Lab 6 - Dynamics: F = ma Introduction: In the previous lab, we measured the acceleration of a car on the air track. In this lab we explore some examples of acceleration from everyday life. In each case, what is the force ( or forces) that cause this acceleration? Is the Earth what force causes that accelerationaccelerating in its movement around the Sun? if so in this lab, the force of gravity exerts a force on some masses on a string. This weight pulls on the masses in the system: the mass of the car, the masses that are placed on the car and the mass" (You could just as easily call it the "total mass" in on the string causes the "system mass" to accelerate." he weight of the m Purpose: To explore the relationship between acceleration, mass, and unbalanced force (also called net car plus additional masses Newton's Second La all of the masses: F = Ma m weight : acceleration. If more force is applied to the "system mass" . it's acceleration will be greate this lab, we test this by taking some mass off the car and placing it on the hanger at the end of the string. Note that the "system mass" has not changed. What we are doing is distributing the on the string ( why?). In the lab we will see if this result see if this results in more acceleration, as we expect it to. We can use the force and the acceleration to calculate the total mass in the system, which we can also determine by direct measurement. We hope they agree with each other!" The details: The acceleration along the air track is given by the equation of motion d = - at? where d is the distance between the photo sensors, and t is the time it takes for the car to travel between the sensors. Solving this equation for a, we get: The unbalanced or net force that causes this acceleration is the weight of the hanging masses he string (other forces cancel out each other): F = Wm =mg where m is the total mass and g is the acceleration due to gravity and is equal to 9.8 mis?. total mass the "system mass", or M. Thus, M is the sum of the mass of the hanger, the mass of change.) the car to the hanger , the total mass stays the same . Thus, the "system mass" does not Newton's Second Law predicts that the net force F is proportional to the acceleration of the masses (which is the same as the acceleration of the car): F = Ma where F is the weight of the mass on the hanger, given above. and a is the a Things to Remember: we use in this lab are in grams (9), and the distances are often medsite of kilograms and meters. (9) to Kilograms (kg), divide by 1000. To convert from milimeters (mm) to meters (m), divide by 1000 To compare the measured value with the actual value: percent difference = [measured value - actual valuel x 100 (actual value) Air track operation: You may turn the air off when the air track is not needed (otherwise the room gets too noisy). Be the air track, making it less accurate. Procedure: Below is a procedure that was carried out leading to the table in the following table 1) Make sure air track is level oto sensors. Record thescar on the triple beam balance. Measure the distance between the 3) Start with no mass on the hanger and 40 g attached to the car. 4) Position the car near the first sensor so that the metal rod is just about to turn on the timer. Experiment to find the best position. It is important that the car be as close as possible to the first sensor. When moving the car along the air track, make sure the air is on. 5) When you're ready to begin, to ir. The car will begin to accelerate 6) After the car has passed the se cord the time displayed on the timer. masses. ) Take 5 g off of the car, and add 5 g to the hanger. Repeat steps 4-6 with these new () When you have filled out the data table, calculate the acceleration. Make a plot of represents these points . The points will not likely fall exactly in a line, but they should be fairly 8) For each trial, calculate the mass using m = - . In each case, the mass you calculate should be eagerto the system mass , which is the total mass of the system (mass of the between the actual "system mass" and the measured "system mass" from the data table. Data, Part I: mass of car (measured with triple beam balance): 0.308 kg actual "system mass" (mass of car + mass of hanger + 40 g): 0.353 kg distance between sensors d: 0.50 hange Convert m Fam 1=2d (kg) .005 2.596 1.814 1.553 1.338 20 1.147 1.093 Discussions & Conclusions our conclusion, discuss whether or not we achieved the goal set out in the "Purpose" Discuss any trends in the data, As you ad w did the time hange? How did the acceleration change? Is this expected? What contributed to the percent difference? How did the equipment affect the results