A –Level Physics: Further Mechanics- Inelastic and Elastic Collisions

Objectives: Spec point: 20. know and understand Newton’s third law of motion and know the properties of pairs of forces in an interaction between two bodies Spec point: 21 understand that momentum is defined as p = mv Spec point: 22 know the principle of conservation of linear momentum, understand how to relate this to Newton’s laws of motion and understand how to apply this to problems in one dimension Additional Skills Gained: Estimation Laying out answers Derivation

Starter Activity You have 2 minutes to discuss and 5 minutes to write an explanation in terms of momentum and energy of how a Newton’s cradle functions

Elastic Vs Inelastic “In an elastic collision, both momentum and total kinetic energy are conserved (same before and after)” “In an inelastic collision, momentum is conserved but as some energy is transferred into other forms, the total kinetic energy is not conserved” Describe why the image on the left shows an inelastic and elastic situation. Inelastic- gradually reduces in vertical displacement and distance so energy has been transferred into another form (lost) therefore kinetic is NOT conserved.

Before we start… In every situation we cover in this topic, we will deal with it in the same tidy way. You will always draw a basic diagram of the situation BEFORE and AFTER the collision/explosion. Underneath/on top of the diagram you add quantities. E.g:

Is it elastic or inelastic? Calculate the kinetic energy before and after to determine whether this collision is elastic or inelastic. BEFORE AFTER Mass: 300kg Start Velocity (u) = 5ms-1 Mass: 300kg Start Velocity (u) = 1ms-1 Mass: 300kg End Velocity (v) = 2ms-1 Mass: 300kg End Velocity (v) = 4ms-1 Before = 3750J and 150J= 3900J total. After= 600J and 2400J= 3000J total. So its inelastic. Combine E(kinetic)= ½ mv2 and p=mv to give an equation for kinetic energy in terms of mass and momentum

CERN: The large hadron collider CERN is a collection of particle accelerators which uses alternating polarity and a magnetic field to speed particles to 99.9% the speed of light. They are then directed at one another and their collisions are analysed. These collisions can tell us the mass of the unknown particles simply by calculating the momentum before and after the collision!

Particle Collision: Worked Example “ A CERN researcher calculates the momentum transfer in an elastic collision to determine the mass of a mystery particle. The mystery particle is moving at 10% the speed of light and it hits a neutron (mass 1.67x10-27kg) causing the neutron to accelerate from rest to 3.4x106ms-1. The mystery particle rebounds at a speed of 1.09x103 Calculate the mass of the mystery particle.” Draw a momentum diagram (before and after) for this question with quantities labelled BEFORE AFTER Mass: Mystery Start Velocity (u) = 3x107ms-1 Mass: 1.67x10-27kg Start Velocity (u) = 0ms-1 Mass: Mystery End Velocity (u) = 1.09x103ms-1 Mass: 1.67x10-27kg End Velocity (u) = 3.4x106ms-1

Step 2: Calculate the total momentum before Continued.. BEFORE AFTER Mass: Mystery Start Velocity (u) = 3x107ms-1 Mass: 1.67x10-27kg Start Velocity (u) = 0ms-1 Mass: Mystery End Velocity (u) = 1.09x103ms-1 Mass: 1.67x10-27kg End Velocity (u) = 3.4x106ms-1 Step 2: Calculate the total momentum before Step 3: As momentum before=momentum after. Solve to find the mass of the mystery particle

A –Level Physics: Further Mechanics- Vector Collision and Impulse

Starter Activity Explain with examples the difference between elastic and inelastic collisions

Impulse Impulse is the “product of a force applied for a certain time” and can be used to get an object moving or to stop its motion. A.k.a: Impulse = Force x Time So as this is = kgms-1 then it’s the same as saying ‘a change in momentum’

2D collisions More often than not, collisions between two objects is not completely in a single plane (e.g. horizontal). Most commonly, collisions occur at an angle. The momentum equations you need to complete are the same in theory, just you need to work out the directional components separately… Type 1: Horizontal and Vertical resolving: As vectors at right angles don’t affect each other (remember horizontal and vertical are isolated). Momentum has to be conserved in each direction. Type 2: Parallel and Perpendicular resolving: For uniformly spherical objects, momentum is only transferred parallel to the line of impact. If one object starts off at rest, its final velocity will be along the line of impact (centre of one sphere to centre of other). Copy diagram on board from page 92 of revision guide

Type 1: Vertical and Horizontal Ball A collides with a stationary ball B, as shown in the diagram on the board. After the collision, the two balls move off as shown in the ‘after’ situation. Ball A has a mass of 40g. Calculate the mass, m, of ball B. To calculate this, you are going to need to resolve in either the horizontal or the vertical plane. Remember, if using either you need to assign a specific direction as ‘positive’. Worked example page 92 revision guide Once you have worked it out for the horizontal OR vertical, then check your answer by doing it for the other!

Type 2: Parallel and Perp. Worked example page 92 revision guide at bottom

Practice Questions 1. A 4.0kg object is travelling south at a velocity of 2.8m/s when it collides with a 6.0kg object travelling East at a velocity of 3.0m/s. If these two objects stick together upon collision, at what velocity do the combined masses move immediately after they collide? 2. A 4.0kg object is moving East at an unknown velocity when it collides with a 6.1kg stationary object. After the collision, the 4.0kg object us travelling at a velocity of 2.8m/s E32ofN and the 6.1kg object us travelling at a velocity of 1.5m/s E41ofS. What was the velocity of the 4.0kg object before the collision? 3. An object explodes into 3 equal masses. One mass moves East at a velocity of 15.0m/s. If a second mass moves at a velocity of 10.0m/s E45oS, what is the velocity of the third mass? 1=2.12m/s@ E 31.9o N 2=4.1 m/s East 3=23.2m/s @W17.8oN