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Transcript

Momentum Objectives Define impulse and momentum. Solve problems using the impulse-momentum equation. Relate Newton’s Third Law of Motion and the Law of Conservation of Momentum. Distinguish between elastic and inelastic collisions. Explain and apply the Law of Conservation of Momentum to collisions and explosions. Solve problems involving one-dimensional collisions and explosions. Solve two-dimensional collision problems using vectors. Key Terms Impulse-Momentum Theorem impulse momentum closed system Law of Conservation of Momentum collision elastic collision inelastic collision explosion recoil Summary Review Impulse and Momentum and Conservation of Momentum An impulse (force applied over a time interval) causes momentum. Momentum is inertia in motion and found by multiplying mass and velocity. To change an object’s momentum, either force, time, mass, or velocity must be changed. Momentum must be overcome to stop motion. Momentum of any closed system is always conserved. Collisions and Explosions A collision is the interaction of two objects. An elastic collision is an interaction in which colliding objects bounce or do not stick together; two objects interact but remain two objects. An inelastic collision is an interaction in which colliding objects stick together or do not bounce; two objects interact to become one object. An explosion is the process of one object becoming two. Problem Solving with Momentum Momentum is always conserved. Always! The overall mass of a system does not change. The Problem Solving Strategy is used when solving collision problems. Impulse and Momentum Demonstration and Notes When looking at Newton’s Second Law of Motion, F ma , we can substitute the basic equation v used to find acceleration, , for a. When rearranged, a new equation is derived: the impulset momentum theorem. Each side of the equation can be looked at individually; the left as impulse, the right as momentum. v F ma F m F t m v t Impulse-Momentum Theorem – equation that relates impulse and momentum. impulse (J) – force applied through a finite time interval; vector quantity measured in N s . J F t momentum () – inertia in linear motion; product of the mass and velocity of an object; vector kg m quantity measured in . s mv The above equations apply to situations where mass remains constant. To make things easier, we will always work with problems where mass is constant. Although the mass will remain constant, the velocity may change. This leads to a variation of the momentum equation, relating momentum to impulse; the impulse acting on an object is equal to its change in momentum. Since F t m v and m v , then F t . Determine how to change the momentum of a baseball that is hit with a bat. There are various ways to change an object’s momentum. One way is to change the impulse causing the momentum. To increase impulse, either the force or time interval must be increased. This is done by hitting harder or following through with the swing. To decrease impulse, either the applied force is reduced or the time of contact is shortened. Another way to change momentum is to change the factors that determine momentum; mass and velocity. To increase momentum, either the mass or velocity of the ball must be increased. To decrease momentum, either the mass or velocity of the ball must be lowered. Determine what object has the greatest momentum, a truck or a roller skate. To answer this question, you need to know several things about each object. Since momentum is determined by both mass and velocity, both quantities must be known. If either object is at rest, it has no momentum. The momentums could be equal if the heavy truck has a very small velocity and the light roller skate has a very large velocity. Determine which vehicle is harder to stop, a truck or a car traveling at the same speed. Motion stops when momentum is overcome. Even though both vehicles are traveling at the same speed, the truck has a larger mass. Therefore, the truck has more momentum which makes it more difficult to stop. This usually requires better brakes and a greater stopping distance. Have two people hold a cotton bed sheet so it hangs above the floor in a J-shape. Predict what would happen if an egg was thrown at the sheet. The egg remains unharmed because although the egg is thrown with a large velocity, the sheet provides a large time interval for the egg to stop thus reducing the stopping force. J F t ( F ) ( t ) Conservation of Momentum Notes According to Newton’s Third Law of Motion, when a bat hits a baseball, the baseball also hits the bat. This can also be thought of in terms of impulse and momentum. The momentum of the baseball changes as a result of the impulse given to it by the bat. In keeping with Newton’s Third Law, the bat also receives an impulse from the baseball. The interaction between the baseball and bat it is viewed as a closed system, allowing momentum to be conserved. closed system – system where nothing is lost and no external forces act. Law of Conservation of Momentum – the momentum of any closed system does not change; in a closed system, the momentum before an interaction equals the momentum after the interaction. o f Introduction to Momentum and Impulse Activity Station A: 1-Dimensional Elastic Collisions Use two carts of the same mass: 1. Keeping one cart at rest, gently push the second cart to collide with the bumper between them. Explain the motion of the two carts. 