Example 11.4 What is the work to be done
to increase the velocity of a car from
30 km h-1 to 60 km h:1 if the mass of
the car is 1500 kg?
Answers
Explanation:
Initial velocity u=30 km/h=30×
18
5
=
3
25
m/s
Final velocity v=60 km/h=60×
18
5
=
3
50
m/s
Mass m=1500 kg
Work done W=
2
1
mv
2
−
2
1
mu
2
⟹ W=
2
m
(v
2
−u
2
)=
2
1500
×((
3
50
)
2
−(
3
25
)
2
)=156187 J
Answer:
Work done is 156250 J.
Explanation:
Given,
The mass (m) of the car is 1500 kg.
Initial velocity of car = u = 30 km / hr = 30 * 5/18 = 25 / 3 m/s
Final velocity of car = v = 60 km / hr = 60 * 5/18 = 50/3 m/s
To find: The work to be done to increase the velocity of a car from
30 km h-1 to 60 km h^-1
Solution:
Initial kinetic energy = Ki = 1/2mu² = 1/2*1500*25/3 * 25/3 = 156250/3 J
Final Kinetic energy = Kf = 1/2mv² = 1/2*1500*50/3*50/3 = 625000/3 J
Work done can be given as change in Kinetic Energy,
i.e W = ΔK.E
or, W = Kf - Ki
or, W = 625000/3 - 156250/3
or, W = 156250 J
Therefore, Work done is 156250 J.