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प्रश्न
During inelastic collision between two bodies, which of the following quantities always remain conserved?
विकल्प
Total kinetic energy.
Total mechanical energy.
Total linear momentum.
Speed of each body.
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उत्तर
Total linear momentum.
Explanation:
If in a collision kinetic energy after collision is not equal to kinetic energy before the collision, the collision is said to be inelastic.
Coefficient of restitution 0 < e < 1
When we are considering the two bodies as systems the total external force on the system will be zero.
Hence, the total linear momentum of the system remains conserved.
Here kinetic energy appears in other forms, i.e. energy may be lost in the form of heat and sound etc. In some cases
`(KE)_"final" < (KE)_"initial"` such as when initial KE is converted into internal energy of the product (as heat, elastic or excitation) while in other cases `(KE)_"final" > (KE)_"initial"` such as when internal energy stored in the colliding particles is released.
Examples: (1) The collision between two billiard balls.
(2) The collision between two automobiles on a road.
In fact, the majority of collisions belong to this category.
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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 elastic 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)?
A bullet of mass 0.012 kg and horizontal speed 70 m s–1 strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.
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?
Define coefficient of restitution.
Answer the following question.
A bullet of mass m1 travelling with a velocity u strikes a stationary wooden block of mass m2 and gets embedded into it. Determine the expression for loss in the kinetic energy of the system. Is this violating the principle of conservation of energy? If not, how can you account for this loss?
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.
Arrive at an expression for elastic collision in one dimension and discuss various cases.
A ball of mass 0.1 kg makes an elastic head-on collision with a ball of unknown mass, initially at rest. If the 0 .1 kg ball rebounds at one-third of its original speed, the mass of the other ball is ______.
In inelastic collision, ____________.
A wooden block of mass 'M' moves with velocity 'v ' and collides with another block of mass '4M' which is at rest. After collision, the block of mass 'M' comes to rest. The coefficient of restitution will be ______.
A smooth sphere of mass 'M' moving with velocity 'u' directly collides elastically with another sphere of mass 'm' at rest. After collision, their final velocities are V' and V respectively. The value of V is given by ______.
A ball of mass m, moving with a speed 2v0, collides inelastically (e > 0) with an identical ball at rest. Show that for head-on collision, both the balls move forward.
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?
Answer carefully, with reason:
Is the total linear momentum conserved during the short time of an inelastic collision of two balls ?
Before collision, what is the position of objects?
