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Physics/D'Amato/2010/Momentum 1 Period: Name: 1. "Constant" and "conserved" 1.1. System, environment, process From time to time, we will find it useful to focus our attention on a certain part of the universe and consider it separately from everything else. We select a number of physical objects and call them the system. Everything else in the universe is called the environment. As time goes by, the system may change. We can pick two clock readings, and call what happens in between a process. Before the process, the system is in its initial state and at the end of the process the system is in its final state. In a sketch, we outline the system objects carefully. If the earth is in the system we show this clearly. Consider the following sketches of a system which includes two carts on a track: Initial state v0 Final state v0 v v a) In the sketch above, what objects are in the system? b) What objects are NOT in the system? c) Describe the process that occurred d) External interactions are between a system object and an object in the environment. Describe at least two external interactions in this process e) Internal interactions are between two system objects. Describe one above. f) Describe a "process" that might occur in a playground. Select system objects and sketch initial and final states. The concept of "system" is similar to "object of interest" except that a system can contain many objects. The choice of system objects is up to the investigator and depends on the problem being addressed. Learning to choose useful systems is part of the skill that makes you a good scientist. Like any other skill, it is developed by trial and error at first, then improved by practice. 2017.05.05 Document1 1/25 Physics/D'Amato/2010/Momentum 1.2. 2 Period: Name: Constant and conserved Constant describes a quantity that does not change over a time interval. For example, the amount of money in my pocket is constant from 6am when I get up to 11am when I go to lunch. The amount does not change. Conserved describes a quantity that may change during a period of time, but does NOT appear from nowhere or disappear without trace. You can always find a system within which a conserved quantity is constant. For example: At 11am I spend $2.75 on lunch in the cafeteria. The amount of money in my pocket changes, but my money does not disappear. The cafeteria lady has it now. 1.3. a) In the "buying lunch" situation, within what choice of system is the quantity of money NOT constant? b) Within what choice of system is the quantity of money constant? Quantities and Symbols Before we apply the concepts of constancy and conservation to physical situations, let's practice using these concepts to describe transformations of a quantity that is familiar to us. a) Use $ to represent a quantity of money. Use the subscripts i and f to indicate initial and final quantities. Use the subscripts P, A, and G to indicate money in your pocket, ATM card, and gift card. Complete the table below Initial value Money in pocket Final value $Pi Money in ATM card Money in gift cart b) Use the symbols above to make a mathematical representation of the quantity "initial net wealth" c) Invent a symbol to represent the quantity "amount I earn or spend" d) Use these symbols to make a mathematical representation of the statement "my total net wealth changes by the amount of money I earn or spend". 2017.05.05 Document1 2/25 Physics/D'Amato/2010/Momentum 1.4. 3 Period: Name: Conservation bar charts Use the symbols we made up to practice the concept of conservation using a familiar quantity. The total amount of money you have remains the same before and after unless you earn some or spend some -- right? Fill in the bar charts. Show that the two sides balance by writing a arithmetic statement equation using the given values (i.e. 30 + 10 - 20 = 10 + 10) Situation and process Conservation bar chart (a) You have no money in your pocket, $60 in your ATM account, and a gift card with $20 on it. You withdraw $20 cash from the ATM. a. Complete the bar chart to match this process. Did you earn or spend any money? before $Pi + $Ai + $Gi + Earn or spend Δ$ after =$Pf + $Af + $Gf +50 0 0 b. Represent this process with an arithmetic statement -50 (b) Next, you buy a snow shovel for $10 cash at Jones Hardware. (The initial state for this process is the same as the final state of the previous process.) a. Represent this