Physics. Impulse & Momentum

Transcription

1 Physics Impulse & Momentum

2 Warm up - Write down everything you know about impulse and momentum.

3 Objectives Students will learn the definitions and equations for impulse, momentum, elastic and inelastic collisions. Students will be able to apply the law of conservation of momentum to analyze collisions

4 What is Momentum? If an object is in motion (on the move) then it has momentum. Momentum = mass x velocity p = m v

5 Momentum Momentum is a vector direction matters! (positive or negative sign matters!) The direction of an object s momentum is the same direction as the object s velocity p = mv

6 Determine the momentum of a... A.60-kg halfback moving eastward at 9 m/s. B.1000-kg car moving northward at 20 m/s. C.40-kg freshman moving southward at 2 m/s.

7 A. p = m*v = 60 kg*9 m/s p = 540 kg m/s, east B. p = m*v = 1000 kg*20 m/s p = kg m/s, north C. p = m*v = 40 kg*2 m/s p = 80 kg m/s, south

8 Impulse Impulse (J) is a change in momentum J = p = F t A change in an object s momentum requires an outside force.

9 Impulse and F vs. t graphs One of our formulas for impulse is J = Ft If there is a graph of the Force vs. time for an object, the area under the curve is the impulse!

10 Physical concepts Stopping distance/stopping time Newton s Third Law Conservation of Linear Momentum closed systems

11 The magnitude of the net force exerted in the x-direction on a 2.5 kg particle varies in time as shown below. 1. Find the impulse of the force. 2. Find the final velocity of the particle if it is originally at rest 3. Find the final velocity of the particle if it was originally moving with a velocity of 3.00 m/s

12 Gohar throws a 0.5 kg ball at a wall at 15 m/s. It is in contact with the wall for 0.10 seconds and rebounds with a speed of 12.5 m/s. What is the impulse delivered to the ball by the wall? What is the force the wall exerts on the ball?

13 You throw a 0.25 kg ball at a wall at 5 m/s. It is in contact with the wall for 0.30 seconds and rebounds with a speed of 4.0 m/s. What is the impulse of the ball? What is the force the wall exerts on the ball?

14 In a crash test, a 1500 kg car collides with a wall. The car hits the wall at v 0 = -15 m/s and rebounds with v = +2.6 m/s. If the collision lasts s, find the impulse caused by the collision and the average force exerted on the car.

15 Stopping force How much force is required to stop a 80.0 kg person traveling at 20 m/s during a time of 2.00 second?

16 Collisions/explosions Law of conservation of momentum: the momentum of a system remains constant in a closed system elastic collisions kinetic energy is conserved in addition to momentum inelastic collisions objects stick together; only momentum is conserved

17 Conservation of Momentum These forces act for the same amount of time Same forces, same time, equal and opposite impulses

18 Perfectly inelastic collisions A perfectly inelastic collision is a collision in which the two objects stick together after the collision. Example: If a 4 kg ball of clay moving 14 m/s collides and sticks to a 3 kg ball originally at rest, how fast is the 7kg mass moving after the collision?

19 Homework There are seven homework problems on the HW set. We will have one quiz on three of the seven 3/11 or 3/12 NOTE: 7(b): cross out velocity and replace with momentum New equations: p = mv J = p= F t p = p i f

20 Warm up - (Perfectly inelastic collision) A 10.0-g bullet is fired into a stationary block of wood (m = 5.00 kg). The relative motion of the bullet stops inside the block. The speed of the bullet-plus-wood combination immediately after the collision is m/s. What was the original speed of the bullet?

21 Examples Stopping a golf ball Slow motion punch Before we watch, think about impulse (F*t) and force of impact ()

22 Demos Impulse with an Egg + bedsheet Basketball + tennis ball Long board fire extinguisher (WallE) Newton s Cradle

23 Types of Collisions Perfectly Elastic Bodies separate after collision All kinetic energy is conserved Perfectly Inelastic Bodies remain attached after collision Kinetic energy not conserved

24 Math Review Solving systems of equations: When you have two unknowns you need two equations to solve for both. Quadratic: Because kinetic energy has the velocity squared, you almost always end up having to solve for a quadratic. For inelastic collisions, they will ALWAYS factor with the original velocity as one of the solutions.

25 Elastic collisions 1. Two billiard balls move toward one another. The balls have identical masses and assume that the collision is elastic. If the initial velocities of the balls are +3 m/s and -2 m/s, what is the velocity of each ball after the collision? 2. Find the final velocity of the two balls if the ball with the initial velocity -2 m/s has a mass equal to half the ball with the initial velocity of +3 m/s. (still an elastic collision)

26 A skater is standing on a frictionless ice rink. Her friend throws a Frisbee straight at her. In which of the following cases is the most momentum transferred to the skater? (a) the skater catches the Frisbee and holds on (b) the skater catches the Frisbee momentarily but then drops it downward. (c) the skater catches the Frisbee, holds on momentarily, then throws it back.

27 Homework There are seven homework problems on the HW set. We will have one quiz on three of the seven 3/11 or 3/12 NOTE: 7(b): cross out velocity and replace with momentum New equations: p = mv J = p= F t p = p i f