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Forces and Motion In this lesson: 1.Newtons Second Law 2.Momentum & Impulse

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Newtons Second Law The common definition of a force is any push or pull. A more interesting and useful definition is any interaction between two (or more) objects. Newtons second law can explain that interaction and the resulting change in motion.

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Newtons Second Law Acceleration is directly proportional to Force This means a large Force causes A large acceleration

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Newtons Second Law Acceleration is inversely proportional to Mass This means a large Mass results in A small acceleration

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Newtons Second Law This relationship is written mathematically as: F=ma

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Newtons Second Law This relationship is written mathematically as: A useful form of Newton's Second Law requires the substitution of the acceleration formula below. F=ma

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Newtons Second Law The substitution results in the following formula: The result is two new concepts: Impulse & Momentum

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Concept Check Question (True or False) Answer 1. Acceleration depends on net force, the mass, and shape of the object. 2. If I triple the net force on an object the acceleration will triple. 3. A ball with a mass of 0.25kg that is thrown with 4N of force will accelerate at 1 m/s/s. 4. If I triple the mass of an object the acceleration will triple. 5. When two objects that were moving at a constant speed collide force is created. Click to check your answers

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Concept Check Question (True or False) Answer 1. Acceleration depends on net force, the mass, and shape of the object. False 2. If I triple the net force on an object the acceleration will triple. True 3. A ball with a mass of 0.25kg that is thrown with 4N of force will accelerate at 1 m/s/s. True 4. If I triple the mass of an object the acceleration will triple. False 5. When two objects that were moving at a constant speed collide force is created. True Click to check your answers

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Momentum Momentum of an object is simply defined as the mass times the velocity. It is usually abbreviated as ρ. Mass measured in kg times velocity measured in m/s results in a momentum with units of kg m/s.

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Solve the following momentum problems: Problem Answer 1. A moving car has momentum. If it moves twice as fast, its momentum is ___________ as much. 2. A steel ball whose mass is 2.0 kg is rolling at a rate of 2.8m/s. What is its momentum? 3. A marble is rolling at a velocity of 1.5 m/s with a momentum of 0.10 kg m/s. What is its mass? 4. Two cars, one twice as heavy as the other, move down a hill at the same speed. Compared to the lighter car, the momentum of the heavier car is ____________ as much. 5. A 5100-kg freight truck accelerates from 4.2 m/s to 7.8 m/s what is its change in momentum?

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Solve the following momentum problems: Problem Answer 1. A moving car has momentum. If it moves twice as fast, its momentum is ___________ as much. twice 2. A steel ball whose mass is 2.0 kg is rolling at a rate of 2.8m/s. What is its momentum? 5.6kg·m/s 3. A marble is rolling at a velocity of 1.5 m/s with a momentum of 0.10 kg m/s. What is its mass? 0.067kg or 67g 4. Two cars, one twice as heavy as the other, move down a hill at the same speed. Compared to the lighter car, the momentum of the heavier car is ____________ as much. Twice 5. A 5100-kg freight truck accelerates from 4.2 m/s to 7.8 m/s what is its change in momentum? kg·m/s

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Take Home Points: Forces result from interactions of objects. Acceleration is directly proportional to force and indirectly proportional to mass. Newtons second law can be written as mv is called momentum; mΔv is change in momentum.

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Presentation Goals Following this presentation you should be able to: Explain the concept of conservation of momentum Apply the conservation of momentum in real world situations to predict outcomes of interactions. Solve conservation of momentum problems using mathematical models.

