First slide

Work

Question

A force of $20 \sqrt{2}$ is acting on a block of 1kg at $45^{\circ}$ above the horizontal. Work done by all the forces in 2s is (g= $10 m s^{- 2}$ )

Moderate

A

1600J
B

1400J
C

1200 J
D

1000J

Solution

$\begin{array}{l} W = \vec{F} \vec{S} \\ W = [Fcos 45^{\circ} \hat{i} + (Fsin 45^{\circ} - mg) \hat{j}] \cdot (S_{X} \hat{i} + S_{y} \hat{j}) \\ W = [20 \hat{i} + (20 - 10) \hat{j}] \cdot [\frac{1}{2} a_{X} t^{2} \hat{i} + \frac{1}{2} a_{y} t^{2} \hat{j}] \\ W = (20 \times \frac{1}{2} \times \frac{20}{1} \times 4) + (10 \times \frac{1}{2} \times 20 \times 4) \\ W = 800 + 400 \\ W = 1200 J \end{array}$

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