202202_Lab_2_Forces

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Oregon Institute of Technology PHY 221 Dr. David Johnston Lab Exploration 2: Forces Objectives • Investigate the interaction of forces between two objects. • Explore the relationship between force, mass, and acceleration. • Derive three empirical laws about forces. Introduction Hitherto, we have been concerned with describing the motion of an object in space, i.e., with kinematics . Henceforth, we will be interesting in what causes motion or, more precisely, a change in motion, which is called dynamics . As we will learn, it is force that is responsible for acceleration, and, hence, for changes in motion. In this exploration, we will be investigating some of the properties of force and how it relates to acceleration and mass. Activity 1: Forces between Two Objects NOTE: ZERO THE FORCE SENSOR(S) BEFORE COLLECTING DATA! 1.1 Carts at Rest 1. Level the dynamics track so that a cart placed on it will remain at rest at multiple points along the track. 2. Open Vernier Graphical Analysis and connect the two carts, one green and one yellow, to your computer. 3. Select only the Force sensor on each cart. 4. Change the sampling rate to 75 samples/sec and the stop method to Manual . 5. Attach the pulley to one end of the track and tie a sufficiently long piece of string to the hook on one of the carts, we will call this Cart 1 . 6. Connect the other end of the string to the second cart, Cart 2 . Then pass the string over the pulley so that pulling straight down on Cart 2 moves Cart 1 across the track. 7. Zero both force sensors when the string connecting them is SLACK.

8. Begin collecting data and gently pull down on Cart with a steadily increasing force, while holding Cart 1 and preventing it from moving. [Note: To get the best data, do not hold cart 1, rather, devise a setup so that cart 1 does not move.] 9. Attach the force vs. time graph below. Be sure to clearly identify which is line is Cart 1 and which line is Cart 2. Force vs. Time Graph (Carts at Rest) Analysis 1. Why do we want the track to be level? Because if the track wasn’t level, then we be unable to see a direct transmission of the forces from the Yellow Cart to the Green Cart. It would also introduce an unintended external force acting upon the carts. 2. Describe what is happening in the graphs. Make specific references to your graph. According to the graphs, there is an increase in the force in the Green and Yellow Cart. However, there is not a constant increase due to human error (i.e. I may have not been pushing down on the cart at a steady pace), which accounts for the increase and decrease in force. 3. What conclusions about interaction forces can you make from this experiment? Make specific references to your graph. That the effect on the Yellow Cart mirrors the Force change in the Green Cart. In other words, as we pull on one cart, we can see the mirrored effects on the other (I.e. Interaction forces = Push/Pull).

4. What do you conclude about the force in the string, which we call tension ? That is the transmission of force from one point to another (i.e. yellow cart to green cart) . 5. (Post-Lab Analysis) After learning about Newton's third law and tension, revisit your answers to questions 3 and 4. Describe how you might or might not change them given your new knowledge. Be sure to include an explanation. I don’t think I would change my answers because I have accounted for the effect of tension on a system in that it acts as a transmission of force which shows why there is a mirror of the force from the green cart to the yellow cart. 1.2 Moving Carts 1. Zero both force sensors when the string connecting them is SLACK. 2. Adjust your setup so that Cart 1 is pulled by Cart 2 as it falls. 3. Note: Please place something soft under Cart 2 to cushion its fall! 4. Click Collect before releasing Cart 2. 5. Release Cart 2 and let it fall. Be sure you record a few moments of data after cart 2 has hit the ground but before Cart 1 reaches the end of the track. 6. Attach the force vs. time graph below. Be sure to clearly identify which is line is Cart 1 and which line is Cart 2. Force vs. Time Graph (Moving Carts)

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Analysis 1. Describe what is happening in the graphs. Pay special attention to the force between the carts before the carts begin to move, after the carts begin to move, and after cart 2 hits the ground. Make specific references to your graph. -Before Movement; Before the movement of the carts, we see a similar amount of mirrored force as seen in the previous experimental portion (in part due to the tension as well as human error of being unable to hold the carts completely still) -After Movement; Directly after releasing the carts, we see that the forces of the two carts are completely the same, allowing us to make observations of a sudden change in force when tension is in play. However, the large spikes that follow it are unnecessary as they signify the moment the carts hit the ground and pulley. -After Collision: According to the graph, we see that the green cart has almost entirely “flatlined” (signifying that the cart is now at rest at the bottom of the table) while the yellow cart is still having some changes in force (possibly due to hitting the pulley) 2. Why do you think the force between the carts decreases when they begin to accelerate? Because if mass is constant, an increase in acceleration will result in a proportianl increase in force (i.e F = m x a) 3. What forces do you think are acting on each of the carts while they are accelerating? Justify your answers. Force and mass. As stated above, there is a direct correlation between acceleration, mass, and force. So in this case: Acceleration = Force/Mass 4. (Post-Lab Analysis) Revisit your responses to questions 2 and 3, above, after learning about forces and Newton's laws. Critique your responses, explaining what was correct and what was incorrect. I don’t think I need to make any revisions. Activity 2: Force, Mass, & Acceleration NOTE: ZERO THE FORCE SENSOR(S) BEFORE COLLECTING DATA! 2.1 Constant Cart Mass, Changing Hanging Mass 1. Disconnect cart 2 from Vernier Graphical Analysis . 2. For the cart still connected to Graphical Analysis , select both the Position and Force sensor. 3. Confirm that the sampling rate is set to 75 samples/sec and that the stop method is Manual .

