6-Phys2211 - Force Mass Acceleration

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Georgia State University *

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2211

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Physics

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Feb 20, 2024

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1 of 6 Phys2211K – Force, Mass, and Acceleration Name: Group Members: Date: TA’s Name: Learning Objectives: I. Understand how net force is related to mass, acceleration, and velocity. II. Use smart carts to measure force, velocity, and acceleration. III. Learn about proportional and inversely proportional graphs. Apparatus: low-friction smart cart, track, two track supports, two cart stoppers, cart masses (four 250 g), pulley, string, mass hanger (5 g), and masses (one 10 g and one 20 g), computer Part A: Identifying Forces and Making Predictions We are going to investigate the connection between the force on a cart and its acceleration. Set up the equipment: Set-up your smart cart and track apparatus as shown below. Set the track on the table so one end is hanging off. Level the track so that the cart will stay at rest and orient the +x direction of the cart toward the pulley so that cart’s velocity and acceleration will be positive in that direction. Attach the pulley so that it is on the end hanging off the table. Hook the length of string on the force sensor hook, run it through the hole of the cart stopper, then over the pulley, and attach to the 5 g “mass hanger” over the end. Adjust the pulley height so that the string is level. Think: Why does the string need to be horizontal? 1. The system of interest here is the cart . List the forces acting on the cart once it has been released. Also draw the free body diagram (FBD) for the system . List of Forces Vertical Up Down Horizontal Right Left FBD Cart stoppers Force sensor hook is attached to the cart Track supports Mass hanger Pulley

2 of 6 2. Prediction : Draw lines on the velocity, acceleration and force graphs below predicting the shapes of the curves for the cart after being released. Part B: Measuring Force and Acceleration Setting up the Sensors and Capstone: Launch Capstone on your computer then start a new experiment and select three displays. Select one display to be velocity, one to be acceleration, and the third to be force. Make sure to select the correct smart cart by matching the smart cart number. Set the number of decimal places to 3 for each variable by choosing Data Summary on the left side menu bar and selecting the Properties for each measurement then selecting Numerical Format . After changing Number of Decimal Places to 3, click OK and proceed to the Properties for the next variable. Detach or make the string go slack before the force sensor and see if the force sensor registers zero. If not see instructor if you need help with this. You may need to change the sign of the force sensor if required. Force should be shown positive when you slightly pull the hook. If required, do this by choosing Data Summary on the left side menu bar and selecting the Properties for the Force Sensor then checking the Change Sign box. First Experiment : Now you are ready to make your first run just with the mass hanger. Have another team member start taking data. Place the cart as shown in the figures above. Let go off the cart as soon as the clicking sound is heard. Catch the cart just before it crashes into the cart stopper. The string should not touch the cart stop during the run. Make any changes if necessary. 3. How does your data compare with your prediction for the velocity graph? 4. How does your data compare with your prediction for the acceleration graph? 5. How does your data compare with your prediction for the force graph? t v Velocity vs time t a Acceleration vs time t F Force vs time

3 of 6 6. Are the sign of the acceleration and the sign of the force the same? __________________ Is this consistent with what you know about the direction of the tension force on the cart and the direction of the acceleration? Explain. 7. Explain how the velocity and acceleration graphs are related to each other. 8. Explain how the acceleration and force graphs are related to each other. 9. Now from these graphs we will measure the magnitudes of the average force and average acceleration of the cart during the time it is moving freely. To do this, select the appropriate data by putting a rectangle around the data points, and then selecting “mean” from the “Statistics” button at the top of the window, which is shown under the summation sign sigma, “Σ”. When you select, choose data only for the appropriate portion of the experiment when the situation is the same as you identified in your free body diagram. That is, you should leave off the time when you are touching the cart and also the time when the hanger is on the floor and the string is slack. If your acceleration vs. time data is noisy, you can instead find the average acceleration using the slope of the velocity vs. time graph as you have done before. Record this data below. Average Force = _________________________________________ Average Acceleration = ____________________________________ Remember there are units for each of these quantities. Have your TA check your graphs and initial below before you go on . TA initials : ____________________

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4 of 6 Part C: Relationship Between Net Force and Acceleration 10. Your task is to figure out the value for the acceleration of the cart for different tensions of the string. Adding different masses onto the hanger will change the tension of the string. Change masses on the hanger and repeat. Record the average force (tension of the string) and the average acceleration for each added mass in the table below. You already found the data for Hanger Only in Question 9. Now complete the rest of Table 1 . Table 1 Magnitude of Acceleration (m/s 2 ) Magnitude of Force (N) Hanger (5 g) Only Hanger (5 g) + 10 g Hanger (5 g) + 20 g Hanger (5 g) + 30 g More Analysis: Copy the acceleration and force data from your table into Excel. Then create a graph of force vs. acceleration. If your graph is far from being a nearly straight line, pick out the most suspicious data point and re- do that run to check your data. You may do one extra mass point if time permits to get a much better graph. 11. Did your force vs. acceleration data give you a linear relationship? 12. What should the slope of the force vs. acceleration graph be equal to? Explain how you know. 13. Add a linear fit and determine the slope. Copy and paste the graph into your Word document. What is the slope of your force vs. acceleration graph? Make sure you include units. Slope = ____________________________ 14. Now determine the mass of your system (the cart). Mass = ____________________________ 15. How does your slope compare to the mass of your system? 16. Summarize the relationship between force, mass, and acceleration found from your data.

5 of 6 Part D: Relationship between Mass and Acceleration 17. Now we want to repeat the experiment by keeping the applied net force on an object constant and changing its mass (cart + additional masses). This will allow us to see how changes in an object’s mass ( independent variable ) affect its acceleration ( dependent variable ) while the applied net force on it is being kept constant ( controlled variable ) . We will keep the net force constant by putting 20 g on the mass hanger for each run. We will change the mass (of the moving object of interest) by adding black rectangular masses to the cart. Record force, mass, and acceleration below. By using a flat scale determine the mass of the smart cart while a force sensor hook is attached to it: __________ g. Table 2 Total Mass (kg) Acceleration (m/s 2 ) Force (N) Cart + force sensor hook Cart + force sensor hook + 250 g Cart + force sensor hook + 500 g Cart + force sensor hook + 750 g Cart + force sensor hook + 1000 g Copy the acceleration and mass data from your table into Excel. Insert a new column and use a formula entry in Excel to calculate 1/mass for each row of your table. Then create a graph of acceleration vs. 1/mass. Is your graph a nearly straight line? If not, pick out the most suspicious data point and re-do that run to check your data. Add a linear fit and determine the slope. Copy and paste the graph into your Word document. 18. What is the slope for the fit of your acceleration vs. 1/mass data? Make sure you include units. Slope = ____________________________ 19. The force should have been nearly the same in all of these runs. Determine the average force on your system from the table above. Remember units. Force = ____________________________ 20. How does your slope compare to the average force on your system? 21. Summarize the relationship between force, mass, and acceleration you found from this part of the experiment.     

6 of 6 Part E: Conclusions 22. What is your overall conclusion about this experiment and what it says about Newton’s Second Law? 23. Give evidence from your experiments to support the conclusions you made above. Instructions on how to submit the graphs: 1. Open a word document and type the names of all present group members. 2. Paste force vs. acceleration graph with fit line from Part C. 3. Paste acceleration vs. 1/mass graph with fit line from Part D. 4. Please be smart about formatting of the Word document so you don’t waste paper. 5. Print your Word document and staple it to this lab write-up for one member of your group.

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