The work to be done to increase the speed of a 0.5 kg ball from 4 m/s to 8 m/s is:

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Question

This question was previously asked in

RRB ALP Electronics Mechanic 21 Jan 2019 Official Paper (Shift 3)

Answer 1

CONCEPT:

Work done:

It is the dot product of Force and Displacement.

Work Done (W) = Force (F) × Displacement (S)

Kinetic energy:

The energy of a particle due to its velocity is called kinetic energy.

It is denoted by K.E.

\(K.E=\frac{1}{2}mV^2\)

where m = mass of the particle and V = velocity of the particle.

Work energy theorem:

The work done by all the forces on a system is equal to change in kinetic energy of the system.

Work done by all the forces (W) = Final K.E – Initial K.E

CALCULATION:

Given that:

Initial velocity (u) = 4 m/s, final velocity (v) = 8 m/s and

Mass (m) = 0.5 kg

Applying the work-energy theorem:

Work done = Change in Kinetic Energy:

ΔK.E = (K.E)₂ - (K.E)₁

\(\Rightarrow \frac{1}{2}m(v^2-u^2)\)

\(\Rightarrow \frac{1}{2}\times\;0.5\times(8^2-4^2)\)

∴ ΔK.E is 12 J