For three situations, the initial and final positions respectivel… - Vidyadip

Question

For three situations, the initial and final positions respectively, along x-axis for the block in Fig are (a) - 3cm, 2cm. (b) 2cm, 3 cm and (c) -2cm, 2cm. In each situation, is the work done by the spring force on the block positive, negative or zero?

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Answer

Since $\text{U}=\frac{1}{2}\text{k}\Big(\text{x}_2^2-\text{x}_2^1\Big),$ energy decreases, so work done by external force is negative. Therefore, work done by spring force is positive.
Since, $\text{U}=\frac{1}{2}\text{k}\Big(\text{x}_2^2-\text{x}_1^2\Big)$ energy increases, so work done by external force is positive. Therefore, work done by spring force is negative.
Since, $\text{U}=\frac{1}{2}\text{k}\Big(\text{x}_2^2-\text{x}_1^2\Big),$ there is no change in K.E., so work done is zero.

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