2. Push the two carts towards each other with equal speeds so they collide in the center of the track with the bumper between them. Explain the motion. 3. Push the two carts towards each other with different speeds, one slow, one faster (but not too fast!). Explain the motion. 4. Repeat steps1-3 with carts of different masses. Write your responses below. 5. Give a real life example of this motion. Station B: 1-Dimensional Inelastic Collisions 1. Keeping one cart at rest, slide the second cart towards it so they collide and stick together. Explain the motion. 2. Push the two carts towards each other with equal speeds so they collide in the center of the track. Explain the motion. 3. Push the two carts towards each other with varying speeds (one faster than the other). Explain the motion. 4. Add mass to one of the carts and repeat steps 1-3. Write your responses below. 5. Give a real life example of this motion. Station C: Explosions 1. Remove any mass from the carts. 2. Place the two carts against each other with the plunger pressed in. 3. Tap the button on the plunger cart with the hammer and observe the motion. Explain the motion you observe. 4. Add a mass to one car and repeat the process. Then repeat again with two masses on one car. How does the addition of mass to one car change the motion? Discuss how it changes the speed and distance of the cart. 5. Give a real life example of this motion other than a traditional explosion. (one object becoming two pieces OR two objects pushing apart) Station D: Simulations – Directions on each slide. Answer questions on a separate sheet of paper and attach. The Cartoon Guide to Physics Momentum and Impulse Read the comic and answer the following questions on a separate piece of paper. 1. What is Newton’s Second Law? 2. Can it be written more than one way? If so, what are the other ways? 3. Which equation did Newton believe should be correct? 4. Is force independent of the rate of change of momentum? 5. Does a runaway baby carriage have momentum? Explain. 6. Can a baby carriage and a runway Mack truck have the same momentum? Why? 7. Could a puny force like our weight stop a runaway Mack truck? 8. What is impulse? 9. If we want to change our momentum and we have a large force will we require a long or short period of time? 10. When the bat meets the ball should the force be very large or very small? Why? 11. What is Newton’s Third Law? 12. Is shooting a gun an example of Newton’s Third Law? 13. Since momentum is conserved when shooting a gun, how are velocity and mass related? 14. Can we have equal and opposite momentums to create a net change of zero? 15. What is an internal force? 16. Are the forces balanced when a flying projectile explodes? 17. Does this explosion conserve momentum? Why? 18. If you’re in the middle of a frictionless ice rink, how can you get to the edge of the rink to get off the ice? 19. What came first, conservation of momentum or Newton’s Third Law? 20. Since there are no external forces in a closed system and our universe is a closed system, is total momentum in the universe constant? Collisions and Explosions Demonstrations and Notes Objects can interact with one another in numerous ways. When dealing with these interactions and applying the Law of Conservation of Momentum, eight different interactions exist. collision – interaction of two objects; two types: elastic and inelastic. elastic collision – interaction in which colliding objects bounce or do not stick together; two objects interact but remain two objects; 2 2; two cases: 1 one- and 1 two-dimensional. Using an air track and two carts of equal mass, slide one cart toward the second cart which is at rest. Observe the motion of the carts before, during, and after the elastic collision. Since momentum is always conserved and the carts are of equal mass, the speed of the incoming cart will equal the speed of the outgoing cart. The carts transfer momentum. Using an air track and two carts of varying mass, slide the lighter cart toward the heavier cart which is at rest. Observe the motion of the carts before, during, and after the elastic collision. The lighter cart bounces back with a high speed and the heavier cart moves opposite the light cart at a low speed. Repeat but slide the heavier cart toward the lighter cart which is at rest. Observe the motion of the carts before, during, and after the elastic collision. The heavier cart continues its motion with a low speed and the lighter cart moves in the same direction as the heavier cart at a high speed. Repeat again using a greater variance of mass. Observe the motion of the carts before, during, and after the elastic collision. The heavier cart continues its motion with a lower speed and the lighter cart moves in the same