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