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## Collisions

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**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**A**B uA Before collision, the total momentum is equal to the momentum of body A © D Hoult 2010**A**B vB After collision, the total momentum is equal to the momentum of body B © 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**Before the collision, the total momentum is equal to the**momentum of body A A B uA © D Hoult 2010**A**B vA vB © 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**If we want to calculate the velocities, vA and vB we will**use the A B vA vB © D Hoult 2010**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**The principle of conservation of momentum can be stated here**as © D Hoult 2010**The principle of conservation of momentum can be stated here**as mAuA = mAvA + mBvB © D Hoult 2010**The principle of conservation of momentum can be stated here**as mAuA = mAvA + mBvB If the collision is elastic then © D Hoult 2010**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**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 ½mAuA2 = ½mAvA2+ ½mBvB2 © D Hoult 2010**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 ½mAuA2 = ½mAvA2+ ½mBvB2 mAuA2 = mAvA2+ mBvB2 © D Hoult 2010**mAuA = mAvA + mBvB**mAuA2 = mAvA2+ mBvB2 From these two equations, vA and vB can be found © D Hoult 2010**mAuA = mAvA + mBvB**mAuA2 = mAvA2+ mBvB2 From these two equations, vA and vB can be found BUT © D Hoult 2010**It can be shown* that for an elastic collision, the velocity**of body A relative to body Bbefore the collision is equal to the velocity of body B relative to body Aafter the collision © D Hoult 2010**It can be shown* that for an elastic collision, the velocity**of body A relative to body Bbefore the collision is equal to the velocity of body B relative to body Aafter 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 Bbefore the collision is equal to the velocity of body B relative to body Aafter the collision uA In this case, the velocity of A relative to B, before the collision is equal to © D Hoult 2010**It can be shown* that for an elastic collision, the velocity**of body A relative to body Bbefore the collision is equal to the velocity of body B relative to body Aafter the collision uA 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 Bbefore the collision is equal to the velocity of body B relative to body Aafter the collision vA vB and the velocity of B relative to A after the collision is equal to © D Hoult 2010**It can be shown* that for an elastic collision, the velocity**of body A relative to body Bbefore the collision is equal to the velocity of body B relative to body Aafter the collision vA vB and the velocity of B relative to A after the collision is equal to vB – vA © D Hoult 2010**It can be shown* that for an elastic collision, the velocity**of body A relative to body Bbefore the collision is equal to the velocity of body B relative to body Aafter 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**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 mAuA = mAvA + mBvB equation 2 © D Hoult 2010**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**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 After the collision, the total momentum is the sum of the momenta of body A and body B © 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