Question

A train moving with a velocity of 30 km/h has a kinetic energy of 52000 J. When the velocity of train is increased to 60 km/h, the work done is:
1. Work done = 0
2. 156000 J
3. 104000 J
4. 52000 J

Answer 1

Correct Answer - Option 2 : 156000 J

CONCEPT:

• Work-energy theorem: It states that the sum of work done by all the forces acting on a body is equal to the change in the kinetic energy of the body i.e.,

Work done by all the forces = Kf - Ki

\(W = \frac{1}{2}m{v^2} - \frac{1}{2}m{u^2} = {\bf{Δ }}K\)

Where v = final velocity, u = initial velocity and m = mass of the body

CALCULATION:

It is given that,
Initial velocity (u) = 30 km/h = (30 × 1000/3600) = 25/3 m/s

Initial Kinetic energy (KE_i) = 52000 = \(\frac{1}{2}mu^2\)

Final Velocity (v) = 60 km/h = (60 × 1000/3600) = 50/3 m/s = 2u

Final kinetic energy (KE_f) = \(\frac{1}{2}mv^2 = \frac{1}{2}m (2u)^2 =4 KE_i \)

KE_f  = 4 × 52000 = 208000 J
According to the work-energy theorem, 

⇒  Work done = Change in K.E
⇒  Work done (W) = Δ K.E = KE_f - KE_i = 208000 - 52000 = 156000 J