PhysicsSolver360 logoPhysicsSolver360°
Powered by Solver360°

Inelastic Collision Calculator

Calculate final velocities in perfectly inelastic collisions with momentum conservation and energy loss analysis

Parameters

kgⓘ
kgⓘ
m/sⓘ
m/sⓘ
Show Trail

Controls

xⓘ

Calculated Values

Final Velocity:
2.67;m/s2.67;m/s
Initial Momentum:
8.00;kg⋅m/s8.00;kg⋅m/s
Final Momentum:
8.00;kg⋅m/s8.00;kg⋅m/s
Initial Kinetic Energy:
27.00;J27.00;J
Final Kinetic Energy:
10.67;J10.67;J
Energy Loss:
16.33;J16.33;J

Examples

Example 1: Equal Mass Collision

Two objects of equal mass (2 kg each) collide inelastically with velocities 5 m/s and -2 m/s.

  • Final Velocity: 1.501.50
  • Initial Momentum: 6.006.00
  • Final Momentum: 6.006.00
  • Energy Loss: 12.2512.25

Example 2: Heavy vs Light Object

A heavy object (5 kg) moving at 3 m/s collides with a light object (1 kg) at rest.

  • Final Velocity: 2.502.50
  • Initial Momentum: 15.0015.00
  • Final Momentum: 15.0015.00
  • Energy Loss: 3.753.75

Example 3: Head-on Collision

Two objects (3 kg and 2 kg) collide head-on with equal but opposite velocities.

  • Final Velocity: 0.800.80
  • Initial Momentum: 4.004.00
  • Final Momentum: 4.004.00
  • Energy Loss: 39.2039.20

Visualization

Inelastic Collisions

An inelastic collision is a collision in which momentum is conserved but kinetic energy is not. Some of the initial kinetic energy is converted to other forms of energy such as heat, sound, or deformation of the objects.

In perfectly inelastic collisions, the objects stick together after the collision and move as a single object. This is the maximum possible energy loss scenario for a given collision.

The conservation of momentum principle still applies: m₁v₁ᵢ + m₂v₂ᵢ = (m₁ + m₂)v_f, where v_f is the final velocity of the combined object.

The final velocity in a perfectly inelastic collision is given by: v_f = (m₁v₁ᵢ + m₂v₂ᵢ)/(m₁ + m₂). This is the velocity of the center of mass of the system.

The kinetic energy lost in the collision can be calculated as: ΔKE = KE_initial - KE_final. This energy is converted to other forms and is not recoverable as kinetic energy.

Key Concepts

  • Momentum Conservation: Total momentum before = Total momentum after
  • Energy Loss: Kinetic energy is not conserved
  • Perfectly Inelastic: Objects stick together after collision
  • Final Velocity: v_f = (m₁v₁ᵢ + m₂v₂ᵢ)/(m₁ + m₂)
  • Energy Loss: ΔKE = ½m₁v₁ᵢ² + ½m₂v₂ᵢ² - ½(m₁+m₂)v_f²
  • Center of Mass: Final velocity equals center of mass velocity

Real-World Applications

  • Automotive crash analysis and safety design
  • Ballistic pendulum experiments
  • Clay and putty collisions
  • Railroad car coupling
  • Spacecraft docking and rendezvous
  • Sports collisions (football tackles, etc.)

Explore Further

More mechanics tools

Physics Equations

Momentum Conservation:
m1v1i+m2v2i=(m1+m2)vfm_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f
Final Velocity:
vf=m1v1i+m2v2im1+m2v_f = \frac{m_1v_{1i} + m_2v_{2i}}{m_1 + m_2}
Initial Kinetic Energy:
KEi=12m1v1i2+12m2v2i2KE_i = \frac{1}{2}m_1v_{1i}^2 + \frac{1}{2}m_2v_{2i}^2
Final Kinetic Energy:
KEf=12(m1+m2)vf2KE_f = \frac{1}{2}(m_1 + m_2)v_f^2
Energy Loss:
ΔKE=KEi−KEf\Delta KE = KE_i - KE_f

Step-by-Step Solution

See how the main results are calculated.

1

Identify Initial Conditions

List the masses and initial velocities of both objects

Result:

Object1:m1=2kg,v1=5m/sObject2:m2=1kg,v2=−2m/sObject 1: m₁ = 2 kg, v₁ = 5 m/s Object 2: m₂ = 1 kg, v₂ = -2 m/s

Explanation:

We need to identify the masses and initial velocities of both objects before the collision.