direction as the heavier cart at a higher speed. Using an air track and two carts of equal mass, slide the two carts toward one another. Observe the motion of the carts before, during, and after the elastic collision. Since momentum is always conserved and the carts are of equal mass, the speed of the carts before the collision will equal the speed of the carts after the collision. The momentum is transferred, but it appears to simply stay with its respective cart. inelastic collision – interaction in which colliding objects stick together or do not bounce; two objects interact to become one object; 2 1; four cases: 3 one- and 1 two-dimensional. Using Pasco low-friction tracks and carts of equal mass, slide one cart toward the second cart which is at rest. Observe the motion of the carts before, during, and after the inelastic collision. Since momentum is always conserved, the overall speed of the carts when combined will continue in the direction of the original momentum but will decrease in magnitude. If either cart was more massive, the final speed would still be decreased. Using Pasco low-friction tracks and carts of equal mass, slide one cart toward the second cart which is moving as a low speed away from the first cart. Observe the motion of the carts before, during, and after the inelastic collision. Since momentum is always conserved, the overall speed of the carts when combined will continue in the direction of the original momentum but will decrease in magnitude. If either cart was more massive, the final speed would still be decreased. explosion – process of one object becoming two, 1 2. recoil – kickback; momentum opposite a projectile. Using Pasco low-friction tracks and carts of equal mass with a plunger, place two carts touching side-by-side with the plunger engaged. Release the plunger and observe the motion of the carts before, during, and after the explosion. Since momentum is always conserved, the overall momentum of each cart when separated will be equal and opposite to one another. If the carts are equal in mass, their speeds are equal in magnitude and opposite in direction. If one cart was more massive, its speed would be less than the lighter cart. Problem Solving with Momentum Notes The key to success when solving any momentum problem is remembering one thing: momentum is always conserved! Since momentum is always conserved, there is technically only one equation necessary. The momentum equation is also needed, but it is simply substituted into the conservation of momentum equation. Once the type of problem is determined, proper set up and substitution will always lead to the correct answer. Don’t forget to include direction! conservation of momentum momentum impulse o f mv F t m v When solving problems, the following procedures will be used. 1. 2. 3. 4. 5. 6. 7. 8. Determine what type of problem is observed – collision or explosion. If a collision, determine what kind – elastic or inelastic. Make a sketch of the situation and label all given and unknown quantities. Determine what variables are known and needed. Recall that momentum is always conserved and set up the proper equation. Substitute the given quantities into the equation using proper units. Solve the equation, carrying units throughout the problem. Check your answer to make sure it makes sense, including direction if necessary. Problem Solving with Momentum o f mv F t m v Eo E f KE 1 mv 2 2 1. A baseball with a mass of 0.15 kg is thrown by a pitcher at a speed of 45 m/s and then hit by a batter. The ball is in contact with the bat for 0.01 seconds and is driven directly into center field with a speed of 55 m/s. What is the momentum of the thrown ball, the batted ball, and the impulse on the ball? 2. Suppose one ice skater has a mass of 60 kg and a second has a mass of 30 kg. They are standing arm-in-arm on the ice. If the 60 kg skater loses his balance and pushes the 30 kg skater to the right at 0.4 m/s, how fast and in what direction will the 60 kg skater move? 3. A 5000 kg train is moving at 10 m/s to the right. It collides with a train of 10000 kg that is moving to the left at 7 m/s. If they stick together, how fast will the two trains move and in what direction? 4. A 500 kg car is cruising down the highway at 5 m/s to the right. While the driver is looking for a good radio station, she drifts across the center line. Unfortunately, a 5000 kg truck is heading right for the car! The truck tries to stop but only manages to slow down to 2 m/s when the two vehicles collide head-on. If they stick together, how fast will the two vehicles move and in what direction? What would happen if the truck did stop but the car still collided into the truck? 5. A 100 kg car is moving 3 m/s north and collides with a 200 kg car going 2 m/s east. If they lock bumpers, how fast and in what direction will they be going after the collision? 