Tag: modelling collisions

Questions Related to modelling collisions

A mass $m$ moves with velocity $v$ and collides inelastically with another identical mass. After collision, the 1st mass moves with velocity $\frac { v }{ \sqrt { 3 }  } $ in a direction perpendicualr to the initial direction of motion. find the speed of the second mass after collision.

modelling collisions collisions momentum work, energy and power physics

  1. $v$

  2. $\sqrt { 3v } $

  3. $\frac { 2 }{ \sqrt { 3 } } v$

  4. $\frac { v }{ \sqrt { 3 } } $

Show answer
Correct Option: C

A body of mass 2.0 kg makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed v. What is the mass of other body and the speed of the center of mass of two bodies ?

modelling collisions collisions momentum work, energy and power physics

  1. $ 1.0 kg and \frac {2}{3}v $

  2. $ 1.2 kg and \frac{5}{8} $

  3. $ 1.4 kg and \frac {10}{17} v $

  4. $ 1.5 kg and \frac {4}{7} v $

Show answer
Correct Option: B
Explanation:
$m _{1}=2\ kg$
$u _{1}=4\ m/s$
$v _{1}=\dfrac {u _{1}}{4}=\dfrac {4}{4}=1\ m/s$
$u _{2}=0$
since nothing is given so we would take it as elastic collision. 
hence conservation of momentum is given by:
$m _{1}u _{1}+m _{2}u _{2}=m _{1}v _{1}+m _{2}v _{2}$
$2\times 4+0=2\times 1+m _{2}v _{2}$
$m _{2}v _{2}=6$
according to the conservation kinetic energy:
$\dfrac {1}{2}m _{1}u _{1}^{2}+\dfrac {1}{2}m _{2}u _{2}^{2}=\dfrac {1}{2}m _{1}v _{1}^{2}+\dfrac {1}{2}m _{2}v _{2}^{2}$
$2\times 16+0=2\times 1+m _{2}v _{2}^{2}$
$m _{2}v _{2}^{2}=30$
$\dfrac {m _{2}v _{2}^{2}}{m _{2}v _{2}}=\dfrac {30}{6}$
$v _{2}=5\ m/s$
$m _{2}=1.2\ kg$


Two objects of mass 3 kg and 2 kg move along x and y ais with $ 4 m/s^2 $ and $ 3 m/s ^2 $ respectively on a horizontal smooth table.after collision the bodies stick together.then :

modelling collisions collisions momentum work, energy and power physics

  1. Heat generated in the process is 15 joules

  2. Heat generated in the process is 18 joules

  3. direction of motion x-axis after collision is $ 60^0 $

  4. direction of x-axis after collision is $ tan{-1} \left( \frac { 1 }{ 3 } \right) $

Show answer
Correct Option: B

$n$ balls each of mass $m$ impinge elastically each second on a surface with velocity $u$. The average force experienced by the surface will be

modelling collisions collisions momentum work, energy and power physics

  1. $mnu$

  2. $2\ mnu$

  3. $4\ mnu$

  4. $mnu/2$

Show answer
Correct Option: B
Explanation:
  • Elastically means the balls get bounced with $same$ speed i.e $u$
  • so the change in momentum will be $P _2-P _1=-mu-mu=-2mu$
  • so the momentum tranferred to the surface will be $-(-2mu)=2mu$
  • thus the total momentum transferred by $n$ balls will be $2mnu$
  • force $F=\dfrac{Momentum}{time}=\dfrac{2mnu}{1sec}=2mnu$

A body moving towards a finite body at rest collides with it. It is possible that :

modelling collisions collisions momentum work, energy and power physics

  1. both the bodies come to rest

  2. both the bodies move after collision

  3. the moving body comes to rest and stationary body starts moving

  4. the stationary body remain stationary and moving body changes its direction

Show answer
Correct Option: B,C
Explanation:

If a body moving towards a finite body at rest collides with it then momentum will be conserved and hence, the velocities after collision are may be in inverse proportion to their masses or may get interchanged. Hence, both the bodies move after collision or the moving body comes to rest and stationary body starts moving.

A body moving towards a finite body at rest collides with it. It is possible that:

modelling collisions collisions momentum work, energy and power physics

  1. both the bodies come to rest

  2. both the bodies moves after collision

  3. the moving body comes to rest and the stationary body starts moving

  4. the stationary body remains stationary, the moving body changes its velocity

Show answer
Correct Option: B,C
Explanation:

both bodies cannot come to rest as  it will violate the law of conservation of momentum.
Option (D) will also violate conservation of momentum.

A mass $m _1$ moves with a great velocity. It strikes another mass $m _2$ at rest in a head on collision and comes back along its path with a low speed after collision. Then :

modelling collisions collisions momentum work, energy and power physics

  1. $m _1 > m _2$

  2. $m _1 = m _2$

  3. $m _1 < m _2$

  4. there is relation between $m _1$ and $m _2$

Show answer
Correct Option: C
Explanation:

In a head-on elastic collision between a small projectile and a more massive target, the projectile will bounce back with low speed and the massive target will be given a very small velocity. Hence, $m _1 < m _2$

A body moving towards a body of finite mass at rest collides with it. It is possible that :

modelling collisions collisions momentum work, energy and power physics

  1. both bodies come to rest

  2. the stationary body remains stationary and the moving body rebounds.

  3. the moving body stop and the body at rest start moving.

  4. all of the above are correct.

Show answer
Correct Option: C
Explanation:

From the very fundamental law of collision we know that in a collision momentum of the system is conserved .
Therefore the only possible option is C.

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

Show answer
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

Show answer
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.