Work Done by Constant and Variable Forces: Practice Problem & Solution
A uniform force of \(F = (3\hat{i} + \hat{j})\text{ N})\) acts on a particle of mass \(2\text{ kg})\). Hence the particle is displaced from position \(\vec{r_1} = (2\hat{i} + \hat{k})\text{ m})\) to position \(\vec{r_2} = (4\hat{i} + 3\hat{j} - \hat{k})\text{ m})\). The work done by the force on the particle is: (2013)
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 \(dr = \vec{r_2} - \vec{r_1} = (2\hat{i} + 3\hat{j} - 2\hat{k})\). Force \(F = (3\hat{i} + \hat{j})\). Work \(W = F \cdot dr\). \(W = (3)(2) + (1)(3) = 6 + 3 = 9\text{ J}\).
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