collisions © d hoult 2010. elastic collisions © d hoult 2010
Post on 24-Dec-2015
223 Views
Preview:
TRANSCRIPT
Collisions
© D Hoult 2010
Elastic Collisions
© D Hoult 2010
Elastic Collisions
1 dimensional collision
© D Hoult 2010
Elastic Collisions
1 dimensional collision: bodies of equal mass
© D Hoult 2010
Elastic Collisions
1 dimensional collision: bodies of equal mass
(one body initially stationary)
© D Hoult 2010
Elastic Collisions
1 dimensional collision: bodies of equal mass
(one body initially stationary)
© D Hoult 2010
© D Hoult 2010
Before collision, the total momentum is equal to the momentum of body A
A B
uA
© D Hoult 2010
After collision, the total momentum is equal to the momentum of body B
A B
vB
© D Hoult 2010
The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies)
© D Hoult 2010
The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies)
mAuA = mBvB
© D Hoult 2010
The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies)
mAuA = mBvB
so, if the masses are equal the velocity of B after
© D Hoult 2010
The principle of conservation of momentum states that the total momentum after collision equal to the total momentum before collision (assuming no external forces acting on the bodies)
mAuA = mBvB
so, if the masses are equal the velocity of B after is equal to the velocity of A before
© D Hoult 2010
Bodies of different mass
© D Hoult 2010
A B
© D Hoult 2010
A B
uA
© D Hoult 2010
A B
uA
Before the collision, the total momentum is equal to the momentum of body A
© D Hoult 2010
A B
vA vB
© D Hoult 2010
A B
vA vB
After the collision, the total momentum is the sum of the momenta of body A and body B
© D Hoult 2010
A B
vA vB
If we want to calculate the velocities, vA and vB we will use the
© D Hoult 2010
A B
vA vB
If we want to calculate the velocities, vA and vB we will use the principle of conservation of momentum
© D Hoult 2010
The principle of conservation of momentum can be stated here as
© D Hoult 2010
mAuA = mAvA + mBvB
The principle of conservation of momentum can be stated here as
© D Hoult 2010
mAuA = mAvA + mBvB
If the collision is elastic then
The principle of conservation of momentum can be stated here as
© D Hoult 2010
mAuA = mAvA + mBvB
If the collision is elastic then kinetic energy is also conserved
The principle of conservation of momentum can be stated here as
© D Hoult 2010
mAuA = mAvA + mBvB
If the collision is elastic then kinetic energy is also conserved
½ mAuA2 = ½ mAvA
2 + ½ mBvB
2
The principle of conservation of momentum can be stated here as
© D Hoult 2010
mAuA = mAvA + mBvB
If the collision is elastic then kinetic energy is also conserved
mAuA2 = mAvA
2 + mBvB
2
½ mAuA2 = ½ mAvA
2 + ½ mBvB
2
The principle of conservation of momentum can be stated here as
© D Hoult 2010
From these two equations, vA and vB can be found
mAuA = mAvA + mBvB
mAuA2 = mAvA
2 + mBvB
2
© D Hoult 2010
From these two equations, vA and vB can be found
mAuA = mAvA + mBvB
mAuA2 = mAvA
2 + mBvB
2
BUT
© D Hoult 2010
It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision
© D Hoult 2010
It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision
* a very useful phrase !© D Hoult 2010
It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision
In this case, the velocity of A relative to B, before the collision is equal to
uA
© D Hoult 2010
It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision
In this case, the velocity of A relative to B, before the collision is equal to uA
uA
© D Hoult 2010
It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision
and the velocity of B relative to A after the collision is equal to
vA vB
© D Hoult 2010
It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision
and the velocity of B relative to A after the collision is equal to vB – vA
vA vB
© D Hoult 2010
It can be shown* that for an elastic collision, the velocity of body A relative to body B before the collision is equal to the velocity of body B relative to body A after the collision
for proof click here
and the velocity of B relative to A after the collision is equal to vB – vA
vA vB
© D Hoult 2010
We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision
equation 1
© D Hoult 2010
We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision
equation 1
equation 2
mAuA = mAvA + mBvB
© D Hoult 2010
We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision
equation 1
equation 2
mAuA = mAvA + mBvB
uA = vB – vA
© D Hoult 2010
© D Hoult 2010
© D Hoult 2010
A B
uA
© D Hoult 2010
Before the collision, the total momentum is equal to the momentum of body A
A B
uA
© D Hoult 2010
After the collision, the total momentum is the sum of the momenta of body A and body B
A B
vA vB
© D Hoult 2010
Using the principle of conservation of momentum
© D Hoult 2010
Using the principle of conservation of momentum
mAuA = mAvA + mBvB
© D Hoult 2010
Using the principle of conservation of momentum
mAuA = mAvA + mBvB
A B
vA vB
© D Hoult 2010
Using the principle of conservation of momentum
mAuA = mAvA + mBvB
A B
vA vB
© D Hoult 2010
Using the principle of conservation of momentum
mAuA = mAvA + mBvB
A B
vA vB
One of the momenta after collision will be a negative quantity
© D Hoult 2010
2 dimensional collision
© D Hoult 2010
2 dimensional collision
© D Hoult 2010
© D Hoult 2010
A B
© D Hoult 2010
A B
Before the collision, the total momentum is equal to the momentum of body A
© D Hoult 2010
© D Hoult 2010
After the collision, the total momentum is equal to the sum of the momenta of both bodies© D Hoult 2010
Now the sum must be a vector sum
© D Hoult 2010
mAvA
© D Hoult 2010
mBvB
mAvA
© D Hoult 2010
mBvB
mAvA
© D Hoult 2010
mBvB
mAvA
© D Hoult 2010
mBvB
mAvA
© D Hoult 2010
p
mBvB
mAvA
© D Hoult 2010
mBvB
mAvA
p
mAuA
© D Hoult 2010
mBvB
mAvA
p
mAuA
© D Hoult 2010
mBvB
mAvA
p
mAuA
© D Hoult 2010
p = mAuA
mBvB
mAvA
p
mAuA
© D Hoult 2010
2 dimensional collision: Example
Body A has initial speed uA = 50 ms-1
© D Hoult 2010
2 dimensional collision: Example
Body A has initial speed uA = 50 ms-1
Body B is initially stationary
© D Hoult 2010
2 dimensional collision: Example
Body A has initial speed uA = 50 ms-1
Body B is initially stationary
Mass of A = mass of B = 2 kg
© D Hoult 2010
2 dimensional collision: Example
Body A has initial speed uA = 50 ms-1
Body B is initially stationary
Mass of A = mass of B = 2 kg
After the collision, body A is found to be moving at speed vA = 25 ms-1 in a direction at 60° to its original direction of motion
© D Hoult 2010
2 dimensional collision: Example
Body A has initial speed uA = 50 ms-1
Body B is initially stationary
Mass of A = mass of B = 2 kg
After the collision, body A is found to be moving at speed vA = 25 ms-1 in a direction at 60° to its original direction of motion
Find the kinetic energy possessed by body B after the collision
© D Hoult 2010
top related