process on the bar chart. Did you earn or spend any money? before $Pi + $Ai + $Gi + Earn or spend Δ$ after =$Pf + $Af + $Gf +50 0 b. Represent this process with an arithmetic statement -50 (c) After returning from the hardware store, you spend two hours shoveling snow for an old lady who pays you 10 $/hr. a. Represent this process on the bar chart. Did you earn or spend any money? before $Pi + $Ai + $Gi + Earn or spend Δ$ after =$Pf + $Af + $Gf +50 0 b. Represent this process with an arithmetic statement -50 (d) When you are finished shoveling, you spend $20 cash to put gas in your car so you can drive to the Best Buy. a. Represent this process on the bar chart. Did you earn or spend any money? before $Pi + $Ai + $Gi + +50 0 b. Represent this process with an arithmetic statement -50 Activity continues … 2017.05.05 Document1 3/25 Earn or spend Δ$ after =$Pf + $Af + $Gf Physics/D'Amato/2010/Momentum 4 Period: Situation and process Name: Conservation bar chart (e) At Best Buy, you purchase a "Cher's Greatest Hits" DVD Box Set for $40. You empty out your gift card and use your ATM card to pay for the rest. a. Represent this process on the bar chart. Did you earn or spend any money? before $Pi + $Ai + $Gi + Earn or spend Δ$ after =$Pf + $Af + $Gf +50 0 b. Represent this process with an arithmetic statement -50 (f) What happens next? What do you do with the Cher DVDs? Continue the story. before $Pi + $Ai + $Gi + Earn or spend Δ$ after =$Pf + $Af + $Gf +50 a. Represent this story on the bar chart. Did you earn or spend any money? 0 b. Represent this process with a mathematical statement -50 (g) You can forget about the Cher DVD's now, if you want. Does this bar chart represent a process that could really happen? If not, explain why not. If so, describe a situation it could match. before $Pi + $Ai + $Gi + Earn or spend Δ$ after =$Pf + $Af + $Gf +50 0 0 -50 (h) Draw the missing bar. before $Pi + $Ai + $Gi + Write a mathematical statement to match the chart. Earn or spend Δ$ after =$Pf + $Af + $Gf +50 Describe a story that could match. 0 -50 (i) Make a chart to match this mathematical statement: before $Pi + $Ai + $Gi + $20 + $0 + $0 + $40 = $20 + $40 + $0 +50 Describe a story that could match. 0 -50 2017.05.05 Document1 4/25 Earn or spend Δ$ after =$Pf + $Af + $Gf Physics/D'Amato/2010/Momentum 5 Period: Name: 1.5. Represent conservation with different choices of system 1.6. This time let's consider a married couple, Chris and Grey, and their pocket money. a) Create symbols and bar charts to represent the same processes for two different choices of system. Complete the table below Chris is the system Process Chris and Grey are the system On his way out the door in the morning, Chris takes $20 from Grey's wallet. (Did net wealth change?) During the day, Chris spends $5 on bagels and $5 on lunch. In the afternoon, Chris is given $10 by Charles who owes him for springs. In the evening, Chris returns $10 to Grey's wallet b) Choose one process and one choice of system in which money is constant. Explain how you know, and what this means. c) Choose one process and one choice of system in which money is conserved but NOT constant. Explain how you know, and what this means. 2017.05.05 Document1 5/25 Physics/D'Amato/2010/Momentum 6 Period: Name: 2. "Throws" and "catches" 2.1. Warm up Fill in the blanks to make sure you remember how to use the concept of Δv Initial motion v (a) Not moving –x direction (b) Moving in –y direction Moving faster in –y direction (c) Moving in –x direction Not moving in x direction (d) –x direction Final motion Motion diagram to match Not moving in x direction (e) (f) (g) x (h) Which has a larger v , a tennis ball that falls into mud and stops, or a tennis ball that falls onto pavement and bounces? (i) Which has a larger v , a tank that accelerates from 0 to 1m/s or a softball pitched underhand? (j) Which has a larger v , a tank that accelerates from 12m/s to 13m/s or a bike that accelerates from 2 to 3 m/s? 2017.05.05 Document1 6/25 Physics/D'Amato/2010/Momentum 2.2. 