AtwoodMachineSE_(2).docx

Name: Vishwa Date: 2023-10-22 Student Exploration: Atwood Machine Vocabulary: acceleration, Atwood machine, Newton’s second law, pulley, tension, weight Prior Knowledge Question (Do this BEFORE using the Gizmo.) 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. How could Jane get to the branch at the same time that Tarzan travels to the ground? Tarzan would need to jump down the branch to pull up jane so that Tarzan and Jane are switched and jane is at the branch while Tarzan travels to the ground. Gizmo Warm-up 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? A similar scenario is shown in the Atwood Machine Gizmo™. An Atwood machine has two weights connected by a rope that passes over a pulley . As one weight moves down, the other will be pulled up. To begin, check that Mass A is 2.0 kg and Mass B is 3.0 kg. 1. Which mass do you think will move down? ___________B_____________ Which mass do you think will move up? _____________A_____________ 2. Click Play ( ). 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 down.

Activity A: Up and down Get the Gizmo ready: ● Click Reset ( ). ● Check that the Pulley is Frictional and has a Mass of 2.0 kg and a Radius of 0.20 m. ● Set Mass A to 1.0 kg and Mass B to 2.0 kg. Question: What controls how quickly the two weights on an Atwood machine move? 1. Predict: How do you think the speed at which the heavier mass descends depends on the weight difference of the two masses? The speed will be faster if one object is heavier 2. Gather data: Click Play . The time it takes for mass B 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 0.90 s 1.0 kg 3.0 kg 0.71 s 1.0 kg 4.0 kg 0.64 s 1.0 kg 5.0 kg 0.60 s 3. Analyze: How does the difference in masses affect the speed at which mass B descends? The speed will increase if the mass is also increased. 4. Think and discuss: What do you notice about the effect of adding more and more mass? (In other words, does each 1-kg addition of mass have the same effect?) When the mass was increased by 1 kg the mass dropped down faster so the time would decrease. 5. Predict: Next, you will investigate different mass combinations in which the mass difference is always the same. If the difference in mass is always 1 kg, how do you think the total mass will affect how quickly the two objects move? When the total mass is higher, it will take a longer period of time for the objects to move. (Activity A continued on next page)

Activity B: Force and acceleration Get the Gizmo ready: ● Click Reset . ● Set the Pulley to Frictionless . ● Set Mass A to 1.0 kg and Mass B to 2.0 kg. Question: How do you measure the forces and acceleration of each mass? 1. Calculate: The weight of an object is equal to the product of its mass and gravitational acceleration, which is 9.81 m/s 2 on Earth’s surface. Weight is measured in newtons. What is the weight of each object? A: 9.8 N B: 19.6 N 2. Observe: On the DESCRIPTION tab, turn on Show numerical values . The diagram shows the forces acting on each mass. The down arrows represent gravitational force. The up arrows represent the tension of the rope that pulls each mass up. A. How does the gravitational force on each object compare to its weight? They are the same B. For which object is the tension greater than the weight? Mass A has a greater tension C. For which object is the tension less than the weight? Mass B has less tension than the weight D. Click Play . What happens? Mass B fell down at 0.78 s 3. Calculate: The acceleration of an object is equal to 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 = v final / t final ). Select the TABLE tab and scroll to the bottom. A. What is the final velocity of object A? 2.55 m/s B. How long did it take for object A to reach the top? 0.78 m/s C. What is the acceleration of object A? 3.72 m/s^2 4. Calculate: The Atwood machine was designed to demonstrate Newton’s second law , which states that force ( F ) is equal to the product of mass ( m ) and acceleration ( a ): F = ma . Because they are connected, you can treat both masses as part of the same system. A. Select the DESCRIPTION tab. What is the total mass of objects A and B? 3.0 kg B. What is the difference between the gravitational force on B and on A? 9.81 N C. Based on Newton’s second law, what is the acceleration of each object? 3.27 m/s^2

(Activity B continued on next page)

Activity C: The effect of the pulley Get the Gizmo ready: ● Click Reset . ● Set the Pulley to Frictional . ● Set Mass A to 1.0 kg and Mass B to 2.0 kg. Question: How does the pulley affect the total mass and acceleration of the system? 1. Explore: In this Gizmo, a “frictional” pulley is one that spins as the rope is pulled over it. Investigate the effects of changing the Mass and Radius of the frictional pulley 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, mass B falls at a slower rate. B. How does increasing the radius of the pulley affect how quickly mass B descends? It had no affect on how quick mass B descends. 2. Measure: Set the Pulley Mass to 2.0 kg. In this situation, the total mass of objects A and B is 3.0 kg and the total 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^2 B. Click Play and 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. Explain: Why was the actual acceleration of mass A you calculated in question 2D less than the expected acceleration calculated in question 2A? Because we only focused on the acceleration in question 2A and ignored the friction.

4. Calculate: Divide the force (9.81 N) by the actual acceleration to find the equivalent mass of the whole system (mass A, mass B, and the pulley). A. What is this value? 4 kg B. Subtract the masses of A and B from the equivalent mass of the system. What is the equivalent mass of the pulley? 1 kg (Activity C continued on next page)

Subtract both values 40.22 - 13.73 = 26.49 N divide by 7.3 26.49 / 7.3 = 3.63