Student Exploration: Atwood Machine

Name:‬ ‭Vedant jain‬ ‭Date:‬ ‭july 5‬ ‭Student Exploration: Atwood Machine‬ ‭ irections: Follow the instructions to go through the simulation. Respond to the questions and‬ D ‭prompts in the orange boxes.‬ ‭Vocabulary‬‭:‬‭acceleration, Atwood machine, Newton’s‬‭second law, pulley,‬ ‭tension, weight‬ ‭ rior Knowledge Question‬‭(Do this BEFORE using the‬‭Gizmo.)‬ P ‭Tarzan is standing on a tree branch, high above the forest floor, and he wants‬ ‭to get down to the ground. Jane is standing on the ground and wants to get‬ ‭onto Tarzan’s branch. Tarzan holds a vine that reaches to the ground.‬ ‭ ow could Jane get to the branch at the same time that Tarzan travels to the‬ H ‭ground?‬ ‭Tarzan would need to jump down in order to pull Jane up.‬ ‭ izmo Warm-up‬ G ‭Tarzan could tie the vine to the branch and then slide down after Jane climbed up. But there‬ ‭may be an even easier way—what if Tarzan jumped over the branch while holding the vine,‬ ‭pulling Jane up as he came down?‬ ‭ similar scenario is shown in the‬‭Atwood Machine‬‭Gizmo. An‬‭Atwood machine‬‭has two‬ A ‭masses connected by a rope that passes over a‬‭pulley‬‭.‬‭As one mass moves down, the‬ ‭other will be pulled up. To begin, check that‬‭Mass‬‭A‬‭is 2.0 kg and‬‭Mass B‬‭is 3.0 kg.‬ ‭1.‬ ‭Which mass do you think will move down?‬ ‭b‬ ‭Which mass do you think will move up?‬ ‭2.‬ ‭Click‬‭Play‬‭(‬ ‭a‬ ‭). What happens?‬ ‭Mass B moved down while mass A moved up.‬ ‭3.‬ ‭What is the force that pulls mass B downward?‬ ‭The weight of mass B pulled it downward.‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭Get the Gizmo ready‬‭:‬ ‭Activity A:‬ ‭Up and down‬ ‭‬ C ● ‭ lick‬‭Reset‬‭(‬ ‭).‬ ‭●‬ ‭Check that the‬‭Pulley‬‭is‬‭Frictional‬‭and has a‬ ‭Mass‬‭of 2.0 kg and a‬‭Radius‬‭of 0.20 m.‬ ‭●‬ ‭Set‬‭Mass A‬‭to 1.0 kg and‬‭Mass B‬‭to 2.0 kg.‬ ‭Question: What controls how quickly the two weights on an Atwood machine move?‬ ‭1.‬ P ‭ redict‬‭: How do you think the speed at which the heavier‬‭object descends depends on the difference‬ ‭between the two masses?‬ ‭The speed may be faster if one object is heavier.‬ ‭2.‬ G ‭ ather data‬‭: Click‬‭Play‬‭. The time it takes for mass‬‭B to hit the bottom is shown at bottom right. Record this‬ ‭time, and then repeat for each combination of masses.‬ ‭Mass A (kg)‬ ‭Mass B (kg)‬ ‭Time (s)‬ ‭1.0 kg‬ ‭2.0 kg‬ ‭0.9‬ ‭1.0 kg‬ ‭3.0 kg‬ ‭0.71‬ ‭1.0 kg‬ ‭4.0 kg‬ ‭0.64‬ ‭1.0 kg‬ ‭5.0 kg‬ ‭0.6‬ ‭3.‬ ‭Analyze‬‭: How does the difference in masses affect‬‭the speed at which mass B descends?‬ ‭The speed is faster if the mass is heavier.‬ ‭4.‬ T ‭ hink and discuss‬‭: What do you notice about the effect‬‭of adding more and more mass? (In other words,‬ ‭does each 1-kg addition of mass have the same effect?)‬ ‭ very time the mass was increased by 1 kg, the mass dropped faster so the time appeared‬ E ‭to decrease‬ ‭5.‬ P ‭ redict‬‭: Next, you will investigate different mass‬‭combinations in which the mass difference is always the‬ ‭same. If the difference in mass is 1 kg, how do you think the total mass will affect how quickly the two‬ ‭objects move?