Chapter 9: Momentum and Conservation Newton s Laws applied
Dynamics of Physics Dynamics are the CAUSES of CHANGE in Physics. Recall that position is changed by velocity. Velocity is changed by acceleration. Acceleration is caused by a net force. Properties that remain constant are described as CONSERVED.
Impulse and Momentum Momentum is described by Newton s 3 laws of motion as the quantity of motion. Depends on inertia. If no net force acts on a body, its velocity is constant. http://www.youtube.com/watch?v=oduzgofy9qa&nr=1 If a net force acts on a body, velocity is changed. (acceleration) Forces on objects change over time. Identify before, during, and after in an interaction.
Developing Impulse F = ma can be rewritten to substitute a rate of change in velocity for acceleration. F m v t multiplying both sides by Δt, then F t m v Impulse is a force over a period of time. (N*s) Since a FORCE causes a velocity to CHANGE, then an IMPULSE causes MOMENTUM to change. (kg*m/s) http://www.youtube.com/watch?v=gtvqtgtfic8&feature=channel
Impulse-Momentum Theorem Can also be stated as v v v mv mv 2 1 2 1 The symbol for Momentum is ρ. Thus, ρ= mv. F t 2 1 Impulse = Change in Momentum The force is not constant, and the impulse is found using the AVERAGE FORCE times the time interval, or finding the area under the curve of a force-time graph. http://www.youtube.com/watch?v=2y57pw_iwlk&feature=related
Using the Impulse-Mmt theorem What is the final momentum of a tennis ball after being hit by a racket? If the area under the curve of a F-t graph shows an average Impulse of 1.4 N-s, then the momentum gained by the ball must be 1.4 kg-m/s. Rearrange the I-M theorem to show: F t 2 If the ball has a mass of 0.060 kg, then its velocity will be 1 v 2 m = 23 m/s
Vectors Velocity is a vector, so momentum is a vector. Force is a vector, so impulse is a vector. Vectors have positive and negative directions associated with them. Traditionally, positive direction is right and left is negative. (how does mv club compare to mv ball in the previous example?)
Saving lives with Physics A large change in momentum comes from a large impulse. Since Impulse is FΔt, you can have a large force OR a large time of contact to produce a large impulse. In a car crash, an air bag extends the TIME of contact to reduce the FORCE of impact. The Impulse is the same whether you hit the air bag, or the steering wheel. Thus the Δmv is the same. Car crash video clip Car crash with seatbelts
Angular Momentum Just like linear momentum is mv, a ROTATING object has momentum also. The momentum of a rotating object is called Angular Momentum and depends on the object s mass, distance from the center axis of rotation, and tangential velocity. If the radius gets smaller, the velocity increases to maintain constant angular momentum. Like water going down the toilet, or a hurricane, or planets around a star (sun). http://www.youtube.com/watch?v=c4ru_kgklzs
Practice Problem A 0.144kg baseball is pitched horizontally at 38.0m/s. After it is hit by the bat, it moves at the same speed, but in an opposite direction. What was the change in momentum of the ball? What was the impulse delivered by the bat?
Batter Up Solution Given: m ball =0.144kg, v=38.0 m/s, +direction = direction after ball leaves bat Unknown: FΔt = Δρ Solve: Δρ= mv 2 -mv 1 =m(v 2 v 1 ) = (0.144kg)(38.0m/s-(-38.0m/s)) = (0.144kg)(76.0m/s) = 10.9 kg-m/s Impulse = change in momentum = 10.9 N-s
Your turn to practice Do pg. 204-205 Practice Problems # 1,2,3,4,5d,6a Do pg.217 #s 1,2,4,6,7 Do pg. 218 #s 22-27
Conservation of Momentum Forces are a result of an interaction between objects moving in opposite directions. During collisions, the force of one object on another is = in strength but opposite in direction to the force of the second object on the first. F BonA F AonB The time interval for the force is the same for both objects, so the Impulse is = and opposite.
What about Momenta? According to the I-M theorem, the final momentum = the impulse + the initial momentum. F t 2 In a collision, the final momenta must be equal to the sum of the initial momenta in a system and thus Momentum is Conserved. A2 B2 A1 B1 1
Defining Closed Systems A system that doesn t gain or lose mass is said to be a closed system. All forces within a closed system are called internal forces. All forces outside a closed system are considered external forces. In a system, objects that collide can either stick together (inelastic collision), or come apart (elastic collision). Momentum of the collision in a closed system with no net external force is still conserved.
Car collision problem A 2275kg car going 28m/s rear-ends an 875kg compact car going 16m/s on ice in the same direction. The cars stick together. How fast does the wreckage move after the collision?
Car crash solution A2 B2 A1 B1 Because the cars stick together, their velocities after the collision are equal. So, v A2 = v B2 = v 2 m A v A1 + m B v B1 = (m A +m B )v 2 m v m v A A1 B B1 v2 ma mb v 2 (2275 kg)(28m / s) (2275 kg (875 kg)(16m / 875 kg) s) So v 2 = 25 m/s, as we can see when mass increases, velocity must decrease to conserve momentum.
Explosions As with the 2 skaters in Fig 9-8, if they both start at rest and A gives B a push, both skaters will move in opposite directions. The push is an internal force. The total momentum of the system must be zero after the push as it was zero before the push. The momenta of the skaters will be equal and opposite after the push. The chemicals in a rocket exploding to propel the rocket are internal forces as they are expelled into space propelling the rocket along. m A v A2 = -m B v B2
Ch 9 Homework Please complete the following: Pg. 210 Prac. Probs. # 7,8,9, &12 Pg. 218 Rev #s 28,34,35, and 36.