6. Block A with a mass of 12 kg moving at 2.4 m/s makes a perfectly elastic head-on collision with block B, mass 36 kg, at rest. Find the velocities of the two blocks after the collision. Assume all motion is in one dimension. Problem Solving with Momentum o f mv F t m v Eo E f KE 1 mv 2 2 1. Arnold Palmer is practicing his golf swing. When using his seven iron, a constant force of 1500 N acts on the 0.75 kg golf ball. Determine the impulse and change in speed of the object when he follows through with his swing (t = 0.015 seconds) and when he chips the shot (t = 0.0005 seconds). 2. A rifle with a mass of 2 kg is used to fire a bullet of mass 0.05 kg. The bullet leaves the gun with a speed of 200 m/s. What is the recoil velocity of the gun? 3. A Cadillac with a mass of 2500 kg collides with a Volkswagen with a mass 1000 kg. Their bumpers lock. The Cadillac is moving at a speed of 23.6 m/s at the time of impact and the Volkswagen is standing still. Determine the speed and direction of the crash. 4. Suppose that in the previous problem the Volkswagen was moving at a speed of 33.3 m/s and the Cadillac at a speed of 4.2 m/s. They collide head-on and lock bumpers. Determine the speed and direction of the crash. 5. A 350 kg car is moving 16 m/s north and collides with a 650 kg truck going 11 m/s east. If they lock bumpers, how fast and in what direction will they be going after the collision? 6. A 16 kg canoe moving to the left at 12 m/s makes an elastic head-on collision with a 4 kg raft moving to the right at 6.0 m/s. Find the velocities of each object after the collision. MOMENTUM LAB PACKET Introduction – What’s Going On? Objects can interact with one another in numerous ways. The two most common interactions are collisions and explosions. This lab contains three parts that apply the concepts of impulse and momentum in an effort to develop a comprehensive understanding of the Law of Conservation of Momentum. Important equations used throughout this lab packet are listed below for reference. o f Percent Error mv v d t measured value accepted value 100 accepted value Each experiment in this packet is based on the Law of Conservation of Momentum. Read each activity and follow the directions listed on the following pages. Remember, when all else fails: The sum of everything physics is usually equal to zero! MOMENTUM LAB PACKET 2-D Elastic Collisions Part I – Setting Up Each group needs a ramp, C-clamp, roll of masking tape, protractor, two meter sticks, two steel balls, two pieces of carbon paper, and a one-by-one meter piece of paper. Clamp the ramp to the lab table so the angled end is slightly hanging over the edge of the table. Also make sure the clamp is turned away from the end of the ramp so it will not interfere with the colliding steel balls. Tape a one-by-one meter piece of paper to the floor under the edge of the ramp. Make sure the paper is positioned in a way that the edge of the ramp is above the paper. Mark the location of the end of the ramp on the paper below. (Use a dot.) Measure the vertical height (y) the ball will fall to the floor. Part II – Collecting Preliminary Data Roll a steel ball down the ramp from the marking bolt. Observe the approximate landing location and place a piece of carbon paper centered on that location. Roll the same steel ball down the ramp twenty times, allowing the ball to hit the carbon paper and mark the landing locations. Draw a circle around the landing marks so that all twenty marks are inside the circle. MOMENTUM LAB PACKET 2-D Elastic Collisions Part III – Collecting Data Adjust the ball holder so it is off-center with respect to the ramp. Mark the location of the ball holder on the paper below. (Use a dot.) Place a steel ball on the ball holder. Roll the other steel ball down the ramp from the marking bolt. Allow the two steel balls to collide and observe the approximate landing locations. Make sure both balls hit the ground at the same time. (Align their centers of mass.) Place a piece of carbon paper centered on each location. Reset the stationary ball on the ball holder and roll the other ball down the ramp, allowing the balls to collide and then hit the carbon paper, marking the landing locations. Repeat twenty times. Draw a circle around each of the landing marks so all twenty marks are inside each circle. Label the circles stationary and moving. Include the trial number. Change the off-set angle of the ball holder and repeat the above steps. MOMENTUM LAB PACKET 2-D Elastic Collisions Part IV – Calculations Draw a straight line from the dot marking the ball holder and collision location to the center of the circle drawn around the no collision data. Draw a second straight line from the dot marking the ball holder and collision location to the center of the circle drawn around the stationary ball data. Draw a third straight line from the dot marking the ball holder and collision location to the center of the circle drawn around the moving ball data. Measure the horizontal distance each ball traveled. Calculate the time it takes for each ball to fall to the ground. Calculate the horizontal velocity for each ball. Complete the data table, including mass of each ball, momentum of each ball, and percent error. The horizontal distance traveled is the component of the line drawn that is in the same direction as the ball rolling with no collision. Part V – Wrap Up In addition to the data table, write a paragraph or two explaining your results. How did you predict the final momentum? How did your predictions compare with what actually happened? What are some reasons contributing to your percent error? Part VI – Just for Fun Put a thin piece of paper over the line for either marble. On that paper, carefully trace the line, marking the beginning and end of the line. Then, without rotating it, slide the paper along the other marble’s line. The beginning of the line for one marble should be put at the end of the line for the other marble. When you do this, what do you notice about where the end of the second line falls? Include a picture. 