2 7.1 The Impulse-Momentum Theorem There are many situations when theforce on an object is not constant.
3 7.1 The Impulse-Momentum Theorem DEFINITION OF IMPULSEThe impulse of a force is the product of the averageforce and the time interval during which the force acts:Impulse is a vector quantity and has the same directionas the average force.
5 7.1 The Impulse-Momentum Theorem DEFINITION OF LINEAR MOMENTUMThe linear momentum of an object is the productof the object’s mass times its velocity:Linear momentum is a vector quantity and has the samedirection as the velocity.
6 7.1 The Impulse-Momentum Theorem When a net force acts on an object, the impulse ofthis force is equal to the change in the momentumof the objectimpulsefinal momentuminitial momentum
7 7.2 The Principle of Conservation of Linear Momentum Internal forces – Forces that objects withinthe system exert on each other.External forces – Forces exerted on objectsby agents external to the system.
8 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 ofthe average external forces acting on the system is zero.
9 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 ofthe average external forces acting on the system is zero.In the top picture the net external force on thesystem is zero.In the bottom picture the net external force on thesystem is not zero.
10 7.3 Collisions in One Dimension The total linear momentum is conserved when two objectscollide, provided they constitute an isolated system.Elastic collision -- One in which the total kineticenergy of the system after the collision is equal tothe total kinetic energy before the collision.Inelastic collision -- One in which the total kineticenergy of the system after the collision is not equalto the total kinetic energy before the collision; if theobjects stick together after colliding, the collision issaid to be completely inelastic.
11 7.3 Collisions in One Dimension Example 8 A Ballistic PendulumThe mass of the block of woodis 2.50-kg and the mass of thebullet is kg. The blockswings to a maximum height of0.650 m above the initial position.Find the initial speed of thebullet.
12 7.3 Collisions in One Dimension Apply conservation of momentumto the collision:
13 7.3 Collisions in One Dimension Applying conservation of energyto the swinging motion:
16 The center of mass is a point that represents the average location for the total mass of a system.
17 Problems to be solved7.8, 7.34, 7.41, 7.44, 7.60, 7.64B7.1 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
18 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
19 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
20 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