4. Display two (2) graphs in Vernier Graphical Analysis , force vs. time and velocity vs. time. 5. Determine the mass of your cart using the electronic balance in the front of the room. Mass of Cart (kg) 0.286 kg 6. Attach one of the hooked masses (be sure to note its mass) to the end of the string where cart 2 was attached. Run the string over the pulley and hold the cart in place so that it does not move. 7. While holding the cart at rest being collecting data. Collect about one second of data with the cart at rest and then release it. 8. Rename this data set: " X kg cart, Y kg hanging ". 9. Keeping the mass of the cart constant, repeat steps 6 - 8 for four additional different hanging masses. 10. Display all five data sets on both the force vs. time graph and the velocity vs. time graph. Be sure to show the Graph Legend on each graph. 11. Attach the force vs. time graph and the velocity vs. time graph below. Force vs. Time Velocity vs. Time

Analysis 1. What happens to the force acting on the cart as the hanging mass changes? Focus on the time when the cart is moving and the force is non-zero. Make specific reference to your graphs. There is a significant increase in the force when observing the increase of hanging mass (satisfying F = m x a). The hanging car exerts a force equal to its weight. 2. Explain how we can determine the acceleration of the cart from the velocity vs. time graph. Acceleration can be found by calculating the slope of the velocity graph. 3. How does the acceleration of the cart change as the force acting on the cart changes? Make specific reference to your graphs. Because we know that Acceleration is equal to the net force divided by mass, we understand that the changes seen in the graph. 4. Plot the acceleration vs. force for the five different values of hanging masses. What type of relationship appears to exist between acceleration and force? Include a screenshot of your plot below. (Be sure your plot has an appropriate title and that all axes are labeled with units!)

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A dependent relationship between acceleration and force. 5. (Post-Lab Analysis) Perform a curve fit. What is the significance of the fit parameter? Compare to the actual physical value by calculating the % difference. Include a screenshot of your plot, with curve fit, below. (Be sure your plot has an appropriate title and that all axes are labeled with units!) The significance of the fit parameter is that the slope can be used to find acceleration, as is mentioned above. 2.2 Constant Hanging Mass, Changing Cart Mass 1. Record the mass of your cart without any added mass. Choose a hanging mass to hang from the other end of the string.

2. While holding the cart at rest being collecting data. Collect about one second of data with the cart at rest and then release it. 3. Rename this data set: " X kg cart, Y kg hanging ". 4. Keeping the mass of the hanging mass constant, repeat steps 1 - 3 first adding the silver masses to the cart one at a time. 5. Display all five data sets on both the force vs. time graph and the velocity vs. time graph. Be sure to show the Graph Legend on each graph. 6. Attach the force vs. time graph and the velocity vs. time graph below. Force vs. Time Velocity vs. Time

Analysis 1. How does the acceleration of the cart change as the mass of the cart changes? Make specific reference to your graphs. We can see that there will be a decrease in acceleration when there is an increase in mass (satisfying A = F/M). This is seen in the most amount of mass having the greatest effect on force (i.e. the light blue line) while the least amount of mass has the least effect on force (i.e. the red line). 2. Plot the acceleration vs. total mass for the five different values of cart masses. What type of relationship appears to exist between acceleration and mass? Include a screenshot of your plot below. (Be sure your plot has an appropriate title and that all axes are labeled with units!) Unfortunately, I am unable to plot for total mass but I do know that the type of relationship between the two are as follows: acceleration is directly proportional to mass difference. (I was able to plot this graph of acceleration vs. time) 3. (Post-Lab Analysis) Perform a curve fit. What is the significance of the fit parameter? Compare to the actual physical value by calculating the % difference. Include a screenshot of your plot, with curve fit, below. (Be sure your plot has an appropriate title and that all axes are labeled with units!)

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Conclusions Summarize what you have learned about force, mass, and acceleration and the relationship between these three quantities. F = M x A (lucky for me, I had to do this lab late, so I already learned about this)