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Problem of the Day An 1800 kg car stopped at a traffic light is struck from the rear by a 900 kg car, and the two become entangled, moving along the same path as that of the originally moving car. a) If the smaller car were moving at 20.0 m/s before the collision, what is the velocity of the entangled cars after the collision ?

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**b) Suppose we reverse the masses of the cars**

– a stationary 900 kg car is struck by a moving 1800 kg car. Is the final speed the same as before ?

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OBJECTIVES Compare and contrast Inelastic collisions and Elastic collisions. Derive the Elastic & Inelastic equations. Use Equations to solve for the momentum and velocity of masses in 1-D collisions. Create an AP Physics Part 2 Free Response momentum problem and solve it on the board.

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DEMO TIME

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**Lesson 4 : Collisions in One-Dimension “perfectly inelastic”**

Elastic Collisions The total KE (as well as total momentum) of the system is the same before and after the collision. Inelastic Collisions The total KE of the system is not the same before and after the collision (even though the momentum of the system is conserved). KE is conserved KE is not conserved “perfectly inelastic” “inelastic”

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**Perfectly Inelastic Collisions**

when the colliding objects stick together m1v1i + m2v2i = (m1 + m2)vf

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Elastic Collisions m1v1i + m2v2i = m1v1f + m2v2f ½ m1v1i2 + ½ m2v2i2 = ½ m1v1f2 + ½ m2v2f2

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DEMO LAB TIME

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Example 4 : AP 1995 #1 A 5 kg ball initially at rest at the edge of a 2 m long, 1.2 m high frictionless table, as shown above. A hard plastic cube of mass 0.5 kg slides across the table at a speed of 26 m/s and strikes the ball, causing the ball to leave the table in the direction in which the cube was moving.

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**The figure below shows a graph of the force exerted on the ball by the cube as a function of time.**

a) Determine the total impulse given to the ball.

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**b) Determine the horizontal velocity of the ball immediately after the collision.**

c) Determine the following for the cube immediately after the collision. i. Its speed ii. Its direction of travel (right or left), if moving

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**d) Determine the kinetic energy dissipated in the collision.**

e) Determine the distance between the two points of impact of the objects with the floor.

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