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During an Impact Forces are transferred –A–Action reaction forces happen Objects undergo acceleration –T–The velocity changes –E–Each objects momentum changes In any interaction between two or more objects: But the Total Momentum of a system* remains constant. *System: group of interacting, interrelated, or interdependent elements or parts that function together as a whole

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During an Impact Total momentum before an interaction This means that… Total momentum after an interaction = Σ is the Greek letter Sigma and mean sum or total So, this equation would read… total momentum initial equals total momentum final

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More ways to represent conservation of momentum: During an Impact total momentum initial equals total momentum final initial momentum of object #1 plus the initial momentum of object #2 equals final momentum of object #1 plus the final momentum of object #2 mass of object #1 times the initial velocity of object #1 plus mass of object #2 times the initial velocity of object #2 equals mass of object #1 times the final velocity of object #1 plus mass of object #2 times the final velocity of object #2

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1) Example - Meteorite A meteorite breaks up into two pieces. The mass of the original meteorite is 16 kg and travels at a rate of 12 m/s The two pieces each have a mass of 8.0 kg. Newtons 1 st law says that unless an outside force is present the speed will remain constant. So the speed of each piece is 12 m/s Compare the momentum before the break up to the momentum after the break up.

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1)Compare the momentum before the break up to the momentum after the break up. Record what you know. Known Possible formulas Show Work Final Answer Unknown

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1) Compare the momentum before the break up to the momentum after the break up. Write a equation that shows the momentum before = the momentum after Known Possible formulas Show Work Final Answer Unknown Before m 1 = 16 kg v 1 =12 m/s After m 2 = 8.0 kg v 2 =12 m/s m 3 = 8.0 kg v 3 =12 m/s

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1) Compare the momentum before the break up to the momentum after the break up. Replace p with the momentum formula Known Possible formulas Show Work Final Answer Unknown Before m 1 = 16 kg v 1 =12 m/s After m 2 = 8.0 kg v 2 =12 m/s m 3 = 8.0 kg v 3 =12 m/s Momentum before = sum of the momentums after p 1 = p 2 +p 3 = +

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1) Compare the momentum before the break up to the momentum after the break up. Plug in your numbers Known Possible formulas Show Work Final Answer Unknown Before m 1 = 16 kg v 1 =12 m/s After m 2 = 8.0 kg v 2 =12 m/s m 3 = 8.0 kg v 3 =12 m/s Momentum before = sum of the momentums after p 1 = p 2 +p 3 m 1 v 1 = m 2 v 2 +m 3 v 3

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1) Compare the momentum before the break up to the momentum after the break up. Solve each side of the equation to confirm if it is true Known Possible formulas Show Work Final Answer Unknown Before m 1 = 16 kg v 1 =12 m/s After m 2 = 8.0 kg v 2 =12 m/s m 3 = 8.0 kg v 3 =12 m/s Momentum before = sum of the momentums after p 1 = p 2 +p 3 m 1 v 1 = m 2 v 2 +m 3 v 3 16 kg(12m/s) = 8.0kg(12m/s)+ 8.0kg(12m/s)

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1) Compare the momentum before the break up to the momentum after the break up. Known Possible formulas Show Work Final Answer Unknown Before m 1 = 16 kg v 1 =12 m/s After m 2 = 8.0 kg v 2 =12 m/s m 3 = 8.0 kg v 3 =12 m/s Momentum before = sum of the momentums after p 1 = p 2 +p 3 m 1 v 1 = m 2 v 2 +m 3 v 3 16 kg(12m/s) = 8.0kg(12m/s)+ 8.0kg(12m/s) 192 kg·m/s = 96 kg·m/s + 96 kg·m/s 192 kg·m/s = 192 kg·m/s They are equal!!

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Total Momentum Even if the meteorite broke up into a thousand little pieces the momentum of all the pieces added together would still equal the momentum of the original meteorite.

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2) A 1.0 kg moving cart (velocity= 60.0 m/s) catches a 2.0 kg brick. What is the speed of the car and brick after? What do you know?

