Lab Report N2L - Phys 221

Lab Report - Phys 221 Newton’s 2nd Law Abstract: In this lab, we sought to prove Newton’s second law through practical applications. We used a cart with a string attached to a force sensor. The string is pulled over a pulley and will have masses of various weights attached to it to pull the cart forward toward the pulley. We also have a motion sensor set up to track the speed at which the car is pulled towards the pulley. We will use these results to determine the acceleration of the cart. Using the force detected by the force sensor, the mass of the cart, and the acceleration of said cart, we will be able to validate Newton’s second law: Force = mass x acceleration. The results we got in this experiment confirm this law to be true with room for acceptable equipment and human error. Results Presentation: Hanging Mass Cart Mass Calculated Tension Measured Tension % Differ Calculated Acceleration Measured Acceleration % Differ Friction Weight 50g 590g .45N .47N 4.26 .67m/s^2 .66m/s^2 1.5 .05N 100g 590g .85N .92N 7.61 1.32m/s^2 1.36m/s^2 2.9 .05N 50g 1180g .48N .49N 2.04 .31m/s^2 .34m/s^2 8.2 .12N 100g 1180g .91N .95N 4.21 .69m/s^2 .64m/s^2 7.2 .12N Sample Calculations: The formula used for calculating tension:

The formula used for calculating acceleration: The formula used for % difference:

Post Lab Questions 1. Draw force diagrams for the cart mass system in Fig. 5-1 and include friction. Use these diagrams to derive equation 2. 2. Utilizing the equation above and the printout of one of your runs determine the mass of the cart. The net force is measured as tension (during the run) minus friction. Change in time is the amount of time the tension acted on the cart while it was accelerating (mark on a printout of the plot). The velocity is the maximum velocity the cart had at the end of the acceleration. You must show time and maximum velocity on your printout to receive full credit.

3. Why are we so insistent that you include the origin in your plot points when plotting Equation 3? There are two very good reasons. One has to do with the (NSL) equation itself and the 2nd has to do with what happens when you apply a linear fit to only two points. When considering Newton’s 2nd Law, F=ma, if you start your plot at the origin it represents zero net forces being enacted on an object. This would also tell us that the acceleration is zero at this point. Another good reason to use the origin is that it helps us determine the direction of the slope and makes math easier when determining the change in the x and y values of the graph. With the help of a line of best fit, this creates an easy way to determine the overall behavior of the slope and graph as a whole. 4. There are two forms of Newton’s 2nd Law. What are those two forms and what are the differences between the two forms? The first form is the standard F=ma. The second form is F=dp/dt with p being the moment which is just equal to ma. The second form takes into account time and is therefore not constant while the first equation is simpler and produces a constant answer.