Impulse AP Physics End Slide What is Impulse

Impulse AP Physics

End Slide What is Impulse? • What do you think of when you hear the term Impulse? (you don’t have to relate it to physics) • Sudden change in behavior? • To do something “on a whim”?

End Slide What is Impulse? • Impulse will cause a change in motion for a given mass. • Impulse depends on how much net force is being applied and how long that force is applied to a mass. • Impulse = Fnet*t • The units are Newton*seconds (N • s)

End Slide Impulse Examples • A baseball is thrown with a force of 800 N for 0. 4 sec. What is the impulse on the baseball? 320 N • s • A hockey player makes a slap shot, exerting a constant force of 30. 0 N on a hockey puck for 0. 16 s. What is the impulse given to the puck? 4. 8 N • s

End Slide Impulse by Graphing • Looking at the graph to the right, what is the impulse over the given time period? • Graphically, how do you find impulse?

End Slide What is the Impulse here? 1. 2. 3. 4. 5. 6. 7. 8. From 0 s to 3 s? From 0 s to 5 s? From 2 s to 4 s? From 1 s to 3 s? From 4 s to 5 s? From 1 s to 5 s? From 3 s to 5 s? 4. 5 N • s 12 N • s 10 N • s 6. 0 N • s 4. 0 N • s 11. 5 N • s 7. 5 N • s

End Slide What is the Impulse here? Example: From 2 s to 5 s? 1/ 2*(4 s-2 s)*(4 N-2 N) = 2 N • s (4 s-2 s)*(2 N-0 N) = 4 N • s (5 s-4 s)*(4 N-0 N) = 4 N • s 2 N • s + 4 N • s = 10 N • s

End Slide Check your understanding… • I start pushing a table and I add more and more force on in the first second. I get to pushing it as hard as I can for one second and somebody helps me put more force for another second. We both get to our max force for one second and begin to decrease our force on the table until we stop pushing all together. What is the total impulse?

End Slide 50 N • s 300 N • s 200 N • s 150 N • s 100 N • s+200 N • s+50 N • s+300 N • s+150 N • s = 1000 N • s

End Slide If friction is -200 N, how long will it take to equal out the impulse put into the table? 1000 N • s -1000 N • s

Work it out J = -1000 N • s = (-200 N)*t t = 5 s End Slide

Momentum AP Physics

End Slide Momentum • Momentum (p) is the product of an object’s mass (m) and velocity (v). • Since velocity has a direction, momentum has a direction; thus momentum is a vector. • For a 2500 kg car moving at 30. 0 m/s North, what is the momentum? p = 75, 000 kg*m/s North

End Slide Momentum Examples • What is the momentum of your book with a mass of 1. 5 kg sitting on your table? 0 kg*m/s • What is the momentum of a 3. 5 kg rock when it gets to the bottom of a 30 m cliff after being dropped? -84. 9 kg*m/s • Find the momentum of a 0. 25 kg ball rolling with a velocity of -3. 0 m/s. -0. 75 kg*m/s

End Slide Change in Momentum (Dp) • Final Momentum (pf) minus Initial Momentum (po). Dp = pf - po • For a 2500 kg car moving at 30. 0 m/s North and then slows to 10. 0 m/s, what is the change in momentum (Dp)? Dp = pf - po = 25, 000 kg*m/s – 75, 000 kg*m/s Dp = -50, 000 kg*m/s

Change in Momentum Examples End Slide • What is the change in momentum of a 3. 5 kg rock when it dropped off of a 30 m cliff? Dp = -84. 9 kg*m/s – 0 kg*m/s = -84. 9 kg*m/s • Find the change in momentum of a 0. 25 kg ball initially rolling with a velocity of – 3. 0 m/s but accelerates and is now rolling with a velocity of +3. 0 m/s. Dp = (0. 75 kg*m/s) – (-0. 75 kg*m/s) = 1. 50 kg*m/s

End Slide Relationship between Impulse and Change in Momentum Newton’s Second Law Fnet = ma t Fnet = m(vf – vo) t t Fnet*t= m(vf – vo) Fnet*t= mvf – mvo J = Dp a = Dv = vf – vo t t J = Fnet*t Dp = mvf – mvo

Real Life Applications for J = Dp AP Physics

End Slide Examples of wanting to stop • If you want to stop, you will have some mass, some initial velocity, and you want your final velocity to be 0 m/s. • How is “damage” minimized on your body in the following examples?

End Slide Wanting to Stop • Car wreck • Use of air bags • Crumple zones • Rock Climbing with a Nylon rope • Nylon allows stretch • Getting hit in boxing • “Riding the punch”

End Slide What do they have in common? • J = Dp and “Dp” will be constant • To minimize “damage”, you want to minimize force • If you increase the time that the force is being applied, the average force will decrease

End Slide Happy/Sad Ball Demo • Which has more change in momentum? • How do you know? • Which type of material would you rather make a wrecking ball out of? Why? • What are “elastic” and “inelastic” collisions?

