Chapter 6 Part 1 Momentum and Impulse. St. Augus:ne Preparatory School October 24, 2016

Transcription

1 Chapter 6 Part 1 Momentum and Impulse St. Augus:ne Preparatory School October 24, 2016

2 Momentum Momentum is a vector quan:ty and can be defined as the quan)ty of mo)on of a moving body, measured as a product of its mass and velocity. Formula: p = mv, where p = momentum (kg*m/s) m = mass (kg) v = velocity (m/s)

3 Would you rather a) Get hit by a baseball moving at 30 m/s or the same baseball moving at 5 m/s b) Get hit by a bowling ball thrown at you with a velocity of 20 m/s or a baseball thrown at you with a velocity of 20m/s c) Get hit by a bowling ball moving at 1 m/s or a piece of ice moving at 50 m/s? d) Get hit by a bicycle travelling at 35 km/h or a motorcycle traveling at 5 km/h?

4 Momentum Momentum depends on both mass and velocity. An object with a small mass can have a large momentum if it has a large velocity. An object with a large mass needs much less velocity to have the same momentum.

5 Sample Problem a) A 2250kg pick up truck has a velocity of 25 m/s to the east. What is the momentum of the truck? b) What velocity would a 1125kg car need to have the same momentum as the truck?

6 Solu:on A 2250kg pick up truck has a velocity of 25 m/s to the east. What is the momentum of the truck? p = mv p = (2250kg)(25m/s) p = kg*m/s p = 5.6 x 10 2 kg*m/s east What velocity would a 1125kg car need to have the same momentum as the truck? p = mv kg*m/s = (1125kg)v v = 50. m/s

7 Sample Problem A 21 kg child on a 4.9 kg bike is riding with a velocity of 4.5 m/s to the northwest. What is the total momentum of the child and bike together?

8 Solu:on A 21 kg child on a 4.9 kg bike is riding with a velocity of 4.5 m/s to the northwest. What is the total momentum of the child and bike together? p = mv p = (21kg + 4.9kg)(4.5m/s) p = kg*m/s p = 1.2 x 10 2 kg*m/s northwest

9 To change the momentum of an object, a force must be applied. It will also take Cme for that force to change the momentum of the object. F = Δp Δt, where F = force (N) Δp = change in momentum (kg*m/s) Δt = change in :me (s)

10 Impulse- Momentum Theorem FΔt = Δp, where F = force (N) Δt = change in :me (s) Δp = change in momentum (kg*m/s) FΔt is what we call impulse. An impulse is something that changes the momentum of an object.

11 Sample Problem A 1400 kg car is travelling west with a velocity of 15 m/s when it collides with a street light pole. If the car comes to a complete stop in 0.30 seconds, what is the force exerted on the car during the collision?

12 Solu:on A 1400 kg car is travelling west with a velocity of 15 m/s when it collides with a street light pole. If the car comes to a complete stop in 0.30 seconds, what is the force exerted on the car during the collision? (note: the velocity will be negacve since it is west) FΔt = Δp F =Δp/Δt F = (mv f mv i ) / (t f t i ) F = [(1400kg)(0.00m/s) (1400kg)(- 15m/s)] / (0.30s 0.00s) F = kg*m/s / (0.30s) F = N F = 7.0 x 10 4 N east Note: The answer is east, since the car was traveling west. The force applied on the car was in the opposite direc8on of the velocity, which is what stopped the car.

13 Airbags Using what the topics covered in this class, why are airbags effec:ve in reducing injuries during car crashes? Airbags and how they func:on h`ps:// W- R_A)

14 1. A 0.50 kg football is thrown with a velocity of 15 m/s to the right. A sta:onary receiver catches the bal and brings it to rest in seconds. What is the force exerted on the ball by the receiver. 2. A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s to the north. The player strikes the ball and causes it to move in the opposite direc:on with a velocity of 22 m/s. What impulse was delivered to the ball by the player?

15 Chapter 6-2 Conserva:on of Momentum St. Augus:ne Preparatory School October 25, 2016

16 Conserva:on of Momentum This theory is extremely similar to the conservacon of mechanical energy that we saw last chapter It states that all of the momentum at the beginning of a situa:on must be present at the end.

17 Conserva:on of Momentum For a situa:on with two different objects (car crash, two pool balls or marbles, two football players, etc.) p i,a + p i,b = p f,a + p f,a Which can be wrote more usefully as: m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f The total momentum of all objects interac8ng with one another remains constant regardless of the nature of the forces between the objects.

18 Example: Two pool balls collide and the following data is obtained. Is momentum conserved? Ball A Mass (kg) Velocity (m/s) Momentum Before collision m/s Ager collision m/s Ball B Mass (kg) Velocity (m/s) Momentum Before collision m/s Ager collision m/s

19 Conserva:on of Momentum When we use the conserva:on of momentum theorem (just like with the conserva:on of mechanical energy) we assume that there is no friccon In a real world situa:on that includes fric:on, we would see that the final momentum would be less than the inical momentum

20 Example Ques:on A 76kg boater, ini:ally at rest in a sta:onary 45kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5m/s to the right, what is the final velocity of the boat?

21 Solu:on m1v1 + m2v1 = m1v2 + m2v2 Since the boat and person are originally at rest, both v1 s are going to = 0. So: 0 = m1v2 + m2v2 0 = (76kg)(2.5m/s) + (45kg)v2-190kg*m/s = (45kg)v m/s = v2 4.2 m/s to the lev = v2

22 Think about the following: Two people stand facing each other on rollerblades. They push on each other and in turn, each person rolls backwards. Considering this is a collision, is momentum conserved?

23 Problem: What velocity does the Earth gain each :me you jump? What velocity would it gain if all of the students at St. Augus:ne jumped together. What velocity would it gain if all of China s popula:on (1.357 billion) jumped in the same loca:on at the same :me? Informa:on given: The mass of the Earth is x kg

24 Chapter 6-3 Elas:c and Inelas:c Collisions St. Augus:ne Preparatory School October 26, 2016

25 Perfectly Elas:c and Inelas:c Collision In a perfectly elas8c collision no kine:c energy is lost. Both momentum and kinecc energy are conserved. In a perfectly inelas8c collision, kine:c energy is changed to some other form, meaning it is lost. Momentum is conserved, while kinecc energy is not conserved. In any type of collision, momentum will be conserved.

26 Formulas For a perfectly elascc collision: m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f For a perfectly inelascc collision: m 1 v 1,i + m 2 v 2,i = (m 1 + m 2 )v f In a perfectly inelas8c collision, the two objects will s8ck together. Therefore, they have the same velocity, allowing us to shorten the formula.

27 Inelas:c Collisions

28 Elas:c Collisions

29 Example 1 A 0.015kg marble moving to the right at 0.225m/s makes an elas:c head- on collision with a 0.030kg marble moving to the leg at 0.180m/s. Ager the collision the smaller marble moves leg at m/s. Assuming neither marble rotates and that the surface is fric:onless, calculate the velocity of the 0.030kg marble ager the collision. Answer: 9.0 x 10-2 m/s to the right

30 Example 2 Two balls collide head- on in a perfectly inelas:c collision. The first ball has a mass of 0.500kg and ini:al velocity of 4.00m/s to the right. The second ball has a mass of 0.250kg and an ini:al velocity of 3.00m/s to the leg. a. What is the final velocity of the two objects? Answer: 1.67 m/s to the right a. What amount of kine:c energy was lost in the collision? Answer: J

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