Question

A block of mass 3kg which is at rest on a surface is pulled horizontally by a force. if the displacement of the block is 15 m in the first 3 s and the surface offers a resistance of 2 N, find the sequence of steps to calculate the magnitude of applied force.

Answer 1

Given :

• Mass of block = 3 kg

• Displacement of block = 15 m

• Time = 3 s

• Frictional force = 2 N

To Find :

• Total force applied to move the block

Solution :

$\large\boxed{ \bf s =ut + \frac{1}{2} {at}^{2} } \\ \\ \tt \implies15 = 0 \times 3 + \frac{1}{2} \times a \times {3}^{2} \\ \\ \tt \implies15 = \frac{1}{2} \times a \times 9 \\ \\\tt \implies a = \frac{15 \times 2}{9} \\ \\ \tt \implies a= \frac{30}{9} \\ \\ \tt \implies a = \frac{10}{3} m {s}^{ - 2}$

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$\large \boxed{\bf Force = mass \times acc.} \\ \\ \tt \implies F = 3 \times \frac{10}{3} \\ \\ \tt \implies F = 10 \: N$

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$\large\bf F_{a} = F{net} + F_{f} \\ \\ \tt F_{a} =10 + 2 \\ \\ \tt F_{a} =12 \: N$

Total force applied on block is 12 N