7 Period: Name: Look for a pattern Watch and describe a series of experiments. Fill in the table and think of an explanation that might account for all of the experiment outcomes. Experiment Sketch the initial state. Draw velocity arrows for both objects. Sketch the final state. Draw velocity arrows for both objects. (a) Jon, on a skateboard, is holding a medicine ball. He throws the ball forward and rolls backwards. The initial speed of the ball is much larger than Chris’s speed. Before throw After throw vci 0 vbi 0 vcf vbf Describe the direction and magnitude of the velocities of both interacting objects Compare the Δv of both objects (b) Jon is standing still and catches a medicine ball thown at him. He rolls backwards holding the ball. His speed (and the speed of the ball after he catches it) is much smaller than the speed of the ball before it hit him Δvb= Δvj= Before throw After throw Describe the direction and magnitude of the velocities of both interacting objects Δvb= Compare the Δv of both objects (c) Jon is moving to the right and catches the ball thrown at him (moving left). He slows down after he catches the ball. Jon and the ball continue to move to the right slower than Jon was moving before he caught the ball. Δvj= Before catch After catch Describe the direction and magnitude of the velocities of both interacting objects Δvb= Compare the Δv of both objects Δvj= (d) Consider the observations above, and find a pattern that describes what happens to the velocity of the two objects involved in a throw or catch 2017.05.05 Document1 7/25 Physics/D'Amato/2010/Momentum 2.3. 8 Period: Name: Predict and test Use the pattern that you devised in 2.2(d) to predict the results of the following experiments. Then compare your prediction with the outcome of the real experiment or with your previous experiences. (b) Cart A is loaded with a block of metal and has a velcro pad on the front. It moves slowly to the right on a low-friction track, and hits the empty and stationary cart B, which has a velcro patch on the side facing cart A. (a) Chris is standing on a skateboard and then he jumps off of it toward the back. Describe your prediction in words and sketch Explain how you made the prediction using the pattern in 2.2(d) Compare to observations (c) Discuss whether the pattern you described in 2.2(d) was successful in predicting the results of these new experiments. 2.4. Explain Suppose you place a rifle on gliders and pull the trigger. A bullet (mass 0.020-kg) shoots at high speed (300 m/s) out of the barrel and the rifle (mass 2.0-kg) recoils back in the opposite direction at speed 3.0 m/s. Does this match the pattern you detected in the experiments above? Explain. 2017.05.05 Document1 8/25 Physics/D'Amato/2010/Momentum 2.5. 9 Period: Name: Physics in the movies What do you see when somebody fires a handgun in the movies? What happens to the handgun and the hand holding it? Can you explain this in terms of the pattern we have discovered? What happens in the movies when somebody (hopefully a bad guy) is shot? Can you explain this in terms of the pattern we have discovered? 2.6. Stopped dead At the National Transportation Safety test facility, they video the collision of two identical cars initially moving at 80 km/h (45 mph) toward each other. Immediately after the collision, the cars are at rest stuck to each other. The velocities before the collision were the same magnitude but in opposite directions. Explain. 2.7. A creative solution You wear ice skates and a backpack on a frozen pond. How might you start moving without pushing off on the ice? Explain. 2.8. Homework Describe what will happen and explain in terms of our new principle: (1) a moving train car is rolled gently toward another train car that is not moving. The two cars touch and lock together. What happens next and why? (2) a small pirate ship fires a large cannon from its rear deck. What happens next and why? 2017.05.05 Document1 9/25 Physics/D'Amato/2010/Momentum 10 Period: Name: 3. Conservation in throws and catches 3.1. Look for a quantity that is conserved Imagine observing the following experiments with two frictionless gliders moving on an air track. Complete the table that follows for each experiment. Try to find a physical quantity that is conserved if the choice of system includes both carts. Experiment Sketch the process before the collision and after the collision. Label known quantities Determine if anything is the same before and after the collision (i.e., is any quantity conserved). Hint: think of mass, speed, velocity, acceleration or some combination of these quantities (a) Cart A (200 g) moving left at a constant 0.70 m/s speed hits identical cart B (200 g) that is stationary. Cart A stops and cart B starts moving at speed 0.70 m/s to the left. (b) Cart A loaded with blocks (total mass of the cart with blocks is 400 g) moving left