‬ ‭I think when the total mass is higher, it will take longer for the objects to move.‬ ‭6.‬ ‭Gather data‬‭: Record the descent time for each combination‬‭of masses.‬ ‭Mass A (kg)‬ ‭Mass B (kg)‬ ‭Time (s)‬ ‭1.0 kg‬ ‭2.0 kg‬ ‭0.9‬ ‭2.0 kg‬ ‭3.0 kg‬ ‭1.10‬ ‭3.0 kg‬ ‭4.0 kg‬ ‭1.28‬ ‭4.0 kg‬ ‭5.0 kg‬ ‭1.42‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭7.‬ ‭Analyze‬‭: Given the same mass difference, how does‬‭the total mass affect how quickly the weights move?‬ ‭ hen the two masses were still different but the total mass was heavier, the objects move‬ W ‭slower.‬ ‭8.‬ T ‭ hink and discuss‬‭: Given the same mass difference,‬‭why do you think the masses move most quickly when‬ ‭the total mass is smallest?‬ ‭ ased on Newton’s Second Law of Motion, an object with a larger mass will have a smaller‬ B ‭acceleration and an object with a smaller mass will have a larger acceleration‬ ‭9.‬ C ‭ hallenge‬‭: Given what you have learned so far, what‬‭combination of unequal masses will result in the‬ ‭longest‬‭time for mass B to reach the bottom?‬ ‭Mass A has 4.9 kg and Mass B has 5.0 kg‬ ‭Try this with the Gizmo. How long did it take for mass B to reach the ground?‬ ‭4.68 seconds‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭Activity B:‬ ‭ orce and‬ F ‭acceleration‬ ‭Get the Gizmo ready‬‭:‬ ‭‬ C ● ‭ lick‬‭Reset‬‭.‬ ‭●‬ ‭Set the‬‭Pulley‬‭to‬‭Frictionless‬‭.‬ ‭●‬ ‭Set‬‭Mass A‬‭to 1.0 kg and‬‭Mass B‬‭to 2.0 kg.‬ ‭Question: How do you measure the forces and‬‭acceleration‬‭of each mass?‬ ‭1.‬ C ‭ alculate‬‭: The‬‭weight‬‭of an object is equal to the‬‭product of its mass and gravitational acceleration, which‬ ‭is 9.81 m/s‬‭2‬ ‭on Earth’s surface. Weight is measured‬‭in newtons. What is the weight of each object?‬ ‭Object A‬ ‭9.8N‬ ‭Object B‬ ‭19,6N‬ ‭2.‬ O ‭ bserve‬‭: On the DESCRIPTION tab, turn on‬‭Show numerical‬‭values‬‭. The diagram shows the forces‬ ‭acting on each mass. The down arrows represent gravitational force. The up arrows represent the‬‭tension‬ ‭of the rope that pulls each mass up.‬ ‭A.‬ H ‭ ow does the gravitational force on‬ ‭each object compare to its weight?‬ ‭They remain the same.‬ ‭B.‬ F ‭ or which object is the tension‬ ‭greater than the weight?‬ ‭The tension is less than mass a.‬ ‭C.‬ F ‭ or which object is the tension less‬ ‭than the weight?‬ ‭The tension is less than mass B.‬ ‭D.‬ ‭Click‬‭Play‬‭. What happens?‬ ‭Mass b fell at 0.78 seconds‬ ‭3.‬ C ‭ alculate‬‭: The acceleration‬‭of an object is equal‬‭to the rate at which its velocity changes. If the initial‬ ‭velocity is zero, the acceleration is equal to the final velocity divided by time‬ ‭(‬‭a‬‭=‬‭v‬‭final‬ ‭/ t‬‭final‬ ‭). Select the TABLE tab and scroll‬‭to the bottom.‬ ‭A.‬ W ‭ hat is the final velocity of mass‬ ‭A?‬ ‭2.55 m/s‬ ‭B.‬ H ‭ ow long did it take for object A‬ ‭to reach the top?‬ ‭0.78m/s‬ ‭C.‬ W ‭ hat is the acceleration of mass‬ ‭A?