End Slide Why is cork in bats against the rules in baseball? • Cork is easily compressed and allows the rest of the bat to compress. • If the bat is able to compress more, the bat acts more like the happy ball than the sad ball. • This allows more change in momentum to be given to the baseball and thus, an unfair advantage.

Using Impulse Graphs AP Physics

End Slide Example • A 7. 0 -kg bowling ball is rolling down the alley with a velocity of 2. 0 m/s. For each impulse, a and b, as show in Figure 9 -3, find the resulting speed and direction of the motion of the bowling ball. 5. 0 N • s -5. 0 N • s

End Slide “+” is “toward pins” and “-” is “away from pins” m=7. 0 kg; vo=2. 0 m/s Part A; J = 5. 0 N • s Part B; J = -5. 0 N • s J = Dp = mvf-mvo 5. 0 N • s = 7 kg*vf – -5. 0 N • s = 7 kg*vf – 7 kg*2 m/s 14 + 5 = 7 vf – 14 + 14 14+ -5 = 7 vf – 14 + 14 7 7 vf = 2. 71 m/s vf = 1. 29 m/s 2. 71 m/s towards pins 1. 29 m/s towards pins

A 30 kg mass undergoes the following End Slide Impulse. Assuming the mass started at 0 m/s, what is its final velocity? 1000 N • s

End Slide J = 1000 N • s J = Dp mv = mv f – mv o o 1000 N • s = (30 kg)vf – (30 kg)*(0 m/s) 1000 = 30 vf - 0 30 30 vf = 33. 3 m/s

Given a 1. 5 kg mass has an initial End Slide velocity of 3. 0 m/s, what is the mass’s final velocity for your time interval? 1. From 0 s to 3 s? 6. 0 m/s 2. From 0 s to 5 s? 11 m/ s 3. From 2 s to 5 s? 9. 7 m/s 4. From 2 s to 4 s? 7. 0 m/ s 5. From 1 s to 3 s? 5. 7 m/ s 6. From 4 s to 5 s? 5. 7 m/s 7. From 1 s to 5 s? 10. 7 m/ s 8. From 3 s to 5 s? 8. 0 m/s

m = 1. 5 kg and vo = 3 m/ End Slide s Example: From 2 s to 5 s? J = mvf – mvo 10 N • s = (1. 5 kg)vf – (1. 5 kg)*(3 m/s) 10 = 1. 5 vf – 4. 5 14. 5 = 1. 5 vf vf = 9. 7 m/s J = 10 N • s 2 N • s 4 N • s

End Slide A rocket with mass 57 grams is fired from rest. The engine’s Force vs. time graph is given to the right. What is the final velocity of the rocket after it’s fired off? 46. 3 m/s

End Slide Richard strikes a 0. 058 -kg golf ball with an average force of 272 N and gives it a velocity of 62. 0 m/s. How long was Richard’s club in contact with the ball? J = Dp Fnet*t = m(vf – vo) 272 t = 0. 058 * 62. 0 272 t = 0. 013 s

Example End Slide A 0. 145 -kg baseball is moving at 35 m/s when it is caught by a player. Find the change in momentum. If the ball is caught with a mitt held in a stationary position so that the ball stops in 0. 050 s, what is the average force exerted on the ball? If, instead, the mitt is moving backward so that the ball takes 0. 500 s to stop, what is the average force exerted by the mitt on the ball?

Questions: 1. Which has more momentum, a supertanker tied to a dock or a falling raindrop? 2. When you jump from a height to the ground, you let your legs bend at the knees as your feet hit the floor. Explain why you do this in terms of the concepts learned in this unit. 3. An archer shoots arrows at a target. Some of the arrows stick in the target, while others bounce off. Assuming that the masses of the arrows are the same, which arrows produce the bigger impulse on the target?

End Slide A 0. 174 -kg softball is pitched horizontally at 26. 0 m/s. The ball moves in the opposite direction at 38. 0 m/s after it is hit by the bat. Ø What is the change in momentum of the ball? Ø What is the impulse delivered by the bat? Ø If the bat and softball are in contact for 0. 80 ms, what is the average force that the bat exerts on the ball.

End Slide Conservation of Momentum A B

End Slide A B Cart A of mass 6. 0 kg is moving at 3. 5 m/s and collides with Cart B with mass 4. 0 kg that is at rest. Cart A moves off at 0. 7 m/s. Ø What is the final velocity of Cart B?

End Slide A 35. 0 -g bullet strikes a 5. 0 -kg stationary piece of lumber and embeds itself in the wood. The piece of lumber and the bullet fly off together at 8. 6 m/s. Ø What is the original speed of the bullet?

End Slide 1. 5 kg 4. 5 kg A thread holds a 1. 5 -kg cart and a 4. 5 -kg cart together. After the thread is burned, a compressed spring pushes the carts apart, giving the 1. 5 -kg cart a speed of 27 cm/s to the left. Ø What is the velocity of the 4. 5 -kg cart?