at 0.70 m/s hits stationary cart B (mass 200 g). After the collision, both carts move left, cart B at speed 0.86 m/s and cart A at speed 0.27 m/s. (c) Cart A (200 g) with a piece of modeling clay attached to the front moves left at 0.70 m/s. Identical cart B (200 g) moves right at constant speed 0.70 m/s. The carts collide, stick together thanks to the clay, and stop. (d) Repeat experiment (c) but this time cart A is loaded (total mass of the cart with blocks is 400 g). After the collision both carts stick together and travel left at speed 0.23 m/s. (e) After you come up with a physical quantity that is conserved in each experiment, decide if a single quantity is conserved in all of the experiments. 2017.05.05 Document1 10/25 Physics/D'Amato/2010/Momentum 3.2. 11 Period: Name: Represent with conservation bar charts Create a conservation bar chart to represent the new quantity in each of the previous experiments Experiment (a) Cart A (200 g) moving left at a constant 0.70 m/s speed hits identical cart B (200 g) that is stationary. Cart A stops and cart B starts moving at speed 0.70 m/s to the left. before Δ after before Δ after before Δ after before Δ after + 0 (b) Cart A loaded with blocks (total mass of the cart with blocks is 400 g) moving left at 0.70 m/s hits stationary cart B (mass 200 g). After the collision, both carts move left, cart B at speed 0.86 m/s and cart A at speed 0.27 m/s. + 0 (c) Cart A (200 g) with a piece of modeling clay attached to the front moves left at 0.70 m/s. Identical cart B (200 g) moves right at constant speed 0.70 m/s. The carts collide, stick together thanks to the clay, and stop. + 0 (d) Repeat experiment (c) but this time cart A is loaded (total mass of the cart with blocks is 400 g). After the collision both carts stick together and travel left at speed 0.23 m/s. + 0 (e) Do your bar charts show conservation of the same quantity for all experiments? State this new principle of conservation in your own words. 2017.05.05 Document1 11/25 Physics/D'Amato/2010/Momentum 3.3. 12 Period: Name: Look for the same pattern in other observations The following table provides more data about the collisions of two dynamics carts, including the masses of the carts, initial velocities of the carts before the collision (vi), and the final velocities after the collision (vf). Sketch before and after Make a conservation bar chart Cart 1: mass = m, vi =+2.0 m/s, vf =+1.0 m/s Cart 2: mass = m, vi = 0 m/s, vf =+1 m/s (a) Cart 1: mass = m, vi =+2.0 m/s, vf =+1.0 m/s Cart 2: mass = m, vi = –2.0 m/s, vf =+1 m/s (b) Cart 1: mass = 2m, vi =+2.0 m/s, vf =+0.5 m/s Cart 2: mass = m, vi = –1.5 m/s, vf =+1.5 m/s (c) Cart 1: mass = 2m, vi =+2.0 m/s, vf = 0 m/s Cart 2: mass = m, vi = –2.0 m/s, vf = +2.0 m/s (d) (e) Determine whether the same quantity is conserved in each of these experiments as was conserved in 3.1(e) 2017.05.05 Document1 12/25 Physics/D'Amato/2010/Momentum 3.4. 13 Period: Name: Real world connections When considering weapons for defense against attacking zombies, the most important consideration is stopping power. If the motion of the undead can be reduced or stopped there may be enough time for a survivor to escape. Two survivors are discussing the merits of the weapons they have looted from the ruins of the sporting goods store. Matt has a high-powered hunting rifle that fires a 0.05kg bullet at 1000m/s. He observes that his bullets often pass right through attacking zombies. Kerry has a shotgun that fires 0.1kg of birdshot at 500m/s. The small particles of ammunition from her weapon penetrate a short distance into the flesh of the zombies but never go all the way through. (a) Matt insists that his high-powered weapon would be much better at stopping a zombie shambling toward them. Use your new principle of conservation to determine whether or not he is correct. What assumptions did you make in your analysis? Matt and his weapon Kerry and her weapon Choice of system objects ammo, zombie ammo, zombie Initial moment Just before ammo strikes zombie Just before ammo strikes zombie Final moment After ammo strikes zombie After ammo strikes zombie Sketch and label initial and final states Calculate initial momentum of ammo Calculate final momentum of ammo. Make reasonable assumptions about its velocity. Calculate initial momentum of zomie. Make reasonable assumptions about its mass and velocity Construct a momentum bar chart for the system and process Which weapon will be more effective in slowing the zombie? Explain. 