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2) What is the speed of the car and brick after? WAIT!! We have 2 variables V 1 and V 2 Known Possible formulas Show Work Final Answer Unknown Before m 1 = 1.0 kg v 1 = 60.0 m/s After m 2 = 1.0 kg v 2 =? m 3 = 2.0 kg v 3 =? Stupid problem cans be solve. Ms Schwartz is just trying to kill my brain

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2) What is the speed of the car and brick after? WAIT!! We have 2 variables V 1 and V 2 Known Possible formulas Show Work Final Answer Unknown Before m 1 = 1.0 kg v 1 = 60.0 m/s After m 2 = 1.0 kg v 2 =? m 3 = 2.0 kg v 3 =? Stupid problem cans be solve. Ms Schwartz is just trying to kill my brain It is solvable but we need to assume something. What can assume?

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2) What is the speed of the car and brick after? The Cart and brick stick together they have the same speed v 2 =v 3 Now Set up your equation Known Possible formulas Show Work Final Answer Unknown After m 2 = 1.0 kg v 2 = v 3 m 3 = 2.0 kg Before m 1 = 1.0 kg v 1 = 60.0 m/s

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2) What is the speed of the car and brick after? Plug in your numbers and Solve Known Possible formulas Show Work Final Answer Unknown Before m 1 = 1.0 kg v 1 = 60.0 m/s After m 2 = 1.0 kg v 2 =? m 3 = 2.0 kg v 3 =? Momentum before = sum of the momentums after p 1 = p 2 +p 3 m 1 v 1 = m 2 v 2 + m 3 v 3

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2) What is the speed of the car and brick after? And the Answer is? Known Possible formulas Show Work Final Answer Unknown Before m 1 = 1.0 kg v 1 = 60 m/s After m 2 = 1.0 kg v 2 =? m 3 = 2.0 kg v 3 =? Momentum before = sum of the momentums after p 1 = p 2 +p 3 m 1 v 1 = m 2 v 2 + m 3 v 3 1.0kg(60.0 m/s) = 1.0kg(v)+ 2.0 kg(v) 60 kg·m/s = 3 kg (v)

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2) What is the speed of the car and brick after? And the Answer is? Known Possible formulas Show Work Final Answer 20.0 m/s Unknown Before m 1 = 1.0 kg v 1 = 60 m/s After m 2 = 1.0 kg v 2 =? m 3 = 2.0 kg v 3 =? Momentum before = sum of the momentums after p 1 = p 2 +p 3 m 1 v 1 = m 2 v 2 + m 3 v 3 1.0kg(60 m/s) = 1.0kg(v)+ 2.0 kg(v) 60 kg·m/s = 3.0 kg (v) 60 kg·m/s/3kg = (v) 20.0 m/s = v

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Watch it change

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What do we know? And Set up the equation 3) A kg truck travelling at 20.0 m/s hits a kg car and they stick together. What is the speed of each after the impact?

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3) What is the speed of the car and truck after? And the Answer is? Known Possible formulas Show Work Final Answer Unknown Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = 0 m/s After m 3 = kg v 3 =? m 4 = kg v 4 =? Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+1000kg(0m/s) = 3000.kg(v)+1000kg(v)

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3) What is the speed of the car and truck after? Known Possible formulas Show Work Final Answer 15.0 m/s Unknown Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = 0 m/s After m 3 = kg v 3 =? m 4 = kg v 4 =? Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+1000kg(0m/s) = 3000.kg(v)+1000kg(v) 60,000 kg·m/s = 4000.kg (v) 60,000 kg·m/s /4000. kg = v 15.0 m/s = v

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Watch it happen

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4) This time the kg car travelling at 20.0 m/s hits the kg truck! Make a prediction: will the end speed be greater or less then 15 m/s? What do you know? Set up the formula

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4) What is the speed of the car and Truck after? And the Answer is? Known Possible formulas Show Work Final Answer Unknown Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = 0 m/s After m 3 = kg v 3 =? m 4 = kg v 4 =? Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(0m/s) = 1000.kg(v)+3000kg(v)

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4) What is the speed of the car and Truck after? Known Possible formulas Show Work Final Answer 5.0 m/s Unknown Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = 0 m/s After m 3 = kg v 3 =? m 4 = kg v 4 =? Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(0m/s) = 1000.kg(v)+3000kg(v) 20,000 kg·m/s = 4000.kg (v) 20,000 kg·m/s /4000.kg =v 5.0 m/s = v

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Watch it happen

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Remember sign of velocity indicates direction

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5) A kg car is travelling at 20.0 m/s. A 3000 kg truck is travelling in the opposite direction at 20.0 m/s. After the collision they stick together. At what speed and in which direction do they go? What do you know?

