Question

The kinetic energy of a body changes from $12\mathrm{J}\mathrm{to}60\mathrm{J}$ due to the action of a force of $5\mathrm{N}$ on an object of mass $4\mathrm{kg}.$ The work done by the force is _____.

Answer 1

Step 1:Given data:

The initial kinetic energy of a body is given as ${\mathrm{w}}_1=12\mathrm{J}$

The initial kinetic energy of a body is given as ${\mathrm{w}}_2=60\mathrm{J}$

The force is given as= $5\mathrm{N}$

Mass of the object is given as = $4\mathrm{kg}.$

Step 2: Formula for calculating Work done:

The reduction in kinetic energy gets produced by the resulting force doing an equivalent amount of negative work.

Hence, if the net work done is taken as positive, the particle's kinetic energy tends to increase by the same amount, which can be given as:

$\mathrm{W}=\mathrm{\Delta }{\mathrm{E}}_{\mathrm{K}}$

Where,

$\mathrm{W}=$ Net work done

$\mathrm{\Delta }{\mathrm{E}}_{\mathrm{K}}=$change in kinetic energy

As here the kinetic energy of a body changing from $12\mathrm{J}\mathrm{to}60\mathrm{J}$, thus the work done can be given as:

$\mathrm{\Delta W}={\mathrm{W}}_2-{\mathrm{W}}_1$

Step 3: Calculation of Work done:
Hence, work done can be calculated as:
$\mathrm{\Delta W}=60-12$
$\Rightarrow \mathrm{\Delta W}=48\mathrm{J}$
Hence, the work done by the force is $48\mathrm{J}.$