1/2 90% + This lab measures the acceleration of a cart on a track caused by an applied force, a tension. In order to complete this laboratory exercise, data will be collected from the entire class. Equipment Tracks, carts and accessories Weight sets Light-gauge strings Photogates and mounting brackets 10-spoke pulleys and LabQuestTM Procedure Level the track and run a string from the cart over the pulley: Each group will be responsible for completing the experiment with two masses: Group #1 Group #2 Group #3 Group #4 Group #5 10 g / 60 g 20 g / 70 g 30 g / 80 g 40 g / 90 g 50 g / 100 g Weigh the cart (it is factory-calibrated for 500 g, but this needs to be verified) mcart = Hang one of the two assigned masses, and make sure that the mass does not hit the floor before the cart reaches the end of the track. Set data collection to 10-spoke pulley, with "in-groove" option; start recording and set the cart free, without a push. * On the LabQuest, add an acceleration graph, select the portion with near-constant values, and use statistical tools to record directly the average value and the standard deviation (which for, e.g. 10 sampled values, is computed as follows:2/2 - 90% + | To (a; + az + ...+ ajo) - a2 i.e., "sigma squared is the average of the squares minus the square of the average") Proceed identically for the other assigned mass, and share your results with the class: Hanging 10 20 30 mass, m [g] 40 50 60 70 80 90 100 Avg. accel. [cm/s?] Standard deviation [cm/s?] Analysis Question 1 Sketch a free-body diagram of the cart, track and hanging mass, labeling all internal and external forces to the system {Cart, String, Mass} Question 2 Write Newton's Second Law for the system to derive an equation giving the acceleration in the form a = f(m), remembering that the mass of the system is meant + m. Table Complete the report table using class data and the formula from Question 2. Graph Create a graph of experimental and theoretical accelerations against hanging mass, using standard deviations as the +/- series for custom vertical error bars. Question 3 Why aren't the graphs linear? Question 4 Are the theoretical accelerations within the error bars? Justify your