Newtons 2nd and 3rd law(1)

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Apr 3, 2024

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Newton’s 2 nd Law: Atwood’s Machine * Background In this experiment you will investigate Newton’s 2 nd Law. This law states that the net (or, total) force on an object is proportional to the acceleration of the object. Or, in equation form If we rearrange the above equation to solve for the acceleration, we see Because the acceleration depends on two variables, mass and force, you will hold one variable constant while the other is varied. The system that you will examine is called Atwood’s Machine . Atwood’s machine consists of two unequal masses that are connected by a string (the mass of the string is negligible) over a pulley (a frictionless, massless pulley). When the masses are released, the gravitational force accelerates both masses. An image of the Atwood’s Machine is shown in Figure 1. Figure 1 Atwood's Machine set up + * Adapted from a PASCO eLab file + Image credit: PASCO Incorporated, Roseville CA Phys 103 - Principles of Physics I Labs

 Draw a free body diagram for each mass. Assume that m 1 is the more massive object. Remember to include tension and the gravitational force. Also, draw an arrow that indicates the direction that each block is accelerating. If any of the forces on the diagrams are equal, circle them.  Next, write out Newton’s 2 nd Law for each of the objects above. We’ve started the first line of each for you.  Because the same string connects both blocks, you should see that the Tension on both blocks is equal! Also, because the blocks are moving together as a single unit, we know that the accelerations must also be equal . Use the fact that F T 1 = F T 2 to combine the equations above and find an expression for the acceleration. Check with your instructor to confirm that you have the correct expression for acceleration. Phys 103 - Principles of Physics I Labs m 1 m 2

Notice that in the equation above you have found a way to determine the acceleration of the objects based on the masses. In particular, the numerator contains the mass difference for the system (how much more massive one block is than the other), and the denominator is the total mass (the combined mass of both blocks). In the following activities, you will experiment with each of those variables. Goal: The purpose of this experiment is to investigate how the acceleration of a system varies when the net force acting on it and the mass are varied. Part I - Varying the Net Force In this part of the lab, you will be changing the mass difference between the two sides. This will effectively vary the net force on the system, while keeping the total mass constant. So, if F net = ma , F net will increase and you will see how “a” will change.  Connect two mass hangers over a pulley to a string. Be sure that they are tied securely and that the descending mass can fall the entire height but without hitting the table.  Set up the Capstone program. Make sure that the 850 Interface is connected and then add a “Photogate with Pulley” sensor. Choose the “Table and Graph” display option. o Because you will need to enter the mass data, we need to set up the table so that you can add your own values. In the first column of the table, click on the “Select Measurement” button and choose “Create New  User Entered Data.” Type “ Acceleration ” as the label for this column. In the second column, click on the “Select Measurement” button, and this time choose “Create New  User Entered Data.” Type as the label for this column.  Add a second graph to your display by dragging and dropping the Graph icon from the right tool bar to your display area. o On the first graph, use the “Select Measurement” buttons to graph velocity (linear speed) vs. time. On the second graph, plot force (from your table) vs. acceleration.  Start with an equal amount of mass on each hanger. For example, you could add a 20g mass to one side (the 5g mass hanger makes a total of 25g). You’re going to be moving mass around, so use a number of smaller masses on the other side that total 20g. At this point, you should have a balanced system. o Now, unbalance the system by moving mass pieces from the ascending side to the descending side. Press the RECORD button then release the system. Press the STOP button before the descending mass reaches its lowest point. Phys 103 - Principles of Physics I Labs

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 Use the Fit tool to find the slope of the velocity versus time line. This is the acceleration of the system. Enter that acceleration and the appropriate force (mass difference) into the table you created. Repeat this experiment at least three more times, each time transferring another piece of mass from one hanger to the other. o Slope #1 = 1.61, slope #2 = 3.39, slope #3 = 5.23  As the net force increased, what happened to the acceleration? Do your results agree with Newton’s 2 nd Law? Explain. As the net force increases, so does the acceleration as the tension against the net force decreases each time. Yes it agrees with Newton’s 2 nd law as there is a decrease in force and in increase in acceleration.  Determine the slope of the force vs. acceleration graph and record it here. What are the units of the slope? What is the physical significance of the slope? How well does the number agree with your experiment? Explain. The slope of the force vs. acceleration is 54.6g. The slope tells us the original mass of the hangers and weights that we originally started with, which was 50g, and it is in a very close range for our mass in this experiment. Part II - Varying the Total Mass In this part of the lab, you will keep the mass difference the same but change the total mass of the system. So, if F net = ma , F net will be constant, “m” will increase and you will see how “a” will change.  If you have a mass imbalance of 2g, how much is the net force acting on the system? (Remember, the net force is the mass difference times gravity.)  Edit your table so that your columns are your inputs of Acceleration and Total Mass. Similarly, edit your graphs so that you are plotting velocity vs. time and total mass (from your table) vs. acceleration. Phys 103 - Principles of Physics I Labs

