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Answer carefully, with reason: If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or

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प्रश्न

Answer carefully, with reason:

If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy.)

संक्षेप में उत्तर
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उत्तर

The potential energy depends on the separation distance between centres; this means that during the collision, the force acting between the bodies is conservative; therefore, energy will be conserved. Thus, the collision will be elastic.

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अध्याय 5: Work, Energy and Power - EXERCISES [पृष्ठ ९०]

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एनसीईआरटी Physics Part 1 and 2 [English] Class 11
अध्याय 5 Work, Energy and Power
EXERCISES | Q 5.8 (d) | पृष्ठ ९०

संबंधित प्रश्न

State if the following statement is true or false. Give a reason for your answer.

In an elastic collision of two bodies, the momentum and energy of each body is conserved.


Answer carefully, with reason:

Is the total linear momentum conserved during the short time of an elastic collision of two balls?


A molecule in a gas container hits a horizontal wall with speed 200 m s–1 and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?


Consider the decay of a free neutron at rest : n → p + e

Show that the two-body decay of this type must necessarily give an electron of fixed energy and, therefore, cannot account for the observed continuous energy distribution in the β-decay of a neutron or a nucleus

 


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.

  1. Colliding bodies are identical.
  2. A very heavy object collides on a lighter object, initially at rest.
  3. A very light object collides on a comparatively much massive object, initially at rest.

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 ball of mass 100 g dropped on the ground from 5 m bounces repeatedly. During every bounce, 64% of the potential energy is converted into kinetic energy. Calculate the following:

  1. Coefficient of restitution.
  2. The speed with which the ball comes up from the ground after the third bounce.
  3. The impulse was given by the ball to the ground during this bounce.
  4. Average force exerted by the ground if this impact lasts for 250 ms.
  5. The average pressure exerted by the ball on the ground during this impact if the contact area of the ball is 0.5 cm2.

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.


Define the following:

Coefficient of restitution


Arrive at an expression for elastic collision in one dimension and discuss various cases.


A ball is thrown vertically down from height of 80 m from the ground with an initial velocity 'v'. The ball hits the ground, loses `1/6`th of its total mechanical energy, and rebounds back to the same height. If the acceleration due to gravity is 10 ms-2, the value of 'v' is


A ball moving with velocity 5 m/s collides head on with another stationary ball of double mass. If the coefficient of restitution is 0.8, then their velocities (in m/s) after collision will be ____________.


A block of mass 'm' moving along a straight line with constant velocity `3vec"v"` collides with another block of same mass at rest. They stick together and move with common velocity. The common velocity is ______.


A cricket ball of mass 150 g moving with a speed of 126 km/h hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for 0.001s, the force that the batsman had to apply to hold the bat firmly at its place would be ______.


The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in figure.


If the length of the pendulum is 1 m, calculate

  1. the height to which bob A will rise after collision.
  2. the speed with which bob B starts moving. Neglect the size of the bobs and assume the collision to be elastic.

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 ______.


The dimension of mutual inductance is ______.


Three identical blocks A, B and C are placed on horizontal frictionless surface. The blocks A and C are at rest. But A is approaching towards B with a speed 10 m/s. The coefficient of restitution for all collision is 0.5. The speed of the block C just after the collision is ______.


Answer carefully, with reason:

Is the total linear momentum conserved during the short time of an inelastic collision of two balls ?


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