2017.05.05 Document1 13/25 Physics/D'Amato/2010/Momentum 14 Period: Name: (b) Jimmy has a shotgun just like Kerry's. He find himself cornered by a 90kg zombie that is shambling toward him at 2m/s. He has four shells left in his repeating shotgun, and no time to reload before he will be torn apart. Can he stop the zombie? Describe the assumptions you made in your analysis. (c) Josh has a 4kg axe which he can swing at 12m/s. When he uses it on a zombie, it thunks into mouldering flesh and stops dead. Katelyn has a big 6kg mallet which she can swing at 8m/s. When she uses it on a zombie, it bounces off the zombie in the opposite direction at almost the same speed. If they are facing identical zombies, shambling at the same speed toward each of them, which has a better chance of stopping the zombie long enough to escape? Explain your answer with conservation bar charts. What assumptions did you make? 2017.05.05 Document1 14/25 Physics/D'Amato/2010/Momentum 15 Period: Name: 4. Solving momentum problems in isolated systems 4.1. Summary and definitions Momentum Momentum is a fundamental physical quantity that is possessed by all objects The momentum p of an object is equal to the object's mass m times the object's velocity v p mv Momentum is a vector quantity in the same direction as velocity. (It has the same sign as velocity on a number line coordinate axis.) System A choice of objects that are considered separately from all other objects for the purpose of analysis Environment All other objects that are not in the system External interaction A force (push or pull) between an object in the environment and an object in the system Internal interaction A force (push or pull) between two objects both in the system Initial state The properties of the system objects at a moment in time Final state The properties of the system objects at a later moment in time Process The properties of the objects in the system change from one state to a different state over a period of time Constant When the total amount of quantity within a system remains the same as time changes, the quantity is said to be constant. Conserved A conserved quantity does not appear from nowhere or disappear without trace. You can always choose a system within which the quantity is constant. The classic example of a conserved quantity is mass. Momentum conservation bar chart This is a tool that allows us to visualize the transfer of momentum within system objects. Sometimes we will draw the bars with precise values, or sometimes we will just show the relative sizes. A properly drawn bar chart will show the same total momentum on the "before" side and the "after" side Each side of the chart shows a bar for each object in the system. The size of the bar is determined by calculating the momentum p of the object in the initial or final state. before p1i Δ p2i after p1f p2f + 0 0 - 2017.05.05 Document1 15/25 Physics/D'Amato/2010/Momentum 16 Period: Name: 4.2. Warm up When no unbalanced forces are exerted on the objects in a system, the total amount of momentum in a system remains constant. Let's practice using this principle to reason about The initial and final states for four processes are shown below. The system includes both blocks and the spring, if present. Which process are possible and which are not according to your knowledge of momentum conservation? Explain your reasons. The numbers indicate the relative mass and the relative speeds of the blocks. (a) (b) (c) (d) 2017.05.05 Document1 16/25 Physics/D'Amato/2010/Momentum 17 Period: Name: 4.3. Bar chart jeopardy before p1i Δ p2i after p1f p2f + 0 0 (a) If the initial momentum of object 1 is equal to 40 kg m /s and its mass is 5kg, convert the bar chart above into a mathematical description constant momentum for two objects. (b) Describe in words and sketch a process consistent with the bar chart and mathematical statement you have formulated. 4.4. Equation jeopardy Come up with a problem that is consistent with each of the two mathematical descriptions of processes provided in the table below. Mathematical description of a process (a) Pose a problem consistent with the process. (24 kg)(–2.0 m/s) + (30 kg)(+3.0 m/s) = (24 kg + 30 kg) v 2017.05.05 Document1 17/25 Physics/D'Amato/2010/Momentum 18 Period: Name: 4.5. Introduction to problem solving Apply the constant-momentum problem solving strategy to these situations Problem solving strategy for momentum in an isolated system. Order of steps is a guide only (a) A 1000-kg rocket traveling west at 40 m/s ejects its booster segment. Immediately after the ejection, the larger 800-kg segment continues west at 60 m/s. Determine the velocity (magnitude and direction) of the ejected booster immediately after the ejection. A. Sketch and list 1. Identify the unknown quantity and select system objects, initial moment, and final moment 2. Sketch the initial and final states 3. Circle the system objects 4. Draw an axis and choose a + direction 5. List all the known quantities using familiar symbols B. Momentum 4. Construct a constant momentum bar chart 5. Complete the bar chart to show constant momentum in the system If you can't find constant momentum, consider changing your selection of system objects and moments. C. Math & Physics 8. Use the conservation bar chart to compose a math statement of constant momentum 10. Substitute known quantities and solve for unknown quantities 11. Evaluate your answer for reasonableness (magnitude, sign, units) 2017.05.05 Document1 18/25 (b) A 1000-kg car, traveling west at 20 m/s, collides with an 800-kg car traveling north at 16 m/s. The cars stick together. Determine the velocity of the cars (magnitude and direction) immediately after the collision. Physics/D'Amato/2010/Momentum 19 Period: Name: 5. Change in the momentum of the system 5.1. Warm up: Calculate the change in momentum (a) A 1998 910-kg Toyota Tercel travels at a speed of 32 m/s. (a) At what speed must a 2002 1950-kg Toyota 4Runner travel to have the same momentum? (b) At what speed must a 7.3-kg bowling ball travel to have the same momentum? (b) Your 0.0567-kg tennis ball traveling at 25 m/s hits a practice wall and rebounds in the opposite direction with the same speed. Determine the ball’s change in momentum (magnitude and direction). (c) A 145-g baseball traveling at 35 m/s is hit by Barry Bonds’ bat so that it rebounds in the opposite direction at 40 m/s. Determine the ball’s change in momentum (magnitude and direction). (d) Tiger Woods’ golf club hits a 0.055-kg golf ball so that it leaves the grass at a speed of 50 m/s. Determine the magnitude of its change in momentum. 2017.05.05 Document1 19/25 Physics/D'Amato/2010/Momentum 20 Period: Name: 5.2. Derive a new expression Cart A of mass m is at moving at velocity vA1 on a horizontal, frictionless track. At clock reading t1 your hand begins to push on the cart with force Fh on A At clock reading t2 the cart is moving at faster velocity vA2 and your hand stops pushing (a) Use the cart as your choice of system and before and after the push as the initial and final states. Sketch the system in the initial and final state, and label all given quantities. (b) Has the total momentum in the system change from before the push to after? If so, identify the external object that caused the change. Sketch a conservation bar chart. (c) Let's try to calculate the quantity of change. Use Newton’s second law and the definition of acceleration to show Fh on A (t2 t1 ) mvA2 mvA1 The term on the left Fh on c (t2 t1 ) is called the impulse due to the external force Fh on c during that time interval. The term on the right mvc2 mvc1 is called the change in the momentum of the cart. 2017.05.05 Document1 20/25 Physics/D'Amato/2010/Momentum 21 Period: Name: (d) Suppose that friction is not negligible. How would you modify the expression for the impulse on the cart to include both the effect of the hand and of friction? (e) Suppose the cart’s forward velocity decreased due to the force of a hand pushing lightly back on it. How would you write the expression for the impulse due to that force? 5.3. Problems including a change in total momentum (a) Junior’s bat contacts a 0.145-kg baseball for 1.3 x 10-3 s. The average force of the bat on the ball is 8900 N. If the ball has an initial velocity of 36 m/s toward the bat, what is the ball's final velocity (magnitude and direction)? (b) John Glenn’s 65-kg body pushes against the inside back wall of a 2000-kg spaceship, causing his speed toward the front to increase from zero to 1.6 m/s. (a) If the push lasts 0.30 s, what is Glenn’s average force on the spaceship? (b) With what speed does the spaceship recoil if initially at rest? 2017.05.05 Document1 21/25 Physics/D'Amato/2010/Momentum 22 Period: Name: 6. Problems with conserved momentum 6.1. Warm up Chris and Grey are married. (a) On Saturday, Chris stays home reading while Grey teaches yoga for 2 hours at $50/hour. When Grey comes home she gives Chris $20 for lunch money. How much does their net worth change during this time? (b) On Sunday afternoon, Grey teaches yoga while Chris goes to the go-kart track with his friends. If the go-kart track charges $40 an hour to race, what is the total change in their net wealth if they are both out for 2.5 hours? 