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Chapter 7 Impulse and Momentum

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**7.1 The Impulse-Momentum Theorem**

There are many situations when the force on an object is not constant.

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**7.1 The Impulse-Momentum Theorem**

DEFINITION OF IMPULSE The impulse of a force is the product of the average force and the time interval during which the force acts: Impulse is a vector quantity and has the same direction as the average force.

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**7.1 The Impulse-Momentum Theorem**

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**7.1 The Impulse-Momentum Theorem**

DEFINITION OF LINEAR MOMENTUM The linear momentum of an object is the product of the object’s mass times its velocity: Linear momentum is a vector quantity and has the same direction as the velocity.

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**7.1 The Impulse-Momentum Theorem**

When a net force acts on an object, the impulse of this force is equal to the change in the momentum of the object impulse final momentum initial momentum

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**7.2 The Principle of Conservation of Linear Momentum**

Internal forces – Forces that objects within the system exert on each other. External forces – Forces exerted on objects by agents external to the system.

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**7.2 The Principle of Conservation of Linear Momentum**

The total linear momentum of an isolated system is constant (conserved). An isolated system is one for which the sum of the average external forces acting on the system is zero.

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**7.2 The Principle of Conservation of Linear Momentum**

The total linear momentum of an isolated system is constant (conserved). An isolated system is one for which the sum of the average external forces acting on the system is zero. In the top picture the net external force on the system is zero. In the bottom picture the net external force on the system is not zero.

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**7.3 Collisions in One Dimension**

The total linear momentum is conserved when two objects collide, provided they constitute an isolated system. Elastic collision -- One in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision. Inelastic collision -- One in which the total kinetic energy of the system after the collision is not equal to the total kinetic energy before the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.

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**7.3 Collisions in One Dimension**

Example 8 A Ballistic Pendulum The mass of the block of wood is 2.50-kg and the mass of the bullet is kg. The block swings to a maximum height of 0.650 m above the initial position. Find the initial speed of the bullet.

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**7.3 Collisions in One Dimension**

Apply conservation of momentum to the collision:

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**7.3 Collisions in One Dimension**

Applying conservation of energy to the swinging motion:

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**7.3 Collisions in One Dimension**

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**7.4 Collisions in Two Dimensions**

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**The center of mass is a point that represents the average location for **

the total mass of a system.

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Problems to be solved 7.8, 7.34, 7.41, 7.44, 7.60, 7.64 B7.1 A 1000kg car moving at 20m/s hits a 2000kg parked car head on. How much mechanical energy is dissipated if the collision is (a) elastic, (b) completely inelastic? Ans.: (a)None, because mechanical energy is conserved during elastic collisions. (b) 13.33×104J

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B7.2 A bullet of mass 10-2kg and initial horizontal velocity of 250m/s strikes and is embedded in a 1kg wooden block. The wooden block hangs on the end of a long string. (a) What is the velocity of the block and bullet after impact? (b) How high will the block and bullet swing upward? Ans: (a) 2.48m/s (b) 0.31m

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B7.3 Two cars approaching each other along streets that meet at a right angle collide at the intersection. After the crash, they stick together. If one car has a mass of 1450kg and an initial speed of 11.5m/s and the other has a mass of 1750kg and an initial speed of 15.5m/s, what will be their speed and direction immediately after impact? Ans: 9.95m/s ; 58.4º

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**B7. 4 A billiard ball moving at 10**

B7.4 A billiard ball moving at 10.0m/s along the positive x-axis collides with a second billiard ball at rest. The balls have identical masses. After the collision, the incoming (or incident) ball moves on with a speed of 7.7m/s at an angle of 40⁰ from the x-axis. What are the speed and direction of motion of the struck ball? Ans: 6.43m/s ; º

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