Lab 4: Newton’s Second Law
September 24, 2013
Partners: Amanda Okeefe, Sara Rojek, Kiran Kandola
The objective of the first part of the experiment was to derive an expression, under conditions with negligible friction, for the acceleration of a cart on a level track when it is attached by a string to a hanging mass at the end of the track. With the value of acceleration and the mass of the weight divided by the mass of the weight plus the mass of the cart, a value for free fall acceleration (g) could be determined. For the second part of the experiment, the objective was to derive a second equation for the value of constant air friction force using the known values of acceleration, free fall acceleration (g), and the various masses of the experiment. Theory:
According to accepted physics, when an object of a larger weight pulls an object of a lesser weight there is a tension that acts between the two objects. However, even though the weights of the two objects are different, the force that each object exerts on the other is equivalent. When considering motion, acceleration is created because the system moves in the direction of the larger weight. If the mass of the larger object increases, the acceleration will also increase due to their proportional relationship. On the other hand, the force of friction acts upon the object being pulled in the inverse direction causing the acceleration to decrease. In this experiment, an object was hung at the end of a track and connected by string to an object on top of the track. When the hanging object was released, the acceleration of the system increased in the downward direction. In regards to friction, the first part of the experiment included the exertion of air against the object on the track making friction negligible. The air was turned off for the second part of the experiment causing friction to act in the opposite direction of the object on the track, slowing it down. Experimental Procedure:
For this experiment, a cart (m1) was set on a track and connected by a string to a second object (m2) of varying masses hung off the edge of the track. The forces that acted upon m1 were normal force (n), weight (w), and tension (T). The normal force exerted on m1 was equal to the weight (w), canceling each other out and leaving tension as the only force exerted. For m2 the force of tension acted in the upwards direction while weight (w) acted in the downwards direction. In the first part of the experiment, the air track was turned on to create a negligible friction (f=0). Five different masses (m2) were hung at the end of the string and released to force the cart towards the end of the track. Even though the five varying masses were less than the mass of the cart, they were still able to move the cart forward due to the force of gravity acting upon m2. Each mass was released three times in which the displacement (x) and time (t) were recorded. To find the acceleration of the system we used the formula a=Δx/½t2. On Microsoft excel, the acceleration was plotted on a graph against m2/m1+m2 in which the slope of the trendline gave us our experimental value for free fall acceleration (g). In the second part of the experiment, the air was turned off so that friction acted upon the cart in the opposite direction. Then, the same procedure as experiment one was carried out. To make up for the force of friction on the cart and to ensure that the acceleration wasn’t slowed, we added heavier weights at the end of the string. The average time was recorded and used to calculate the acceleration, which was also used in an equation with the accepted value of free fall acceleration to find μ. The values of μ for m2 should have been exactly the same but due to human error, mainly with recording time, the values of μ were close. (all calculations found on attached sheets) Discussion/Conclusion:
For the first part of this experiment, the calculated value for g was 9.89 m/s2, which is extremely close to the accepted value for g. In the second part of this experiment, the value for μ when m2=120g was 0.278, 0.306 when m2=140g, and 0.329 when m2=160g, averaging out to 0.304. When m2=200g and 220g, the calculated value of acceleration was way too high, giving us an impossible value for μ (in the negatives). Therefore, we removed these two trials and assumed that with masses higher than 160g, the cart is pulled so hard that it slightly lifts off the track. With this, it experiences no opposing force of friction and the time for the cart to move down the track becomes incorrect.