Advertisements
Advertisements
प्रश्न
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 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?
Advertisements
उत्तर १
Mass of the trolley, M = 200 kg
Speed of the trolley, v = 36 km/h = 10 m/s
Mass of the boy, m = 20 kg
Initial momentum of the system of the boy and the trolley
= (M + m)v
= (200 + 20) × 10
= 2200 kg m/s
Let v' be the final velocity of the trolley with respect to the ground.
Final velocity of the boy with respect to the ground = v' - 4
Final momentum = Mv' + m(v' - 4)
= 200v' + 20v' - 80
= 220v' – 80
As per the law of conservation of momentum:
Initial momentum = Final momentum
2200 = 220v' – 80
∴ v' = 2280 / 220 = 10.36 m/s
Length of the trolley, l = 10 m
Speed of the boy, v'' = 4 m/s
Time taken by the boy to run, t = 10/4 = 2.5 s
∴ Distance moved by the trolley = v'' × t= 10.36 × 2.5 = 25.9 m
उत्तर २
Let there be an observer travelling parallel to the trolley with the same speed. He will observe the initial momentum of the trolley of mass M and child of mass m as zero. When the child jumps in opposite direction, he will observe the increase in the velocity of the trolley by Δv.
Let u be the velocity of the child. He will observe child landing at velocity (u – Δu) Therefore, initial momentum = 0
Final momentum = MΔ v – m (u – Δv)
Hence, MΔ v – m (u – Δv) = 0
Whence Δv =mu/ M + m
Putting values Δv =4 x 20/ 20 + 220 = ms-1
∴ Final speed of trolley is 10.36 ms-1.
The child take 2.5 s to run on the trolley.
Therefore, the trolley moves a distance = 2.5 x 10.36 m = 25.9 m.
संबंधित प्रश्न
State if the following statement is true or false. Give a reason for your answer.
Total energy of a system is always conserved, no matter what internal and external forces on the body are present.
Answer carefully, with reason:
In an inelastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e., when they are in contact)?
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision?
Define coefficient of restitution.
Answer the following question.
Discuss the following as special cases of elastic collisions and obtain their exact or approximate final velocities in terms of their initial velocities.
- Colliding bodies are identical.
- A very heavy object collides on a lighter object, initially at rest.
- A very light object collides on a comparatively much massive object, initially at rest.
Solve the following problem.
A marble of mass 2m travelling at 6 cm/s is directly followed by another marble of mass m with double speed. After a collision, the heavier one travels with the average initial speed of the two. Calculate the coefficient of restitution.
Explain the characteristics of elastic and inelastic collision.
In Rutherford experiment, for head-on collision of a-particles with a gold nucleus, the impact parameter is ______.
A block of mass 'm' moving on a frictionless surface at speed 'v' collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle 'θ' with its initial direction and has speed 'v1'. The speed of the second block after collision is ______.
Two bodies of masses 3 kg and 2 kg collide bead-on. Their relative velocities before and after collision are 20 m/s and 5 m/s respectively. The loss of kinetic energy of the system is ______.
A body of mas 'm' moving with speed 3 m/s collides with a body of mass '2m' at rest. The coalesced mass will start to move with a speed of ______.
A bullet fired from gun with a velocity 30 m/s at an angle of 60° with horizontal direction. At the highest point of its path, the bullet explodes into two parts with masses in the ratio 1:3. The lighter mass comes to rest immediately. Then the speed of the heavier mass is
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V as shown in figure.
If the collision is elastic, which of the following (Figure) is a possible result after collision?
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact).
- Kinetic energy.
- Total linear momentum?
Give reason for your answer in each case.
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and required 1 s to cover. How long the drunkard takes to fall in a pit 13 m away from the start?
A ball is thrown upwards from the foot of a tower. The ball crosses the top of tower twice after an interval of 4 seconds and the ball reaches ground after 8 seconds, then the height of tower is ______ m. (g = 10 m/s2)
A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms-1 gets embedded in it, then loss of kinetic energy will be ______.
Which of the following real-life scenarios is the best example of a collision as defined in the source?
