Question

Certain force acting on $20\mathrm{kg}$ mass changes its velocity from $5\mathrm{m}/\mathrm{s}$ to$10\mathrm{m}/\mathrm{s}$. Calculate the work done by the force.

Answer 1

Step 1: Given data and Formula used

Momentum$=20\mathrm{kg}$,

Initial velocity$=5\mathrm{m}/\mathrm{s}$

Final velocity$=10\mathrm{m}/\mathrm{s}$

The kinetic energy in terms of mass and velocity is $\mathrm{K}.\mathrm{E}.=\frac{1}{2}{\mathrm{mv}}^2$

Where,

K.E. is the kinetic energy.

m is the mass

v is the velocity of the object.

Step 2: Concept used

The work done is equal to the change in kinetic energy of an object.

Step 3: Kinetic energy when the object was moving with a velocity of $5\mathrm{m}/\mathrm{s}$.

$\mathrm{K}.\mathrm{E}.=\frac{1}{2}\times 20\times 5^2$

$=250\mathrm{J}$

Step 4: Kinetic energy when the object was moving with a velocity $10\mathrm{m}/\mathrm{s}$.

$\mathrm{K}.\mathrm{E}.=\frac{1}{2}\times 20\times {10}^2$

$=1000\mathrm{J}$

Step 5: To find the work done by the force

Work done = Change in kinetic energy

$=1000\mathrm{J}–250\mathrm{J}$

$=750\mathrm{J}$

Therefore, work done by the force is $750\mathrm{J}$.