First slide

Work done by Diff type of forces

Question

A block of mass 10 kg , moving in x direction with a constant speed of 10 $m s^{- 1}$ , is subjected to a retarding force F = 0.1 x J/m during its travel from x = 20 m to 30 m. Its final KE will be

Moderate

A

275 J
B

250 J
C

475 J
D

450 J

Solution

$Here, m = 10 kg, v_{i} = 10 m s^{- 1}$
Initial kinetic energy of the block is
$K_{i} = \frac{1}{2} m v_{i}^{2} = \frac{1}{2} \times (10 kg) \times {(10 m s^{- 1})}^{2} = 500 J$
work done by retarding force
$W = \int_{x_{1}}^{x_{2}} F_{r} d x = \int_{20}^{30} - 0.1 x d x = - 0.1 {[\frac{x^{2}}{2}]}_{20}^{30}$
$= - 0.1 [\frac{900 - 400}{2}] = - 25 J$
According to work energy theorem,
$\begin{array}{l} W = K_{f} - K_{i} \\ K_{f} = W + K_{i} = - 25 J + 500 J = 475 J \end{array}$

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