Elastic Collision Formula Examples

Example 1: A 5 kg ball moving east at a speed of 6 m/s strikes a 2 kg ball at rest. Calculate the velocities of the two balls assuming a perfectly elastic collision.

Solution:

Given,

• m₁ = 5 kg,
• u₁ = 6 m/s,
• m₂ = 2 kg,
• u₂ = 0

To Find, v₁, v₂

We have,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

∴ (5 × 6) + (2 × 0) = 5v₁ + 2v₂

∴ 30 + 0 = 5v₁ + 2v₂

∴ 30 = 5v₁ + 2v₂  ⇢ (Equation 1)

u₁ + v₁ = u₂ + v₂

∴ 6 + v₁ = 0 + v₂

∴ 6 = -v₁ + v₂  ⇢ (Equation 2)

From Equation 1 and 2,

∴ v₂ = 8.57 m/s

Put v₂ = 8.57 in Equation 2,

-v₁ + 8.57 = 6

∴ v₁ = 2.57 m/s

Example 2: When a body of mass 4 kg collides with another body at rest, it continues to move in the same direction at a speed of one-third of its original speed. Determine the second body’s mass.

Solution:

Given,

• m₁ = 4 kg
• v₁ = u₁/3
• u₂ = 0

To Find, m₂

We have,

v₁ = ((m₁ – m₂) / (m₁ + m₂)) × u₁ + (2m₂u₂) / (m₁ + m₂)

∴ u₁/3 = ((4 – m₂) / (4 + m₂)) × u₁

∴ 4 + m₂ = 12 – 3m₂

∴ 4m₂ = 12 – 4

∴ m₂ = 2 kg

Example 3: A 1 kg ball travelling at 15 m/s collides head-on with another ball of unknown mass at rest, rebounding with a velocity of 10 m/s. What is the other ball’s mass?

Solution:

Given,

• m₁ = 1 kg
• u₁ = 15 m/s
• v₁ = -10 m/s (rebounds)
• u₂ = 0

to Find, m₂

We have,

v₁ = ((m₁ – m₂) / (m₁ + m₂)) × u₁ + (2m₂u₂) / (m₁ + m₂)

∴ -10 = ((1 – m₂) / (1 + m₂)) × 15

∴ -2 + (-2m₂) = 3 – 3m₂

∴ m₂ = 5 kg

Example 4: Assume that m₁ is 3 kg, m₂ is 5 kg, u₂ is at rest, v₁ is 2.2 m/s, and v₂ is 2 m/s in a specific example. What is the value of u₁?

Solution:

Given,

• m₁ = 3 kg
• m₂ = 5 kg
• u₂ = 0
• v₁ = 2.2 m/s
• v₂ = 2 m/s

To Find, u₁

We have,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

∴ 3 × u₁ + 5 × 0 = 3 × 2.2 + 5 × 2

∴ 3u₁ = 6.6 + 10

∴ u₁ = 5.53 m/s

Example 5: If u₁ is 4 m/s, u₂ is 2 m/s, and v₂ is 6 m/s, the following equation can be used. What is the significance of v₁?

Solution:

Given,

• u₁ = 4 m/s
• u₂ = 2 m/s
• v₂ = 6 m/s

To Find, v₁

u₁ + v₁ = v₂ + u₂

∴ 4 + v₁ = 6 + 2

∴ v₁ = 8 – 4

∴ v₁ = 4 m/s

Elastic Collision is the collision in which the kinetic energy of the system is conserved. A collision occurs when two or more object comes in direct contact with each other. the collision can be of two types that includes, Elastic Collision and Inelastic Collision.

In this article, we will learn about, Elastic Collision, Examples of Elastic Collision, Difference between Elastic Collision and Inelastic Collision, and others in detail.