2-D Elastic Collisions Data Table Before Collision Data g= m/s2 y= m tfall = sec x= m vx = m/s mball = kg m-ball = kgm/s s-ball = kgm/s total = kgm/s After Collision Data Trial 1 Moving Ball Trial 2 Stationary Ball Moving Ball y (m) tfall (sec) x (m) vx (m/s) mball (kg) ball (kgm/s) total (kgm/s) Error (%) Stationary Ball MOMENTUM LAB PACKET Inelastic Collisions Part I – Setting Up Each group needs a ramp, index card, two photogates, two carts, launcher, two bumpers, two bumper-legs, black spring, and three mass blocks. Cut a strip from the index card two to three centimeters wide. Tape the strip (perpendicularly) to the cart with the plunger mechanism. Connect the bumpers to each end of the track. Attach the bumper-legs to the underside of the ramp at the 20 cm and 100 cm locations. Attach the launcher to one of the carts. Place one photogate at the 45 cm mark. Place the second photogate at the 60 cm mark. Place the edge of the cart without a plunger almost even (around 57 cm) with the second photogate. Part II – Collecting Data Using gate mode, the photogates will measure the time it takes for the index card to pass through them. Knowing the distance and time of the moving index card, the speed of the cart-system can be calculated. Place the black spring on the plunger and slide that through the left bumper. Pull the edge of the launching cart to the 10 cm mark. Release the cart to launch it. Using the memory function, record the times from the photogates for two trials of each mass combination. Vary the mass of the cart-system and retime. See the data table for mass changes. Part III – Calculations Using the time from each photogate, calculate the speed of the cart before and after the inelastic collision. Complete the data table, including calculated initial and final momentum for each cartsystem, predicted final momentum, and percent error. Part IV – Wrap Up In addition to the data table, write a paragraph or two explaining your results. How did you predict the final momentum? How did your predictions compare with what actually happened? What are some reasons contributing to your percent error? MOMENTUM LAB PACKET Explosions Part I – Setting Up Each group needs a ramp, index card, two photogates, two carts, two bumpers, two bumper-legs, and mass blocks. Cut two strips from the index card, each one to two centimeters wide. Tape the strips (perpendicularly) to the left side of each cart. Attach the bumper-legs to the bottom of the ramp. Connect the bumpers to each end of the ramp. Place one photogate at the thirty centimeter mark. Place the second photogate at the ninety centimeter mark. Load the plunger and place the two carts together, splitting the sixty centimeter mark. Part II – Collecting Data Using gate mode, the photogates will measure the time it takes for the index cards to pass through them. Knowing the distance and time of the moving index card, the speeds of the cart-system can be calculated. Tap the plunger-release with the hammer to explode the cart-system and allow the carts to move through the photogates. Using the memory function, record the times from the photogates for two trials of each mass combination. Vary the mass of the cart-system and retime. See the data table for mass changes. Part III – Calculations Using the time from each photogate, calculate the speed of each cart after the explosion. Complete the data table, including initial momentum for each cart, calculated and predicted final momentum of cart two, and percent error. Part IV – Wrap Up In addition to the data table, write a paragraph or two explaining your results. How did you predict the final momentum of cart two? How did your predictions compare with what actually happened? What are some reasons for error? Inelastic Collisions Data Table Total Mass Cart 1 Total Mass Cart 2 (kg) (kg) Mass Cart 1 Mass Cart 2 Mass Cart 1 Mass Cart 2 +0.5 kg Mass Cart 1 Mass Cart 2 +1.0 kg Mass Cart 1 +0.5 kg Mass Cart 2 Width of Flag Photogate Time One (m) (sec) Original Momentum v1 m1v1 m2v2 (m/s) (kg·m/s) (kg·m/s) Total Mass Predicted mtvf Width of Flag (kg) (kg·m/s) (m) Photogate Time Two (sec) vf (m/s) Experimental mtvf (kg·m/s) Error (%) Explosions Data Table Total Mass Cart 1 Total Mass Cart 2 (kg) (kg) Mass Cart 1 Mass Cart 2 Mass Cart 1 Mass Cart 2 +0.50 kg Mass Cart 1 Mass Cart 2 +0.75 kg Mass Cart 1 Mass Cart 2 +1.00 kg Mass Cart 1 +0.5 kg Mass Cart 2 +1.00 kg Original Width Momentum of Flag of System One (kg·m/s) (m) Photogate Time One (sec) Final Momentum v1 (m/s) m1v1 (kg·m/s) Width of Flag Predicted Two m2v2 (m) (kg·m/s) Photogate Time Two (sec) v2 (m/s) Experimental m2v2 (kg·m/s) Error (%) MOMENTUM LAB PACKET The Egg Drop Part I – You’re On Your Own! Your job as a group is to design a vessel that protects an egg when thrown from a three story building. There are a few rules when it comes to your vessel: Raw egg must be sealed in provided sandwich bag. Scissors may be used but cannot be included in final project. You may work with ONE partner or work alone, groups of three are not permitted! Grades are based upon success of drop (10 points), building criteria (10 points), and write up (10 points). (See rubric on back.) Part II – Wrap Up Your write up should include your rationale for the design you chose including the concepts of impulse and momentum that support your rationale. Discuss any ideas that you thought of and why you decided not to use them, or how you improved on them for your final project. State your results. If your design was successful, state what you think the key element of your success was, if you did not have success, state what you would change to improve on your design. Each group turns in one write up after they drop their egg drop vessel. The Egg Drop Rubric Building Criteria: 5 pts for following directions, project built using only the materials given, in the allotted time. (25 minutes) ______/ 5 Earn up to 5 points for UNUSED materials as listed: MATERIAL POINTS AWARDED Plate – 1 1 pt Dixie Cup – 1 1 pt ½ sheet of paper – 1 0.5 pt Straw – 2 0.5 per straw Cotton Ball – 2 0.5 per cotton ball String – 60cm 0.5 per 20 cm Popsicle Stick – 2 0.5 per stick Paper Clip – 2 0.5 per clip Rubber Band – 2 0.5 per band Pipe Cleaner – 2 0.5 per pipe cleaner Toothpick – 4 0.5 per 2 toothpicks Tape – 100cm 0.5 per 20 cm TOTAL (5 points max) TOTAL PER ITEM Egg Drop Success ............................................................................................... _____ /10 pulverized --------------------------------------------------------------------------- +1 cracked in half ---------------------------------------------------------------------- +3 oozing crack ------------------------------------------------------------------------- +5 hairline crack ------------------------------------------------------------------------ +7 dent, nick, or bumps --------------------------------------------------------------- +8 OK ----------------------------------------------------------------------------------- +10 Write Up.............................................................................................................. _____ /10 Rationale (physics concepts)------------------------------------------------------ +5 What physics concepts (specifically from this chapter) made you think your design would succeed? Stated results ------------------------------------------------------------------------ +2 Did your egg survive? pulverized? somewhere in between? Improvements/keys to success---------------------------------------------------- +3 If it survived: What was the key component to your success? Use physics concepts to explain your success. If it did not survive: What improvements would you make if you could do it again? Use physics concepts to explain your failure and your improvement ideas. TOTAL FOR PROJECT ----------------------------------------------------- _____ /30 POINTS Momentum Chapter Review 1. Describe how to change an object’s momentum. 2. Explain how the Egg Drop Lab is related to the Egg and Bed Sheet Demo. 3. What is meant by a closed system? (From the definition “momentum of any closed system is always conserved.”) The Handy Physics Answer Book What is momentum? Momentum is a value that describes the amount of inertia and motion an object has, and is derived by the formula = m v, or mass times velocity. A small car traveling at 20 mph has much less momentum than a large truck traveling at the same velocity because the truck has more mass. Momentum is often discussed in sports. Football players quite frequently referred to how much momentum they have. It is advantageous in football not only to have a lot of mass, but a lot of velocity as well. The more momentum a player has, the more difficult it is to stop the player. What is an impulse? An impulse describes how a change in momentum occurs. In order to change an object’s motion or momentum, a force needs to be applied to the object for a period of time. The amount of force and the length of time it is applied will control how much effect the impulse has on the object. Why do people bend their legs when landing after a jump? When someone jumps, they typically bend their legs on the landing. An impulse is experienced, and the amount of force and length of time the force was applied determine how much the landing will hurt the legs. Therefore, by bending his or her legs, the jumper will increase the amount of time in the collision by gradually slowing down instead of immediately bringing the body to a halt. This results in a decrease of force between the legs and the ground. If