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5) What is the speed of the car and Truck after? Known Possible formulas Show Work Final Answer Unknown Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = 20.0 m/s After m 3 = kg v 3 =? m 4 = kg v 4 =? Wait a sec. Something is not right with the signs in the known. What is it?

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Remember sign of velocity indicates direction. And the truck is going in the opposite direction. Set up the problem

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5) What is the speed of the car and Truck after? And the Answer is? Known Possible formulas Show Work Final Answer Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = m/s After m 3 = kg v 3 =? m 4 = kg v 4 =? Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(-20.0m/s) = 1000.kg(v) kg (v) Unknown

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5) What is the speed of the car and Truck after? Known Possible formulas Show Work Final Answer m/s Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = m/s After m 3 = kg v 3 =? m 4 = kg v 4 =? Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(-20.0m/s) = 1000.kg(v) kg (v) -40,000 kg·m/s = 4000.kg (v) -40,000 kg·m/s /4000.kg = v m/s = v Unknown

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Watch What happens.

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6) Objects can bounce rather then stick together. This time all the momentum of the kg truck travelling at 20.0 m/s gets passed to the kg car that is travelling at 20.0 m/s in the opposite direction. What is the speed of the car? Set up the problem

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6) What is the speed of the car after? And the Answer is? Known Possible formulas Show Work Final Answer Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = m/s After m 3 = kg v 3 =? m 4 = kg v 4 = 0 m/s Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(-20.0m/s) = 1000.kg(v) kg (0) Unknown

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6) What is the speed of the car after? Known Possible formulas Show Work Final Answer Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = m/s After m 3 = kg v 3 =? m 4 = kg v 4 = 0 m/s Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(-20.0m/s) = 1000.kg(v) kg (0) -40,000 kg·m/s = 1000.kg (v) -40,000 kg·m/s /1000.kg = v m/s = v Unknown

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Watch What happens

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7) A1000. kg car travelling at 20.0 m/s hits a stationary kg truck. The truck starts to move at a rate of 10.0 m/s. How fast does the car go? What do you know? Set up the equation.

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7) How fast does the car go? And the Answer is? Known Possible formulas Show Work Final Answer Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = 0.0 m/s After m 3 = kg v 3 =? m 4 = kg v 4 = m/s Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(0 m/s) = 1000.kg(v)+3000 kg(10.0m/s) Unknown

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7) How fast does the car go? Known Possible formulas Show Work Final Answer Before m 1 = kg v 1 = 20.0 m/s m 2 = kg v 2 = 0.0 m/s After m 3 = kg v 3 =? m 4 = kg v 4 = m/s Momentum before = sum of the momentums after p 1 +p 2 = p 3 +p 4 m 1 v 1 +m 2 v 2 = m 3 v 3 + m 4 v kg(20.0m/s)+3000kg(0 m/s) = 1000.kg(v)+3000 kg(10.0m/s) 20,000 kg·m/s = 1000.kg (v)+ 30,000 kg·m/s 20,000 kg·m/s- 30,000 kg·m/s = 1000.kg (v) -10,000 kg·m/s /1000.kg = v m/s = v Unknown

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Watch what happens.

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Take home points The total momentum before a collision must equal the total momentum after the collision. –This is known as the Law of Conservation of Momentum Using this concept we can calculate the speed of an object after the collision.

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Now Complete the additional Conservation of Momentum problems in your packet.

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