 Start with the same mass on each hanger (make it a small mass). Now, add 2g to one hanger to imbalance the system. Press the RECORD button then release the system. Press the STOP button before the descending mass reaches its lowest point.  Use the Fit tool to find the slope of the velocity versus time line. This is the acceleration of the system. Enter that acceleration and the appropriate total mass into the table you created. Repeat this experiment at least three more times, adding an equal amount of mass (>20 g) to both hangers so that the 2g imbalance remains but the total mass of the system increases.  As the total mass increased, what happened to the acceleration? Do your results agree with Newton’s 2 nd Law? Explain. As the total mass increased, acceleration decreased, and yes the results agree with Newton’s 2 nd law because mass and acceleration have an inverse relationship, therefore when mass increases, it will cause acceleration to decrease. Summary Questions 1. What happens to the acceleration of a system when the applied force (net force) increases and the mass of the system does not change? The acceleration of the system would increase because acceleration and net force are proportional to each other, therefore when one increases, so does the other. 2. What happens to the acceleration of a system when the mass of the system increases but the applied force does not change? The acceleration would decrease because of the inverse relationship between acceleration and mass, meaning acceleration does not need net force to change but needs mass to change. Phys 103 - Principles of Physics I Labs

Newton’s Third Law * Background Newton’s 3 rd Law is the law of reactions. That is “every force has another force that is equal in magnitude but opposite in direction.” You might know it more colloquially as “for every action there is an equal and opposite reaction.” In this lab, we will work with Newton’s 3 rd Law to examine these action-reaction pairs (also known as force pairs). Part I - Predictions for Two Carts For each diagram shown, cars A and B are tied to each other by a string.  The arrows show the direction in which the cars are being pulled. Which car, if any, do you think is pulling harder on the string? A or B? Or, do you think it depends on other factors? Explain your choice and your reasoning. Part II - Data Collection and Analysis for Two Carts For this experiment, set up a PASCO track. You will need two silver dynamics carts to use as A and B, and you will also need two force sensors so that one can be attached to each car. Attach the force sensor to the top of the car (indicated by an “ S ” on the diagrams) using the long screw provided.  In the Capstone program, connect two Economy Force Sensors to the 850 Interface. Create a single graph with two lines - a force vs. time graph for each sensor.  For each experiment, connect the two dynamics carts with string as shown, press the RECORD and follow the directions for where to pull on the carts. Sketch the graph created, and explain how the forces compare in each case. * Adapted from a ScienceWorkshop500 lab by PASCO, Inc . Phys 103 - Principles of Physics I Labs A B A B A B A B

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Experiment Graph Compare F Pull A and B away from each other Load B with a mass, then pull A and B away from each other Move A and B to the right with a sharp horizontal pull on B Load B with mass, then move A and B to the right with a sharp horizontal pull on B.  What can you conclude about the forces that the cars apply on the string when they are pulling on each other?  How are the forces affected by the mass of the carts? Phys 103 - Principles of Physics I Labs A B A B A B A B S S S S S S S S

 How are the forces affected by the motion of the carts?  How do your results compare to your original predictions? If you predicted some incorrectly, explain where your reasoning was not consistent. Part III - Predictions for Three Carts For each diagram shown, cars A and B are still pulling on strings, but there is a third car between them.  The arrows show the direction in which the cars are being pulled. Which car, if any, do you think is pulling harder on the string? A or B? Or, do you think it depends on other factors? Explain your choice and your reasoning. Part IV - Data Collection and Analysis for Three Carts For this experiment, set up a PASCO track. You will need two silver dynamics carts to use as A and B, and you will also need two force sensors so that one can be attached to each car. Attach the force sensor to the top of the car (indicated by an “ S ” in the diagrams) using the long screw provided.  For each experiment, connect the two dynamics carts with string as shown, press the RECORD and follow the directions for where to pull on the carts. Sketch the graph that is created, and explain how the forces compare in each case. Experiment Graph Compare F Phys 103 - Principles of Physics I Labs A B A B A B

Put the force sensors on A and B and pull A and B away from each other Put the force sensors on A and B and pull A and B to the right with a sharp horizontal pull Put the force sensors on A and B, so that they are each measuring a different string. Pull on B with a sharp horizontal force  What can you conclude about the forces that the cars apply on the string when they are pulling on each other?  How are the forces affected by the mass of the carts?  How are the forces affected by the motion of the carts?  How do your results compare to your original predictions? If you predicted some incorrectly, explain where your reasoning was not consistent. Phys 103 - Principles of Physics I Labs A B A B A B S S S S S S

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Summary Question Summarize your findings. In particular, pay attention to the differences you noticed between cases. Explain what caused the differences. Phys 103 - Principles of Physics I Labs

Newton’s Third Law Follow Up Question Block A with a mass of is sitting next to block B with a mass of on a frictionless surface. An outside force of pushes on the left side of block A, as shown in the diagram. 1. Draw three Free Body Diagrams (FBDs) below: one for the whole system, one for block A, and one for block B. On each, include the following information: a. the direction of every force on the system/object b. above your FBD, draw an arrow showing the direction of the acceleration (or, write ). c. draw a coordinate system showing the direction where the x-axis and y-axis increase 2. Write out Newton’s 2 nd Law equations for both directions for all three FBDs on the facing page. This should give you a total of six equations. 3. Use the equations you’ve found to find: a. the acceleration of the system, b. the force between the two blocks, that is, the force on block B from block A, c. Is F AB = F BA ? Explain why they should or should not be. d. Is F AB the opposite direction to F BA ? Explain why or why not this should be. Phys 103 - Principles of Physics I Labs A B A B F push B A

Newtons 2nd and 3rd law(1)

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