6.2. Warm up Practice reasoning with the change in momentum or "impulse": 𝐼 = ∆𝑝 = 𝐹net external ∆𝑡 (a) The rails of the Washington D.C. Metro train track exert a 2.0 x 10 5 N friction force on the train causing it to stop in 50 s. Choose system objects so that the tracks exert an impulse on the system objects. Calculate the impulse. (b) Peter is on ice skates, initially at rest. His father pushes him from behind with an average force of 12N. If Peter's momentum increases by 46 kg m/s how long did his father push? (c) A 400g cart on a frictionless track is rolling at 3 m/s. A hand pushes lightly on the front of the cart until it stops. If the cart takes 1.2 seconds to stop, what was the average force of the hand on the cart? (d) Your heart pumps about 80g of blood with each beat. Each beat lasts about 0.17s. The blood starts at rest and reaches a speed of about 1 m/s. What is the impulse exerted by the heart on this amount of blood? What is the average force exerted on the blood by the heart? 2017.05.05 Document1 22/25 Physics/D'Amato/2010/Momentum 23 Period: Name: 6.3. Real problems Address these real college-level momentum problems using the problem solving strategy Order of steps is a guide only Junior’s bat contacts a 0.145-kg baseball for 1.3 x 10-3 s. The average force of the bat on the ball is 8900 N. If the ball has an initial velocity of 36 m/s toward the bat, what is the ball's final velocity (magnitude and direction)? 1. Choose system objects read imagine 2. Sketch initial moment and label known quantities (include +/- axis) sketch At least twice 3. Sketch final moment and label known quantities 4. Identify external object(s) exerting unbalanced forces on system object(s) 5. Write an expression for 𝐹net ext 6. Write an expression for the net impulse exerted on system objects by external objects ∆𝑝 = 𝐹net ext ∆𝑡 7. Construct a conservation bar chart for momentum in the system 8. Use the conservation bar chart to construct a mathematical statement of conservation of momentum: 𝑝Ai + 𝑝Bi + ∆𝑝 = 𝑝Af + 𝑝Bf 9. Substitute known quantities and solve for unknown quantities 10. Evaluate your answer for reasonableness (magnitude, sign, units) 2017.05.05 Document1 Jason Kidd high in the air drops a 0.60-kg basketball so that it reaches the floor falling vertically at 6.0 m/s. The ball rebounds upward at a speed of 5.2 m/s. Determine the ball's change in momentum (magnitude and direction). Determine the average net force of the floor on the ball if the collision lasts 0.12 s. 23/25 Physics/D'Amato/2010/Momentum 24 Period: Name: 6.4. Real problems Address these real college-level momentum problems using the problem solving strategy Order of steps is a guide only (a) John Glenn’s 65-kg body pushes against the inside back wall of a 2000-kg spaceship, causing his speed toward the front to increase from zero to 1.6 m/s. If the push lasts 0.30 s, what is Glenn’s average force on the spaceship? With what speed does the spaceship recoil if initially at rest? 1. Choose system objects 2. Sketch initial moment and label known quantities (include +/- axis) 3. Sketch final moment and label known quantities 4. Identify external object(s) exerting unbalanced forces on system object(s) 5. Write an expression for 𝐹net ext 6. Write an expression for the net impulse exerted on system objects by external objects ∆𝑝 = 𝐹net ext ∆𝑡 7. Construct a conservation bar chart for momentum in the system 8. Use the conservation bar chart to construct a mathematical statement of conservation of momentum: 𝑝Ai + 𝑝Bi + ∆𝑝 = 𝑝Af + 𝑝Bf 9. Substitute known quantities and solve for unknown quantities 10. Evaluate your answer for reasonableness (magnitude, sign, units) 2017.05.05 Document1 24/25 (b) The bone in the upper part of the cheek (the zygomatic bone) can be fractured by a 900-N force lasting 6.0 ms or longer. A hockey puck can easily provide such a force when hitting an unprotected face. (a) What change in velocity of a 0.11-kg hockey puck is needed to provide that impulsive force? Physics/D'Amato/2010/Momentum 2017.05.05 Document1 25 25/25 Period: Name: