Tag: modelling collisions

Questions Related to modelling collisions

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.

During an "elastic collision " , 
a) there is no loss of kinetic energy
b) the bodies are perfectly elastic
c) temporarily some of the kinetic energy is used to deform the bodies
d) after collision the bodies regain the original shape keeping the total energy constant

modelling collisions collisions momentum work, energy and power physics

  1. only "a" is true

  2. a, c, d are true

  3. b, c, d are true

  4. a, b, c ,d are true

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Correct Option: D
Explanation:

In an elastic collision, e is equal to 1. Therefore, the kinetic energy used in causing deformation of the bodies is recovered completely in the reformation since the reformation is complete. So no energy is lost. 

Identify the correct statements from the following :

a) The collisions between the nuclei and fundamental particles are considered as elastic collisions.
b) Emission of an alpha particle by $U^{235}$ is an "elastic collision".
c) The collision between two ivory balls is considered as " elastic collision".
d) A running man jumps into a train. It is an "elastic collision".

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

Show answer
Correct Option: C
Explanation:

A collision is considered elastic collision if the kinetic energy before collision is equal to the kinetic energy after collision.

In collision of nuclei and fundamental particles, unless there is emission of gamma rays, kinetic energy of the system remains constant.

In Alpha particle emission, energy is not being released in any other form. Hence kinetic energy of the system will remain same before and after the emission.

In collision of two ivory balls, the balls being extremely hard, no deformation happens and for most practical purposes energy is assumed to not being converted into any other form such as heat(which happens when there is friction or deformation).

In the case of a running man jumping on to the train, friction and deformation happens in order for the man to continue moving along with the train. Thus energy was converted into other forms. Hence, it is an example of inelastic.