‬ ‭3.72m/s^2‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭4.‬ C ‭ alculate‬‭: The Atwood machine was designed to demonstrate‬‭Newton’s second law‬‭, which states that‬ ‭force (‬‭F‭)‬ is equal to the product of mass (‬‭m‬‭) and‬‭acceleration (‬‭a‬‭):‬‭F‬‭=‬‭ma‬‭. Because they are connected,‬ ‭you can treat both masses as part of the same system.‬ ‭A.‬ S ‭ elect the DESCRIPTION tab. What is the‬ ‭total mass of masses A and B?‬ ‭3.0kg‬ ‭B.‬ W ‭ hat is the difference between the‬ ‭gravitational force on B and on A?‬ ‭9.81N‬ ‭C.‬ B ‭ ased on Newton’s second law, what is the‬ ‭acceleration of each mass?‬ ‭3.27m/s^2‬ ‭5.‬ P ‭ ractice‬‭: Each mass is pulling the rope in the opposite‬‭direction with a force equal to its weight. Therefore,‬ ‭the net force is equal to the weight difference between mass A and mass B. For each combination of‬ ‭masses, calculate the total mass, net force, and acceleration.‬ ‭ ext, measure the final velocity, time, and acceleration for each combination using the Gizmo. Include all‬ N ‭units.‬ ‭Mass A‬ ‭Mass B‬ ‭Total‬ ‭ ass‬ m ‭Net‬ ‭force‬ ‭Calculated‬ ‭Final‬ ‭acceleration‬ ‭velocity‬ ‭Time‬ ‭Measured‬ ‭acceleration‬ ‭1.0 kg‬ ‭3.0 kg‬ ‭4‬ ‭19.62N‬ ‭4.9‬ ‭3.13‬ ‭0.64‬ ‭4.89‬ ‭2.5 kg‬ ‭3.5 kg‬ ‭6‬ ‭9.81N‬ ‭1.63‬ ‭1.80‬ ‭1.10‬ ‭1.64‬ ‭4.0 kg‬ ‭5.0 kg‬ ‭9‬ ‭-9.81 N‬ ‭1.09‬ ‭1.48‬ ‭1.35‬ ‭1.1‬ ‭1.0 kg‬ ‭5.0 kg‬ ‭6‬ ‭39.24N‬ ‭6.54‬ ‭6.54‬ ‭0.55‬ ‭6.58‬ ‭6.‬ A ‭ nalyze‬‭: How well did your calculated values for acceleration‬‭match up with the measured values? What‬ ‭are the possible sources of error?‬ ‭Calculated very closely, an error may have been rounding incorrectly‬ ‭7.‬ E ‭ xplore‬‭: Click‬‭Reset‬‭. Select the BAR CHART tab and‬‭turn on‬‭Show numerical values‬‭. Set‬‭Mass A‬‭and‬ ‭Mass B‬‭to 2.0 kg. Click‬‭Play‬‭. On the SIMULATION pane‬‭you will notice that, while the objects do not‬ ‭move, a small‬‭Pull‬‭button appears below mass A. Click‬‭this button to apply an instantaneous force on‬ ‭mass A.‬ ‭A.‬ ‭What are the velocities of masses A and B?‬ ‭ ass A = -7.5 m/s and Mass B = 7.5‬ M ‭m/s‬ ‭B.‬ A ‭ re masses A and B accelerating? Explain‬ ‭how you know.‬ ‭ es, because there is a change in‬ Y ‭velocity‬ ‭8.‬ T ‭ hink and discuss‬‭: Suppose you were designing an elevator. How could you use the concept of an Atwood‬ ‭machine to minimize the force required to move the elevator up and down? If possible, discuss your‬ ‭answer with your classmates and teacher.‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭ he elevator and weight could be close in weight but not equal. The weight would need to‬ T ‭be heavier so that the elevator may need to move up.‬ ‭Activity C:‬ ‭ he effect of the‬ T ‭pulley‬ ‭Get the Gizmo ready‬‭:‬ ‭‬ C ● ‭ lick‬‭Reset‬‭.‬ ‭●‬ ‭Set the‬‭Pulley‬‭to‬‭Frictional‬‭.‬ ‭●‬ ‭Set‬‭Mass A‬‭to 1.0 kg and‬‭Mass B‬‭to 2.0 kg.‬ ‭Question: How does the pulley affect the total mass and acceleration of the system?‬ ‭1.‬ E ‭ xplore‬‭: In this Gizmo, a “frictional” pulley is one‬‭that spins as the rope is pulled over it. Investigate the‬ ‭effects of changing the‬‭Mass‬‭and‬‭Radius‬‭of the frictional‬‭pulley on the speed of objects A and B.