Work, Power and Energy
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Question : 28
Total: 30
A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s – 1
Solution:
Here, mass of trolley, m 1 = 200
speed of the trolleyv
mass of the child,m 2 = 20
Before the child starts running, momentum of the system
p 1 = ( m 1 + m 2 ) v = ( 200 + 20 ) 10 = 2200 kg m s – 1
When the child starts running, with a velocity of 4 m/s in a direction opposite to trolley, supposev ′
Obviously, speed of the child relative to earth( v ′ – 4 )
∴ Momentum of the system when the child is running,
p 2 = 200 v ′ + 20 ( v ′ – 4 ) = 220 v ′ – 80
As no external force is applied on the system
∴ p 2 = p 1
220 v ′ – 80 = 2200
220 v ′ = 2200 + 80 = 2280
v ′ =
= 10.36 m s − 1
Time taken by the child to run a distance of 10 m over the trolley,
t =
= 2.5 s
Distance moved by the trolley in this time = Velocity of trolley × time
= 10.36 × 2.5 = 25.9 m
speed of the trolley
mass of the child,
Before the child starts running, momentum of the system
When the child starts running, with a velocity of 4 m/s in a direction opposite to trolley, suppose
Obviously, speed of the child relative to earth
∴ Momentum of the system when the child is running,
As no external force is applied on the system
Time taken by the child to run a distance of 10 m over the trolley,
Distance moved by the trolley in this time = Velocity of trolley × time
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