2

Calculate Initial Total Momentum

Find the total momentum before the collision

Equation:

pinitial=m1v1+m2v2p_{initial} = m_1v_1 + m_2v_2

Calculation:

pinitial=2×5+1×−2p_{initial} = 2 \times 5 + 1 \times -2
pinitial=10.00+−2.00p_{initial} = 10.00 + -2.00
pinitial=8.00kg⋅m/sp_{initial} = 8.00 \mathrm{kg}\cdot\mathrm{m}/\mathrm{s}

Result:

pinitial=8.00kg⋅m/sp_{initial} = 8.00 \mathrm{kg}\cdot\mathrm{m}/\mathrm{s}

Explanation:

The total momentum is the sum of the momentum of both objects before the collision.

3

Apply Conservation of Momentum

Set initial momentum equal to final momentum

Equation:

pinitial=pfinalp_{initial} = p_{final}

Calculation:

8.00=m1v1′+m2v2′8.00 = m_1v_1' + m_2v_2'
8.00=2v1′+1v2′8.00 = 2v_1' + 1v_2'

Result:

2v1′+1v2′=8.002v_1' + 1v_2' = 8.00

Explanation:

Conservation of momentum states that the total momentum before the collision equals the total momentum after the collision.

4

Inelastic Collision Equation

Use inelastic collision formula where objects stick together

Equation:

v′=m1v1+m2v2m1+m2v' = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}

Calculation:

v′=2×5+1×−23v' = \frac{2 \times 5 + 1 \times -2}{3}
v′=10.00+−2.003v' = \frac{10.00 + -2.00}{3}
v′=2.67m/sv' = 2.67 \mathrm{m}/\mathrm{s}

Result:

v1′=v2′=2.67m/sv_1' = v_2' = 2.67 \mathrm{m}/\mathrm{s}

Explanation:

In inelastic collisions, the objects stick together and move with the same final velocity.

5

Verify Conservation of Momentum

Check that momentum is conserved

Equation:

pfinal=m1v1′+m2v2′p_{final} = m_1v_1' + m_2v_2'

Calculation:

pfinal=2×2.67+1×2.67p_{final} = 2 \times 2.67 + 1 \times 2.67
pfinal=5.33+2.67p_{final} = 5.33 + 2.67
pfinal=8.00kg⋅m/sp_{final} = 8.00 \mathrm{kg}\cdot\mathrm{m}/\mathrm{s}

Result:

pfinal=8.00kg⋅m/s=pinitialcheckmarkp_{final} = 8.00 \mathrm{kg}\cdot\mathrm{m}/\mathrm{s} = p_{initial} checkmark

Explanation:

The final momentum equals the initial momentum, confirming that momentum is conserved in the collision.

Frequently Asked Questions (FAQ)

What is an inelastic collision?

An inelastic collision is a collision where momentum is conserved but kinetic energy is not. Some kinetic energy is converted to other forms of energy like heat, sound, or deformation.

What is the difference between elastic and inelastic collisions?

In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, only momentum is conserved - some kinetic energy is lost to other forms of energy.

What is a perfectly inelastic collision?

A perfectly inelastic collision is one where the objects stick together after the collision and move as a single object. This results in the maximum possible energy loss.

Why do objects stick together in perfectly inelastic collisions?

Objects stick together due to strong attractive forces, deformation, or other mechanisms that prevent them from separating after the collision.

Is the final velocity always positive in inelastic collisions?

No, the final velocity can be positive, negative, or zero depending on the initial momenta and masses of the colliding objects.

Practice MCQs

  1. In a perfectly inelastic collision, what happens to the objects after collision?
  2. Which quantity is conserved in inelastic collisions?
  3. Two objects of equal mass collide inelastically. If one is at rest, the final velocity is:
  4. What happens to the kinetic energy in inelastic collisions?
  5. The final velocity in a perfectly inelastic collision equals:

Related Calculators

These tools connect to the same physics concepts used in this calculator.

Projectile MotionCalculate and visualize the path of objects under the influence of gravity.Newton's LawsApply the three laws of motion to solve force and acceleration problems.Circular MotionAnalyze objects moving in circular paths with centripetal acceleration.Conservation of MomentumSolve problems involving collisions and momentum conservation.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Ideal Gas LawCalculate pressure, volume, temperature, and moles for ideal gases.Related Thermodynamics topic.Bernoulli's PrincipleCalculate fluid velocities, pressures, and flow rates using Bernoulli's equation.Related Fluid Mechanics topic.