the legs were kept stiff and straight, the time to stop the motion would have been very short, resulting in a very large force and painful experience. Regardless of how the landing takes place, the impulse will be the same; however, by changing the variables that define impulse, the jumper will be able to walk away from landing, instead of experiencing serious hip and leg injuries. The Handy Physics Answer Book What function does an air bag serve in an automobile collision? Whenever a vehicle experiences a front-end collision, the automobile experiences an impulse or change in momentum. The driver and passengers in the car have inertia and will continue to travel forward until the dashboard, seatbelt, or air bag forces them to stop. The force exerted on the passengers when hitting the dashboard could be quite serious and would be devastating if traveling at typical highway speeds. The function of an air bag is to provide a cushion-like effect to gradually bring the passengers to a halt, instead of allowing them to hit the dashboard or windshield with a tremendous force. Through the use of an air bag, the time to stop the passengers is extended, resulting in a smaller force on the individual’s body. This safety feature, along with the seatbelt, has helped prevent death and serious injury for many motorists. When were air bags first introduced? Although air bags are currently popular, the idea of an air cushion was proposed back in the 1960s. The first air bags were designed to accommodate unbelted male drivers, 170 pounds and 5 feet 9 inches tall. In the early ‘70s, the automobile industry debated whether or not it should install air bags in vehicles. Many companies believe that children and short adults might be at risk for injury from the air bags and instead felt that more emphasis should be placed on having motorists wear seat belts. What is the conservation of momentum? According to the conservation of momentum, there is a fixed amount of momentum for the entire universe. Additional momentum cannot be gained or lost in universe, but only transferred from one object to another. For example, if an ice skater with a mass of 50 kg was skating with a velocity of 2 m/s, his momentum would be 100 kg·m/s. If another person were at rest on the ice, that person would have a momentum of 0 kg·m/s. Both the skaters together would have a total momentum of 100 kg·m/s. That amount of momentum will be conserved regardless of any collision between the skaters. The 100 kg·m/s of momentum can be transferred between the skaters. If the moving skater collides with the stationery skater, some of the momentum of the moving skater would be transferred to the stationery skater. Depending upon the type of collision, the momentum of each skater would be different. The moving skater would lose momentum because it would transfer some of its momentum to the other skater, yet the momentum of skater one plus skater two would remain at 100 kg·m/s. Momentum Problem Set o f mv F t m v Eo E f KE 1 mv 2 2 1. A basketball with a mass of 1.05 kg is shot by the point guard at a speed of 12 m/s and then blocked by a defenseman. The ball is in contact with the defenseman for 0.05 seconds and is driven directly opposite the shot at a speed of 3 m/s. What is the momentum of the shot ball, the blocked ball, and the impulse on the ball? 2. A 0.9 kg squirrel falls out of his tree and lands in the center of a frozen pond. Luckily, the squirrel is holding a 0.28 kg nut. If the squirrel knows enough physics, what can he do to get to the edge of the pond and return safely to his tree? (Assume the ice is a friction-free environment.) Calculate the speed of the squirrel if the nut has a speed of 2 m/s. 3. A hunter is walking through the woods at 4 m/s. A shotgun with a mass of 9 kg is used to fire a bullet of mass 0.4 kg while walking. The bullet leaves the gun with a speed of 125 m/s. What is the recoil velocity of the gun? 4. A 76 kg Big Wheel collides with a 167 kg bicycle. Their wheels get tangled and lock up when they hit head-on. The Big Wheel was moving at a speed of 9.4 m/s and the bicycle at 5.3 m/s at the time of impact. Determine the speed and direction of the crash. 5. A 0.35 kg pellet is shot at 1.6 m/s east and sticks in a 0.68 kg target moving at 1.1 m/s north. Determine their speed and direction after the collision? 6. As everyone should know, bullets bounce from Superman’s chest. Suppose Superman, mass 104 kg, while not moving, is struck by a 4.2 g bullet moving with a speed of 835 m/s If the collision is elastic, find the speed the bullets bounce from Superman’s chest and the speed that Superman has after the collision. (Assume the bottoms of his superfeet are frictionless.) 7. By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor. As the plate falls, its momentum has only a vertical component, and no component parallel to the floor. After the collision, the component of the total momentum parallel to the floor must remain zero, since the net external force acting on the plate has no component parallel to the floor. Using the data shown in the drawing, find the masses of pieces 1 and 2.