Question

Certain force acting on a 20 kg mass changes its velocity from 5 m s-1 to 2 m s-1 . Calculate the work done by the force. ​

Answer 1

By, Work-Energy Theorem,

$W = \triangle K.E. \\ W = KE _{f} - KE _{i} \\ \\ W = \frac{1}{2} m {v}^{2} - \frac{1}{2} m {u}^{2} \\ \\ W = \frac{1}{2} m( {v}^{2} - {u}^{2} ) \\ \\ W = \frac{1}{2}(20) ( {2}^{2} - {5}^{2} ) \\ \\ W = (10)(-21) \\ W = -210J$

Answer 2

We know that the work done here is kinetic energy.

So, the formula of kinetic energy is given by:

Kinetic Energy = 1/2 × mv^2

• Kinetic energy when the object was moving with a velocity of 5 m/s:

Kinetic energy = 1/2 × 20 × ( 5 )^2

= 10 × 25

= 250 J ( Joules )

• Kinetic energy when the object was moving with a velocity of 2 m/s:

Kinetic energy = 1/2 × 20 × ( 2 )^2

= 10 × 4

= 40 J ( Joules )

Work done = Change in kinetic energy

= 40 J - 250 J

= -210 J

The work done by the force is -210 Joules because the force decreased the velocity of the object.

Negative work follows when the force has a component opposite or against the displacement.