How is momentum conserved in a two-dimensional collision?

Separately in each of two perpendicular directions, using components.

What is an elastic collision?

One in which total kinetic energy is conserved.

What is an inelastic collision?

One in which some kinetic energy is transferred to other forms, such as thermal energy or sound.

Is momentum conserved in an inelastic collision?

Yes, if no resultant external force acts. Only kinetic energy is not conserved.

How do two identical objects move after an elastic, non-head-on collision with one at rest?

They move off at right angles to each other.

How do you show a collision is elastic?

Calculate the total kinetic energy before and after; they are equal.

How do you derive Ek = p²/2m?

Substitute v = p/m into Ek = ½mv².

In 2D collisions, what is the momentum perpendicular to the original direction if one object starts at rest?

Zero before the collision, so the perpendicular components after must cancel.

In the ICT core practical, how are speeds found?

From the distance moved between frames, calibrated with a ruler, divided by the time between frames.

Give a source of uncertainty in the video analysis of collisions.

Reading the positions of the spheres, the ruler calibration, or friction on the surface.

Collisions in two dimensionsEdexcel A-Level Physics: Flashcards

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State the principle of conservation of linear momentum.

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State the principle of conservation of linear momentum.: The total momentum of a system is constant, provided no resultant external force acts on it.
How is momentum conserved in a two-dimensional collision?: Separately in each of two perpendicular directions, using components.
What is an elastic collision?: One in which total kinetic energy is conserved.
What is an inelastic collision?: One in which some kinetic energy is transferred to other forms, such as thermal energy or sound.
Is momentum conserved in an inelastic collision?: Yes, if no resultant external force acts. Only kinetic energy is not conserved.
How do two identical objects move after an elastic, non-head-on collision with one at rest?: They move off at right angles to each other.
How do you show a collision is elastic?: Calculate the total kinetic energy before and after; they are equal.
What is the formula for kinetic energy in terms of momentum?: Ek = p²/2m
How do you derive Ek = p²/2m?: Substitute v = p/m into Ek = ½mv².
In 2D collisions, what is the momentum perpendicular to the original direction if one object starts at rest?: Zero before the collision, so the perpendicular components after must cancel.
In the ICT core practical, how are speeds found?: From the distance moved between frames, calibrated with a ruler, divided by the time between frames.
Give a source of uncertainty in the video analysis of collisions.: Reading the positions of the spheres, the ruler calibration, or friction on the surface.

Exam questions on Collisions in two dimensions

A snooker cue ball of mass 0.17 kg, travelling at 2.0 m s⁻¹, strikes a stationary ball of identical mass. After the collision the cue ball moves at 1.2 m s⁻¹ at 53° to its original direction, and the other ball moves off at 1.6 m s⁻¹ on the other side of the original direction.
Calculate the angle between the direction of motion of the second ball and the original direction of the cue ball.2 marks
A car of mass 1500 kg travelling east at 12 m s⁻¹ collides at a junction with a van of mass 1000 kg travelling north at 15 m s⁻¹. The vehicles lock together and move off as one body.
Calculate the speed of the wreckage immediately after the collision.2 marks
A neutron of mass 1.67 × 10⁻²⁷ kg and momentum 3.34 × 10⁻²¹ kg m s⁻¹ collides with a stationary proton, whose mass can be taken as 1.67 × 10⁻²⁷ kg. After the collision the neutron has momentum 2.74 × 10⁻²¹ kg m s⁻¹ at 35° to its original direction, and the proton has momentum 1.92 × 10⁻²¹ kg m s⁻¹ at 55° on the other side of the original direction.
Show that the kinetic energy of a non-relativistic particle of mass m and momentum p is p²/2m, and use it to calculate the initial kinetic energy of the neutron.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).