Tag: modelling collisions

Questions Related to modelling collisions

In an elastic collision between two particle :

modelling collisions collisions momentum work, energy and power physics

  1. the total kinetic energy of the system is always conserved.

  2. the kinetic energy of the system before collision is equal to the kinetic energy of the system after collision.

  3. the linear momentum of the system is conserved.

  4. the mechanical energy of the system before collision is equal to the mechanical energy of the system after collision.

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Correct Option: B,C,D
Explanation:
Total kinetic energy of the system is not conserved always. 
Total kinetic energy of a system is conserved just before and after the collision only in case of perfectly elastic collision.

According to law of conservation of momentum, total linear momentum of the system is always conserved irrespective of elastic or inelastic collision

According conservation of energy, total mechanical energy of a system is always conserved irrespective of elastic or inelastic collision.
Hence total mechanical energy of the system before collision is equal to the mechanical energy of the system after the collision. 

A ball hits the floor and rebound after inelastic collision. In this case :

modelling collisions collisions momentum work, energy and power physics

  1. the momentum of the ball just after the collision is the same as that just before the collision

  2. the mechanical energy of the ball remains the same in the collision

  3. the total momentum of the ball and the earth is conserved

  4. the total energy of the ball and the earth is conserved

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Correct Option: C
Explanation:

Momentum of the system changes only due to external force (OR impulse).
When a ball hits the floor and gets rebound, then no external force (Impulse) acts on the ball as well as the floor, thus total momentum of the "ball + earth" system remains conserved.
 Also some of the mechanical energy of the ball is always lost in an inelastic collision due to its deformation, hence it cannot remain conserved in this collision.

A ball of mass 0.20 kg falls freely from a certain height and rebounds elastically with a speed of $40 \,ms^{-1}$. The change in momentum of the ball is :

modelling collisions collisions momentum work, energy and power physics

  1. $4\,kg \,ms^{-1}$

  2. $8\,kg \,ms^{-1}$

  3. $16\,kg \,ms^{-1}$

  4. $40\,kg \,ms^{-1}$

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Correct Option: C
Explanation:

Change in momentum, $\Delta p =- 2mv$
$= 2 \times 0.2\times 40 = 16 kg ms^{-1}$(magnitude)

A ball rebounds after colliding with the floor, then in case of inelastic collision:

modelling collisions collisions momentum work, energy and power physics

  1. The momentum of the ball before and after collision is same.

  2. The mechanical of the ball before and after collision is same.

  3. The total momentum of the earth-ball system is conserved

  4. The total kinetic energy of earth and ball is conserved

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Correct Option: C
Explanation:

Momentum of Earth ball system is conserved because no external force is acting on the system.

Which of the following statements is true for collisions-

modelling collisions collisions momentum work, energy and power physics

  1. Momentum is conserved in elastic collisions but not in inelastic collisions

  2. Total kinetic energy is conserved in elastic collisions but momentum is not conserved

  3. Total kinetic energy is not conserved in inelastic collisions but momentum is conserved

  4. Total kinetic energy and momentum both are conserved in all types of collisions

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Correct Option: C
Explanation:

Total momentum and total energy of a system always remain conserved.

In inelastic collisions, some of the kinetic energy goes into the heat energy, with total energy and momentum still being conserved.

For inelastic collision between two spherical rigid bodies: 

modelling collisions collisions momentum work, energy and power physics

  1. The total kinetic energy is conserved

  2. The total potential energy is conserved

  3. The linear momentum is not conserved

  4. The linear momentum is conserved

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Correct Option: D
Explanation:

In any type of collision, linear momentum is conserved, unless external force acts on the system. elasticity determines the loss in KE. elastic => no loss. inelastic => max. loss of KE ($KE _i - KE _{COM}$)

During a pool game the cue ball is shot at the red ball. When the cue ball strikes the red ball, the cue ball stops dead, and the red ball moves away at the same velocity the cue ball had before the collision. The type of collision represented in this example is:

modelling collisions collisions momentum work, energy and power physics

  1. An elastic collision

  2. A perfectly inelastic collision

  3. An inelastic collision

  4. All of the above

  5. None of the above

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Correct Option: A
Explanation:

In an elastic collision there is no loss of kinetic energy. If in the given case , balls are of same masses then their kinetic energies will also be same because their velocities are equal and as said , only one ball is moving before and after collision therefore total kinetic energy is constant i.e. it is an elastic collision.

    total kinetic energy before collision= total kinetic energy after collision
                                    $1/2mv^{2}+0=0+1/2mv^{2}$

Identify which of the following quantities remain conserved during an elastic collision?

modelling collisions collisions momentum work, energy and power physics

  1. momentum only

  2. momentum and potential energy

  3. kinetic energy only

  4. momentum and kinetic energy

  5. momentum end velocity

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Correct Option: D
Explanation:

During collision, net external force acting on the colliding bodies is zero, thus total momentum of the system is conserved in all types of collision.

But total kinetic energy of the system is conserved only in case of elastic collision.
Hence option D is correct.

A bullet is fired into a wooden block. If the bullet gets embedded in wooden block, then:

modelling collisions collisions momentum work, energy and power physics

  1. momentum alone is conserved

  2. kinetic energy alone is conserved

  3. both momentum and kinetic energy are conserved

  4. neither momentum nor kinetic energy are conserved

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Correct Option: A
Explanation:

The case is of an inelastic collision. In such collisions, energy(kinetic energy) is lost and is therefore not conserved. But, the momentum of the system is conserved in every collision .

During one dimensional collision or head on collision :

a) The bodies move along the line joining their centre of mass before and after collision.
b) The bodies should move in opposite direction.
c) The bodies change their direction after collision.
d) The bodies move along the line joining their centre of mass before and after collision either in same direction or in opposite direction.

modelling collisions collisions momentum work, energy and power physics

  1. Only a is correct

  2. Only a & b are correct

  3. a, b & c are correct

  4. Only a and d are correct

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Correct Option: D
Explanation:

By the definition of head on collision, the two bodies have to move along the line joining their centers and their velocities can be in any directions (only two possible here).