Inelastic Collision: Formula, Two Dimensions and Kinetic Energy

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Inelastic collision is defined as one in which the kinetic energy is converted into another kind of energy such as heat during the impact whereas a fully elastic collision is defined as one in which the kinetic energy loss is zero. In case of an inelastic collision the momentum is conserved but not the kinetic energy. An inelastic collision can be observed in a ballistic pendulum, a clay ball which doesn't bounce back, rather it breaks when it falls to the ground and changes shape. 

Keyterms: Collison, Kinetic Energy, Elastic collision, Momentum, Velocity, Non-conservative forces

Also Read: Potential Energy


Elastic Collisions

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Both the conservation of kinetic energy and the conservation of momentum is observed in this type of collision. This means that there is no dissipative force acting during the collision, resulting in the kinetic energy of the objects remaining unchanged before and after the contact.

Elastic Collision

Elastic Collision

There is some energy loss when macroscopic objects collide. They're never genuinely flexible. As in the swinging balls apparatus, the contact between two hard steel balls is rarely elastic. It is also demonstrated that collisions between ideal gases are remarkably similar to elastic collisions, and this knowledge is used to create theories for gas pressure contained inside a container.

The video below explains this:

Inelastic Collision Detailed Video Explanation:


Inelastic Collision

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An inelastic collision is one in which some energy is wasted during the collision between two objects. Momentum is conserved in inelastic collisions, but not the kinetic energy. The majority of collisions in daily life are inelastic. The perfectly inelastic collision is a special example of this.

Inelastic Collision

Inelastic Collision

Perfectly Inelastic Collision

A perfectly inelastic collision is a type of inelastic collision that is extremely rare. Two items also stick together after colliding. When a wet mud ball is hurled against a wall, for example, the mud ball sticks to the wall.

Conservation of momentum is applied individually along each axis in two-dimensional inelastic collisions. Because momentum is a vector equation, there is only one momentum conservation equation. Similarly, there will only be one energy conservation equation.

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Inelastic Collision Formula

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V = (M1V1+M2V2)/(M1+M2)

Where,

  • V= Final velocity
  • M1= mass of the first object in kgs
  • M2= mass of the second object in kgs
  • V1= initial velocity of the first object in m/s
  • V2= initial velocity of the second object in m/s

Inelastic Collision in Two Dimension

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In a two-dimensional inelastic collision, momentum conservation is applied individually along each axis. Because momentum is a vector equation, each dimension has just one conservation of momentum equation. In the same way, there is just one energy conservation equation.

Also Check: Reversible and irreversible processes


Inelastic Collision Examples

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The majority of collisions we see in our daily lives are inelastic collisions. Given below is the list of some of them.

  • The ball is thrown from a given height and is unable to return to its original position.
  • If you throw a soft mud ball against a wall, it will stick to it.
  • A collision between two automobiles
  • A car colliding with a tree

Inelastic Collision Kinetic Energy

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In an inelastic collision the kinetic energy is not preserved. Internal friction causes kinetic energy to be lost. It may transform into atomic vibrational energy, generating a heating effect and deformation of the bodies.

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Points To Remember

  • Momentum is conserved in an inelastic collision.
  • The complete amount of energy is conserved.
  • In an inelastic collision the kinetic energy is not conserved.
  • An inelastic collision involves non-conservative forces.

Previous Year Questions

  1. The approximate depth of an ocean is 2700m. The compressibility of water is…? [BITSAT 2015]
  2. A ball whose density is 0.4×103kg/m3 falls into the water from a height of 9cm. To what …? [BITSAT 2013]
  3. Water is supplied to different localities from a tank. The pressure of water is? [JIPMER 1996]
  4. A beaker of radius of 6 cm is filled with mercury up to a height of 12 cm... [AMUEEE 1998]
  5. A boy has 60kg weight. He wants to swim in a river with the help of a wooden log…? [MU OET 2011]
  6. A large drop of oil (density 0.8g/cm3 and viscosity η0 ) floats up through a column of…? [BITSAT 2012]
  7. In an ideal gas at temperature TT, the average force that a molecule applies … [JEE Mains 2015]
  8. An ideal gas is expanding such that … [JEE Advanced 2008]
  9. Cv and Cp denote the molar specific heat capacities of a gas at … [JEE Advanced 2009]
  10. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature … [JEE Mains 2019]
  11. Two gases – argon (atomic radius 0.07nm, atomic weight 40) … [JEE Mains 2020]
  12. A vertical closed cylinder is separated into two parts by a frictionless … [JEE Mains 2019]
  13. An ideal gas occupies a volume of … [JEE Mains 2019]
  14. Consider two ideal diatomic gases … [JEE Mains 2020]
  15. If 1022 gas molecules each of mass 10−26 kg collide with a surface … [JEE Mains 2020]

Sample Questions 

Ques 1. What are the circumstances in which an inelastic collision occurs? (2 marks)

Ans. When the maximum amount of kinetic energy of colliding objects/systems is wasted, an inelastic collision happens in physics. In a perfectly inelastic collision, the clashing particles stick together. In these circumstances, the kinetic energy lost is utilized to join the two bodies.

Ques 2. Do cars stick together in an inelastic collision? (1 mark)

Ans. When things collide in an inelastic collision, some people believe they must cling together. Objects, on the other hand, only stick together when they collide in a perfectly inelastic collision. Even if the objects bounce off one other or move apart from each other, the collision is still considered to be inelastic as long as the kinetic energy is not preserved.

Ques 3. In an inelastic collision, is kinetic energy conserved? (1 mark)

Ans. In an inelastic collision, kinetic energy is not conserved. There's a good likelihood that kinetic energy will be lost in an inelastic collision. An inelastic collision can result in the system's momentum being conserved. In this collision, kinetic energy conservation failed. This occurs because kinetic energy is converted into a different form of energy.

Ques 4. Is a Two-Car Collision Elastic or Not? Explain? (2 marks)

Ans. We know that kinetic energy conservation is not maintained. The kinetic energy is converted to sound energy, heat energy, and object deformation. When two objects collide and bounce back to their original positions, this is known as an elastic collision. As a result, a collision between two cars is not elastic, but rather inelastic.

Ques 5. Is it possible to carry out perfectly elastic collisions? (1 mark)

Ans. It's not possible. Only in subatomic particles is this possible. The objects in this type of collision cling together after impact.

Ques 6. How do you know if a collision is elastic or inelastic? (1 mark)

Ans. The collision is elastic if the kinetic energy is the same. The collision is inelastic if the kinetic energy changes, regardless of whether the objects cling together or not.

Ques 7. What is an example of a perfectly inelastic collision? (1 mark)

Ans. Perfectly inelastic collisions include a bullet impacting a bag of sand, a proton catching electrons, and a guy leaping into a moving wagon. An elastic collision is one where there isn't any loss of the net kinetic energy inside the system as a result of the collision.

Ques 8. Is perfectly inelastic collision possible in real life? (1 mark)

Ans. Shooting a bullet into a block of wood is a typical example of this. A ballistic pendulum is a name for this effect. The bullet enters the wood and causes it to move, but it suddenly "stops" within it.

Ques 9. A 2200kg car traveling at 30m/s collides with another 2200kg car that is at rest. The two bumpers lock and the cars move forward together. What is their final velocity? (4 marks)

Ans. Because the two cars cling together after colliding, this is an example of an inelastic collision. It's safe to believe that momentum is conserved.

Let's name the first car "1" and the second car "2" to make the equation easier to understand.

We may construct the following equation using conservation of momentum and the momentum equation, p=mv.

m1v1 initial+m2v2 initial=(m1+m2)vfinal

The automobiles will have the same final velocity because they will stick together. The second car begins at a standstill, and the first car's velocity is known. Solve for the final velocity using these data.

(2200kg*30m/s)+(2200kg*0m/s)=(2200kg+2200kg)vfinal

66000kg⋅m/s=(4400kg) vfinal2

66000kg*m/s/4400kg=vfinal

15m/s=vfinal


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CBSE CLASS XII Related Questions

1.

A tank is filled with water to a height of 12.5cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

      2.

      A parallel plate capacitor made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s−1.

      1. What is the rms value of the conduction current?
      2. Is the conduction current equal to the displacement current?
      3. Determine the amplitude of B at a point 3.0 cm from the axis between the plates.
      A parallel plate capacitor made of circular plates

          3.
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          (a) What is the magnetic moment associated with the solenoid?
          (b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of \(7.5 × 10^{-2}\  T\) is set up at an angle of \(30º\) with the axis of the solenoid?

              4.

              An object of size 3.0 cm is placed 14cm in front of a concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

                  5.
                  A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is

                    • 0
                    • 1 m

                    • 2 m

                    • 3 m

                    6.
                    A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is

                      • $0.1\,kgm^2s^{-1}$
                      • $0.04\,kgm^2s^{-1}$
                      • $0.025\,kgm^2s^{-1}$
                      • $0.01\,kgm^2s^{-1}$
                      CBSE CLASS XII Previous Year Papers

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