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Collisions © D Hoult 2010
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Elastic Collisions © D Hoult 2010
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1 dimensional collision
Elastic Collisions 1 dimensional collision © D Hoult 2010
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1 dimensional collision: bodies of equal mass
Elastic Collisions 1 dimensional collision: bodies of equal mass © D Hoult 2010
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1 dimensional collision: bodies of equal mass
Elastic Collisions 1 dimensional collision: bodies of equal mass (one body initially stationary) © D Hoult 2010
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1 dimensional collision: bodies of equal mass
Elastic Collisions 1 dimensional collision: bodies of equal mass (one body initially stationary) © D Hoult 2010
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© D Hoult 2010
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A B uA Before collision, the total momentum is equal to the momentum of body A © D Hoult 2010
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After collision, the total momentum is equal to the momentum of body B
vB After collision, the total momentum is equal to the momentum of body B © D Hoult 2010
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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
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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
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so, if the masses are equal the velocity of B after
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
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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
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Bodies of different mass
© D Hoult 2010
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A B © D Hoult 2010
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A B uA © D Hoult 2010
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Before the collision, the total momentum is equal to the momentum of body A
© D Hoult 2010
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A B vA vB © D Hoult 2010
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After the collision, the total momentum is the sum of the momenta of body A and body B
vA vB © D Hoult 2010
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If we want to calculate the velocities, vA and vB we will use the
© D Hoult 2010
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If we want to calculate the velocities, vA and vB we will use the principle of conservation of momentum A B vA vB © D Hoult 2010
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The principle of conservation of momentum can be stated here as
© D Hoult 2010
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The principle of conservation of momentum can be stated here as
mAuA = mAvA + mBvB © D Hoult 2010
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The principle of conservation of momentum can be stated here as
mAuA = mAvA + mBvB If the collision is elastic then © D Hoult 2010
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The principle of conservation of momentum can be stated here as
mAuA = mAvA + mBvB If the collision is elastic then kinetic energy is also conserved © D Hoult 2010
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The principle of conservation of momentum can be stated here as
mAuA = mAvA + mBvB If the collision is elastic then kinetic energy is also conserved ½ mAuA2 = ½ mAvA2 + ½ mBvB2 © D Hoult 2010
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The principle of conservation of momentum can be stated here as
mAuA = mAvA + mBvB If the collision is elastic then kinetic energy is also conserved ½ mAuA2 = ½ mAvA2 + ½ mBvB2 mAuA2 = mAvA2 + mBvB2 © D Hoult 2010
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From these two equations, vA and vB can be found
mAuA = mAvA + mBvB mAuA2 = mAvA2 + mBvB2 From these two equations, vA and vB can be found © D Hoult 2010
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From these two equations, vA and vB can be found
mAuA = mAvA + mBvB mAuA2 = mAvA2 + mBvB2 From these two equations, vA and vB can be found BUT © D Hoult 2010
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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
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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
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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 uA In this case, the velocity of A relative to B, before the collision is equal to © D Hoult 2010
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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 uA In this case, the velocity of A relative to B, before the collision is equal to uA © D Hoult 2010
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and the velocity of B relative to A after the collision is equal to
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 vA vB and the velocity of B relative to A after the collision is equal to © D Hoult 2010
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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 vA vB and the velocity of B relative to A after the collision is equal to vB – vA © D Hoult 2010
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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 vA vB and the velocity of B relative to A after the collision is equal to vB – vA for proof click here © D Hoult 2010
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We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision equation 1 © D Hoult 2010
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We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision equation 1 mAuA = mAvA + mBvB equation 2 © D Hoult 2010
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We therefore have two easier equations to “play with” to find the velocities of the bodies after the collision equation 1 mAuA = mAvA + mBvB equation 2 uA = vB – vA © D Hoult 2010
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© D Hoult 2010
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© D Hoult 2010
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A B uA © D Hoult 2010
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A B uA Before the collision, the total momentum is equal to the momentum of body A © D Hoult 2010
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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
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Using the principle of conservation of momentum
© D Hoult 2010
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Using the principle of conservation of momentum
mAuA = mAvA + mBvB © D Hoult 2010
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Using the principle of conservation of momentum
mAuA = mAvA + mBvB A B vA vB © D Hoult 2010
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Using the principle of conservation of momentum
mAuA = mAvA + mBvB A B vA vB © D Hoult 2010
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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
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2 dimensional collision
© D Hoult 2010
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2 dimensional collision
© D Hoult 2010
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© D Hoult 2010
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A B © D Hoult 2010
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A B Before the collision, the total momentum is equal to the momentum of body A © D Hoult 2010
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© D Hoult 2010
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After the collision, the total momentum is equal to the sum of the momenta of both bodies
© D Hoult 2010
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Now the sum must be a vector sum
© D Hoult 2010
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mAvA © D Hoult 2010
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mAvA mBvB © D Hoult 2010
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mAvA mBvB © D Hoult 2010
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mAvA mBvB © D Hoult 2010
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mAvA mBvB © D Hoult 2010
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mAvA p mBvB © D Hoult 2010
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mAvA p mAuA mBvB © D Hoult 2010
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mAvA p mAuA mBvB © D Hoult 2010
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mAvA p mAuA mBvB © D Hoult 2010
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mAvA p mAuA mBvB p = mAuA © D Hoult 2010
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2 dimensional collision: Example
Body A has initial speed uA = 50 ms-1 © D Hoult 2010
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2 dimensional collision: Example
Body A has initial speed uA = 50 ms-1 Body B is initially stationary © D Hoult 2010
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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
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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
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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
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