant Force (Vector) – Rankers Physics

Work Done by Constant and Variable Forces: Practice Problem & Solution

A particle moves from a point \(P_1 = (-2\hat{i} + 5\hat{j})\) to \(P_2 = (4\hat{j} + 3\hat{k})\) when a force of \(F = (4\hat{i} + 3\hat{j})\text{ N})\) is applied. How much work has been done by the force? (2016 - II)
5 J
2 J
8 J
11 J

Short Solution (Best for NEET):

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:

Displacement \(dr = \vec{r_2} - \vec{r_1} = (2\hat{i} - \hat{j} + 3\hat{k})\). Force \(F = (4\hat{i} + 3\hat{j})\). Work \(W = F \cdot dr\). \(W = (4)(2) + (3)(-1) = 8 - 3 = 5\text{ J}\).

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