Tag: collisions

Questions Related to collisions

A wagon of 20 metric tonnes moves with 10 m/s  and collides  inelastically with stationary  wagon of 60 metric tonnes.   Find  loss of kinetic energy 

modelling collisions collisions momentum work, energy and power physics

  1. 250 KJ

  2. 750 KJ

  3. 500 KJ

  4. 650 KJ

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Correct Option: D
Collision is a physical process in which two or more objects, either particle masses or rigid bodies, experience very high force of interaction for a very small duration. It is not essential for the objects to physically touch each other for collision to occur. Irrespective of the nature of interactive force and the nature of colliding bodies, Newton's second law holds good on the system. Hence, momentum of the system before and after the collision remains conserved if no appreciable external force acts on the system during collision.
The amount of energy loss during collision, if at all, is indeed dependent on the nature of colliding objects. The energy loss is observed to be maximum when objects stick together after collision. The terminology is to define collision as 'elastic' if no energy loss takes place and to define collision as 'plastic' for maximum energy loss. The behaviour of system after collision depends on the position of colliding objects as well. A unidirectional motion of colliding objects before collision can turn into two dimensional after collision if the line joining the centre of mass of the two colliding objects is not parallel to the direction of velocity of each particle before collision. Such type of collision is referred to as oblique collision which may be either two or three dimensional.

Which of the following collision is one-dimensional?
modelling collisions collisions momentum work, energy and power physics

  1. Head on collision

  2. Perfectly elastic collisions

  3. Perfectly inelastic collisions

  4. Oblique collisions

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Correct Option: A
Explanation:

Head-on collision is always one dimensional the centre of mass of each body move in the same direction after collision as they were moving before collision. 

Two bodies of identical mass $m$ are moving with constant velocity $v$ but in the opposite direction with velocity of $A$ which is equal to $0.3\ m/s$. After collision the two balls come to rest when the velocity of $B$ is:

modelling collisions collisions momentum work, energy and power physics

  1. $0.15\ m/s$

  2. $1.5\ m/s$

  3. $-0.15\ m/s$

  4. $none\ of\ these$

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Correct Option: C

Which one of the following statements is true?

modelling collisions collisions momentum work, energy and power physics

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

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

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

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

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Correct Option: C
Explanation:

The law of conservation of momentum is true in all type of collisions, but kinetic energy is conserved only in elastic collision. The kinetic energy is not conserved in inelastic collision but the total energy is conserved in all type of collisions.

If one body collides with another body of same mass at rest inelastically, the ratio of their speeds after collision shall be-

modelling collisions collisions momentum work, energy and power physics

  1. e

  2. $\displaystyle \frac{1-e}{1+e}$

  3. $\displaystyle \frac{1+e}{1-e}$

  4. $\displaystyle \frac{1}{e}$

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Correct Option: B
Explanation:

Let ${u} _{1}$ be the speed of body initially before collision.
${u} _{2}=0$
Let ${v} _{1}$ be speed of particle 1 after collision and ${v} _{2}$ be speed of particle 2 after collision.
Using law of conservation of momentum
$m{u} _{1}=m{v} _{1}+m{v} _{2}$
${u} _{1}={v} _{1}+{v} _{2}$
Coefficient of restitution will be given by
$e=\dfrac{{v} _{2}-{v} _{1}}{{u} _{1}}=\dfrac{{v} _{2}-{v} _{1}}{{v} _{1}+{v} _{2}}$
$e{v} _{1}+e{v} _{2}={v} _{2}-{v} _{1}$
Dividing throughout by ${v} _{2}$ and rearranging leads to
$\dfrac{{v} _{1}}{{v} _{2}}=\dfrac{1-e}{1+e}$

Which of the following statement is true?

modelling collisions collisions momentum work, energy and power physics

  1. Kinetic energy and momentum both are conserved in all types of motion.

  2. Momentum is conserved in elastic collision but not in inelastic collision.

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

  4. Kinetic energy is conserved in elastic collision but not in inelastic collision.

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Correct Option: D
Explanation:

Linear momentum is conserved in elastic as well as inelastic collision but kinetic energy is conserved only in case of elastic collision but some kinetic energy is lost in inelastic collision.

Why are shockers used in scooters and cars? Explain.

modelling collisions collisions momentum work, energy and power physics

  1. decreases friction

  2. Increase the time of impact

  3. increases friction

  4. decorative

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Correct Option: B
Explanation:

A shocker is a mechanical or hydraulic device designed to absorb and damp shock impulses. It does this by converting the kinetic energy of the shock into another form of energy (typically heat) which is then dissipated. So, shocker is used.

During collision
a) There is a change in momenta of individual bodies
b) The change in total momentum of the system of colliding particle is zero
c) The change in total energy is zero
d) The law of conservation of momentum is not valid

modelling collisions collisions momentum work, energy and power physics

  1. only a & b are true

  2. only b & c are true

  3. a, b & c are true

  4. b, c & d are true

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Correct Option: C
Explanation:

Energy conservation is valid everywhere i.e. total energy is conserved everytime. In collision, the kinetic energy of the system may get lost. However, the momentum of the system is always conserved and so the change in the momentum of the system is zero.

During "inelastic collision "

a) There is a loss of kinetic energy.
b) Some of the kinetic energy is used to deform the body.
c) Some of the kinetic energy is liberated as heat.
d) There is a loss of mass energy.

modelling collisions collisions momentum work, energy and power physics

  1. Only a is true

  2. Only b and c are true

  3. a,b & c are true

  4. b, c & d are true

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Correct Option: C
Explanation:

We know that during an inelastic collision, there is a loss of kinetic energy, some of the kinetic energy is used to deform the body and some of the kinetic energy is liberated as heat. But their is no loss of mass-energy.

During elastic collision which of the following things happens ?
a) The colliding bodies experience large force during small interval of time
b) The colliding bodies need not touch each other
c) The kinetic energy remain conserved 
d) The linear momentum remain conserved

modelling collisions collisions momentum work, energy and power physics

  1. Only $a$ and $b$ happen

  2. Only $b$ and $c$ happen

  3. $a , b$ and $c$ happen

  4. All are true

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Correct Option: D
Explanation:
Kinetic energy is lost from a system of colliding objects because the collision transforms kinetic energy into other forms of energy - sound, heat and light energy. When the colliding objects don't really collide in the usual sense (that is when the collision force is a non-contact force), the system of colliding objects does not lose its kinetic energy and thus kinetic energy is conserved.
Since there is no external force , linear momentum of system will be conserved.
Also, the time of impact in elastic collision is very small and so the colliding bodies experience large force during small interval of time.
Hence all the statements are true.