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Chapter 7: Impulse, Momentum, and Collisions

Chapter 7: Impulse, Momentum, and Collisions. Up to now we have considered forces which have a constant value throughout the motion and no explicit time duration

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Chapter 7: Impulse, Momentum, and Collisions

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  1. Chapter 7: Impulse, Momentum, and Collisions • Up to now we have considered forces which have a constant value 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 usually take the mean value F t tf t0 t

  2. 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 KE) - a vector, points in same direction as the velocity - units of kg m/s = N s • Linear momentum and KE are related

  3. 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 KE before and after the impact. Determine the impulse. Solution: Given: m = 750 kg,

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

  5. 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

  6. Example – Problem 7.13 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? y 0 Solution: Given: m = 0.500 kg, h0=1.20 m, h3=0.7 m, h1=h2=0 3 1 2

  7. 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

  8. 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

  9. 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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