‬ ‭A.‬ ‭How does increasing the mass of the pulley affect how quickly mass B descends?‬ ‭When the pulley is increased in weight, it caused mass B to fall at a slower rate.‬ ‭B.‬ ‭How does increasing the radius of the pulley affect how quickly mass B descends?‬ ‭changing the pulley radius had no effect.‬ ‭2.‬ M ‭ easure‬‭: Set the‬‭Pulley Mass‬‭to 2.0 kg. In this situation,‬‭the total mass of objects A and B is 3.0 kg and‬ ‭the net force on the system is 9.81 N.‬ ‭A.‬ I‭gnoring the pulley, what is the expected acceleration of‬ ‭masses A and B?‬ ‭3.27 m/s^s‬ ‭B.‬ C ‭ lick‬‭Play‬‭and select the TABLE tab. What is the final‬ ‭velocity of mass A?‬ ‭2.21 m/s‬ ‭C.‬ ‭How long did mass A take to reach this velocity?‬ ‭0.90 s‬ ‭D.‬ ‭What is the acceleration of mass A?‬ ‭2.46 m/s^2‬ ‭3.‬ E ‭ xplain‬‭: Why was the actual acceleration of mass A‬‭you calculated in question 2D less than the expected‬ ‭acceleration calculated in question 2A?‬ ‭Because we did not consider the friction in question 2A, only focused on the acceleration.‬ ‭4.‬ C ‭ alculate‬‭: Divide the force (9.81 N) by the actual‬‭acceleration to find the equivalent mass of the whole‬ ‭system (mass A, mass B, and the pulley).‬ ‭A.‬ ‭What is this value?‬ ‭4kg‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭B.‬ S ‭ ubtract the masses of A and B from the‬ ‭equivalent mass of the system. What is the‬ ‭equivalent mass of the pulley?‬ ‭1kg‬ ‭5.‬ ‭Make a rule‬‭: In general, how do you think the equivalent‬‭mass of the pulley will relate to its actual mass?‬ ‭ o find the mass of the pulley, you need to find the sum of the masses when they are‬ T ‭subtracted from the mass of the whole system.‬ ‭6.‬ ‭Test‬‭: Click‬‭Reset‬‭. Set‬‭Mass A‬‭to 1.0 kg,‬‭Mass B‬‭to‬‭3.0 kg, and the‬‭Pulley Mass‬‭to 4.0 kg.‬ ‭A.‬ ‭What is the net force on masses A and B?‬ ‭19.62 N‬ ‭B.‬ C ‭ lick‬‭Play‬‭, and select the TABLE tab. What‬ ‭is the final velocity?‬ ‭2.55 m/s‬ ‭C.‬ ‭What is the time?‬ ‭0.78 s‬ ‭D.‬ ‭What is the acceleration?‬ ‭3.27 m/s^2‬ ‭E.‬ B ‭ ased on the force and acceleration and‬ ‭Newton’s second law (‬‭F‬‭=‬‭ma‬‭), what is the‬ ‭equivalent mass of the system?‬ ‭6 kg‬ ‭F.‬ S ‭ ubtract the masses of A and B from this‬ ‭value to find the equivalent mass of the‬ ‭pulley:‬ ‭2 kg‬ ‭G.‬ D ‭ id this experiment confirm the rule you‬ ‭made in question 5? Explain.‬ ‭ es, because when you subtract the‬ Y ‭sum of all of the masses from the whole‬ ‭system you get the mass of the pulley.‬ ‭7.‬ A ‭ pply‬‭: What will be the acceleration of an Atwood‬‭machine with a frictional pulley with the following mass‬ ‭values? When you are done, use the Gizmo to check your answer.‬ ‭Pulley: 3.6 kg‬ ‭Mass A: 1.4 kg‬ ‭Mass B: 4.1 kg‬ ‭Acceleration:‬ ‭3.63 m/s^2‬ ‭Show your work:‬ M ‭ ass A = 1.49 x 9.81 = 13.73 NMass B = 4.1 x 9.81 = 40.22‬ ‭N40.22 - 13.73 = 26.49 N26.49 / 7.3 = 3.63‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved