What is meant by a collision in one dimension?

It is a collision in which all the bodies move along the same straight line both before and after the impact, so their momenta can be handled as positive and negative numbers along that line.

A 4.0 kg body moving at 6.0 m s⁻¹ strikes a stationary 2.0 kg body and continues forward at 2.0 m s⁻¹. Calculate the velocity of the 2.0 kg body afterwards.

Momentum gives 24 = (4.0 × 2.0) + 2.0v, so 2.0v = 16 and v = 8.0 m s⁻¹ in the original direction; checking back, 8.0 + 16 = 24 kg m s⁻¹, which is the momentum before.

A 3.0 kg body moving right at 4.0 m s⁻¹ meets a 2.0 kg body moving left at 5.0 m s⁻¹ head-on, and they stick together. Calculate their common velocity.

Taking right as positive, the total momentum is 12 − 10 = 2.0 kg m s⁻¹, so v = 2.0 ÷ 5.0 = 0.40 m s⁻¹ to the right; checking back, 5.0 × 0.40 = 2.0 kg m s⁻¹, which is the total before.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

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Linear Momentum and Impulse

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Linear Momentum and Impulse

Collisions in one dimension

3 things to know
Unit AS 1

Overview

Collision in one dimension and steps used to solve a one-dimensional collision problem.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the momentum equation for a one-dimensional collision between two bodies, defining each symbol.

Numbers

A 2.0 kg trolley travelling at 5.0 m s⁻¹ collides with a stationary 3.0 kg trolley and the two stick together. Calculate their common velocity.

Process

Outline the steps used to solve a one-dimensional collision problem.

Questions from this subtopic

Each one with the model answer underneath.

1
What is meant by a collision in one dimension?
Model answer
It is a collision in which all the bodies move along the same straight line both before and after the impact, so their momenta can be handled as positive and negative numbers along that line.
2
State the momentum equation for a one-dimensional collision between two bodies, defining each symbol.
Model answer
The equation is m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where m₁ and m₂ are the two masses in kilograms, u₁ and u₂ are their velocities before the collision and v₁ and v₂ their velocities after, all in m s⁻¹.
3
Outline the steps used to solve a one-dimensional collision problem.
Model answer
Choose one direction along the line as positive, write down the mass and velocity of each body before and after with the correct signs, set the total momentum after equal to the total before, and solve for the unknown, giving both its magnitude and its direction.
4
A 2.0 kg trolley travelling at 5.0 m s⁻¹ collides with a stationary 3.0 kg trolley and the two stick together. Calculate their common velocity.
Model answer
Momentum gives 2.0 × 5.0 = 5.0 × v, so v = 10 ÷ 5.0 = 2.0 m s⁻¹ in the original direction; checking back, 5.0 × 2.0 = 10 kg m s⁻¹, which is the momentum before.
5
A 4.0 kg body moving at 6.0 m s⁻¹ strikes a stationary 2.0 kg body and continues forward at 2.0 m s⁻¹. Calculate the velocity of the 2.0 kg body afterwards.
Model answer
Momentum gives 24 = (4.0 × 2.0) + 2.0v, so 2.0v = 16 and v = 8.0 m s⁻¹ in the original direction; checking back, 8.0 + 16 = 24 kg m s⁻¹, which is the momentum before.
6
A 3.0 kg body moving right at 4.0 m s⁻¹ meets a 2.0 kg body moving left at 5.0 m s⁻¹ head-on, and they stick together. Calculate their common velocity.
Model answer
Taking right as positive, the total momentum is 12 − 10 = 2.0 kg m s⁻¹, so v = 2.0 ÷ 5.0 = 0.40 m s⁻¹ to the right; checking back, 5.0 × 0.40 = 2.0 kg m s⁻¹, which is the total before.

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