Download File - The Physics Doctor

A –Level Physics:
Further MechanicsInelastic 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.
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
Mass: 300kg
Mass: 300kg
Mass: 300kg
Start Velocity (u)
= 5ms-1
Start Velocity (u)
= 1ms-1
End Velocity (v)
= 2ms-1
End Velocity (v)
= 4ms-1
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
Mass: Mystery
Mass: 1.67x10-27kg
Start Velocity (u) Start Velocity (u)
= 3x107ms-1
= 0ms-1
AFTER
Mass: Mystery
Mass: 1.67x10-27kg
End Velocity (u)
= 1.09x103ms-1
End Velocity (u)
= 3.4x106ms-1
Continued..
BEFORE
Mass: Mystery
Mass: 1.67x10-27kg
Start Velocity (u) Start Velocity (u)
= 3x107ms-1
= 0ms-1
AFTER
Mass: Mystery
Mass: 1.67x10-27kg
End Velocity (u)
= 1.09x103ms-1
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 MechanicsVector 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).
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’.
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.
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?