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Chapter 9: Impulse, Momentum, and Collisions Up to now we have considered forces which have a constant value (except the spring) throughout the motion and no explicit time duration Now, lets consider a force which has a time duration (usually short) and with a magnitude that may vary with time – examples: a bat hitting a baseball, a car crash, a asteroid or comet striking the Earth, etc. It is difficult to deal with a time-varying force, so we might take the mean value F t t0t0 tftf tt

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Define a new quantity by multiplying the force by the time duration - a vector, points in the same direction as the force - has units of N s Define another quantity, but which gives a measure of the motion (similar to K) - a vector, points in same direction as the velocity - units of kg m/s = N s Linear momentum and K are related

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Example A car of mass 760 kg is traveling east at a speed of 10.0 m/s. The car hits a wall and rebounds (moving west) with a speed of 0.100 m/s. Determine its momentum and K before and after the impact. Determine the impulse. Solution: Given: m = 750 kg,

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Now, from the definition of acceleration and Newton’s 2 nd Law:

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Impulse-Momentum Theorem The Impulse-Momentum Theorem says that if an impulse (force*time duration) is applied to an object, its momentum changes In this example, the impact of the car with the wall applies an impulse to the car car’s p changes

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Example Problem A 0.500-kg ball is dropped from rest at a point 1.20 m above the floor. The ball rebounds straight upward to a height of 0.700 m. What are the magnitude and direction of the impulse of the net force applied to the ball during the collision with the floor? 0 12 3 y Solution: Given: m = 0.500 kg, h 0 =1.20 m, h 3 =0.7 m, h 1 =h 2 =0

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Method: need momentum before and after impact need velocities use conservation of energy Conservation of mechanical energy is satisfied between 0 and 1 and between 2 and 3, but not between 1 and 2

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Collisions Involves two (or more) objects which may have their motion (velocity, momentum) altered by collisions These concepts are applicable to the collisions of atoms, billiard balls, cars, planetary objects, galaxies, etc. Say, we have a collection of interacting particles numbered 1, 2, 3, … We can define the Total Momentum of the system (all the particles) as just the sum of all the individual momenta

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Imagine that these particles interact in some way – collide and scatter As long as there are no net external forces acting on the system (collection of objects), the Total Linear Momentum does not change Which means the Total Linear Momentum is the same before the collision, during the collision, and after the collision Conservation of Linear Momentum

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Momentum and Impulse. March 24, 2009 Momentum and Momentum Conservation Momentum Impulse Conservation of Momentum Collision in 1-D Collision.

Momentum and Impulse. March 24, 2009 Momentum and Momentum Conservation Momentum Impulse Conservation of Momentum Collision in 1-D Collision.

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