Introduction As you read in your pre-lab, this experiment is meant to give you some hands-on experience with the relationship between mass and force through measurements of acceleration. Since it's unlikely that you have an air track at your current location, we are going to use an online simulator so that you can run these experiments and take your own data. The one piece of outside equipment you will need is a timing device, which could simply be the stopwatch feature on your phone or wristwatch or, if you're so inclined, a standard handheld stopwatch that you might have handy. Experiment O: Familiarize yourself with the online simulator The simulator we will be using is here: Forces and Motion: Basics Friction Acceleration You can click on the "Motion" simulator, which is what you will be using, and take some time to learn your way around it. Steps you need to do to get it ready for your data-taking: 1. In the upper right corner you should see a green box listing Force, Values, Masses, and Speed. You should click the checkboxes next to each of these so that you can see them all when the simulation is run. 2. You should click the Pause button that appears just below the green box so that your simulation doesn't auto-run when you start applying forces. After completing these steps, you can see that in the upper left there is now a speedometer that will display the speed in m/s. Also, on the track at the center of the screen you can see an animated person standing next to a cart that currently holds a 50 kg box. At the bottom center of the screen you have controls to set the Applied Force that the animated person will apply to the cart+mass. If you click on one of the arrows there or use the slider bar, you can change the applied force (in Newtons) to the left or right and your animated person will move into position to push with that Applied Force shown. Try setting up an Applied Force of 100 N to the right. Click the Play button in the upper right. You should see that the 50 kg mass now has a speed (indicated on the speedometer) that increases over time. If you wait long enough you will see that your cart+mass has a maximum speed of 40 m/s. To refresh the simulation for a new run, you can click on the refresh button @ . Notice that clicking refresh resets your check boxes and pause condition. So repeat steps 1 and 2 after hitting refresh to get ready for a new run. You also have the option of changing the mass on your cart by dragging and dropping an additional box, a refrigerator, a person (child or adult) or a trashcan onto the cart. Try it. Notice that you can also combine some of these masses onto the cart. How will you take data? Let's demonstrate. Set up your cart+mass again with a mass of 50 kg and have your animated person set up to push with a force of 150 N to the right. Now, get your handy timer ready and time the animated person pushing your 50 kg mass for a few "timed runs". Basically, simultaneously click Play and start your timer and then simultaneously click Pause and stop your timer. Record the time that elapsed and the speed of your 50 kg mass after hitting Pause. As an example, if | do this three times, | get the following: Time Speed 445s 134 m/s 7.90s 237 m/s 9.83s 29.5 m/s As these data show, the speed is increasing over time. If we take these data and plot and do a linear fit to them we get something like the following: Example Data 35 30 =2:9917x+0.0811. Next As these data show, the speed is increasing over time. If we take these data and plot and do a linear fit to them we get something like the following: Example Data 35 30 =2.9917x+0.0811. 8 =25 o = E20 3 15 = 2 . & 10 5 0 0 2 a 6 8 10 12 Time (s) The trend line that was included in this plot shows we have a slope of about 3 m/s2. Using Eqn. 1 for Newton's second law, you should be able to convince yourself that this makes sense, since we had force of 150 N, which when divided by our mass of 50 kg would give us this result. Exercise 1: Apply a constant force In this experiment, you will keep the net force constant while changing the mass of your system (mass+cart). To do this, you will simply apply a fixed force in the simulation while adding different masses to the cart. You should observe that the acceleration is inversely proportional to the mass of the system. Set up your simulation to apply a constant force of 200 N to the right. Take data for 5 different masses, recording for each mass the velocity over at least 3 different time intervals (as we illustrated in Exercise 0) so that you can obtain the acceleration. Find the slope for each of these data, and record your data and results on this sheet: Experiment 6 Table 6.1.pdf Note you are also asked to show your work for Trial #1. Exercise 2: Analyzing constant force data Here you will use Excel to determine the relationship between the acceleration you found in Exercise 1 and the mass of the system. Plot the acceleration versus the reciprocal of the mass. Label this plot with a title and horizontal and vertical axis labels that include units. Include a trendline fit to the data with the R? value. The slope of your graph is the applied force. e Pt aehm s e acan ol T il il o B il B i B o O i o B s Next > Exercise 2: Analyzing constant force data Here you will use Excel to determine the relationship between the acceleration you found in Exercise 1 and the mass of the system. Plot the acceleration versus the reciprocal of the mass. Label this plot with a title and horizontal and vertical axis labels that include units. Include a trendline fit to the data with the RZ value. The slope of your graph is the applied force. * Print out your graph and include on it the following additional items o Show a percent difference calculation between the force you applied in the simulation and the force you determined from your graph o Identify or discuss the relationship that is being used to infer that the slope of your graph is the applied force Exercise 3: Maintaining a constant mass In this experiment, you will keep the system's mass constant while changing the applied force . You should observe that the observed acceleration is proportional to the force applied to the system. Set up your simulation with a mass of your own choosing that you will hold constant for all of your measurements. Take data for 5 different applied forces, recording for each trial run the speed over at least 3 different time intervals so that you can obtain the acceleration. Finding the slope for each of these data, record your data on this sheet: Experiment 6 Table 6.2.pdf 4, Note you are also asked to show your work for Trial #3. Exercise 4: Analyzing constant mass data Plot your data from Exercise 3 as force versus acceleration using Excel. The slope will be equivalent to the mass of the system. Print out your graph and include on it the following additional items o Identify or discuss the relationship that is being used to infer that the slope of your graph is the mass of the system o Show a percent difference calculation between the mass used in your trials and the mass you determined from your graph Exercise 5: Concluding Remarks Briefly answer to the following question: Did your results support Newton's second law? Use data from your trials to support your answer. Items to Turn In You should be handing in your two filled out data sheets and sample calculations (Tables 6.1 and 6.2), the graphs and calculations from Exercises 3 and 4, and your answer to the final question posed in Exercise 5. Combine these into one PDF file before turning them in. Next