Alissa Castano- PHYS1P91-Lab5

TABLES: 50g, 100g, 150g UNIT VALUE UNCERTAINTY iOLab Weight g 200.7 0.5 UNIT VALUE UNCERTAINTY Trial 1 weight (with iOLab) N 3.14 0.03 Trial 2 Weight (with iOLab) N 3.95 0.02 Trial 3 Weight (with iOLab) N 4.13 0.03 UNIT VALUE UNCERTAINTY Pulling Force iOLab N 0.31 0.02 Pulling Force Trial 1 N 0.41 0.03 Pulling Force Trial 2 N 0.49 0.03 Pulling Force Trial 3 N 0.53 0.03 UNIT VALUE UNCERTAINTY Slope unitless 0.1245 N/A Y-intercept N -0.0204 N/A UNIT VALUE UNCERTAINTY Ramp Angle degrees 10 0.05 UNIT VALUE UNCERTAINTY A_up m/s 2 -1.109 0.006 A_down m/s 2 -0.520 0.003 μ _k N/A 0.03046 N/A UNIT VALUE UNCERTAINTY A_up m/s 2 -1.00 0.01 A_down m/s 2 -0.549 0.007

μ_ k N/A 0.02369 N/A UNIT VALUE UNCERTAINTY A_up m/s 2 -1.117 0.004 A_down m/s 2 -0.537 0.004 μ_ k N/A 0.03004 N/A UNIT VALUE UNCERTAINTY Average μ_ k N/A 0.028 0.004 FIGURES: Figure 1: Force-time graph of iOlab being pulled with no added weight.

Figure 5: Acceleration-time graph of trial one, iOlab ramp experiment. Figure 6: Free body diagrams of iOlab rolling up and down ramp.

DISCUSSION: What does the value of A represent? What does the Y intercept represent, what should it be? The linear equation (y= Ax + b) for the slope was found to be 0.1245, and the y-intercept -0.0204. The value of A (0.1245) represents the relationship between the pulling force necessary to drag the iOlab, and the weight of the iOlab (including the added masses). In this equation, A also represents the coefficient of friction multiplied by the force applied on the block. As for the y-intercept (b), it represents how much initial pulling force is needed to pull the iOlab with no additional weight on it. The slightly negative y-intercept (-0.0204) implies that despite there being no weight, there is still some force needed to drag the iOlab. Can you identify the point from the position graph where the maximum height was reached? Can you identify that same point from the velocity graph? Figure 3 illustrates the position-time graph for the motion of the iOlab on the ramp. As seen in the figure, there is an obvious peak in the graph representing the highest point reached by the iOlab. The highest point on the position-time graph is the highest point reached by the iOlab before it rolled down the ramp. As for the velocity-time graph, you cannot truly identify the highest point reached by the iOlab, because the velocity graph does not display the position of the iOlab, only its velocity. That being said, one can identify the time (in seconds), when the iOlab reached its highest point. This would be when a point on the velocity-time graph touches zero (see figure 4). As the iOlab reaches its peak after rolling up as high as it can, it changes direction (rolls back down). This change makes the velocity zero. Therefore, it is possible to identify the time when iOlab reached zero on the velocity graph (when y=0). When comparing figure 3, and figure 4, it's possible to see that both graphs illustrate that the iOlab reached its peak point right before 1 second on both graphs. Which coefficient of kinetic friction less between your two experiments? Why might this be? For the first experiment (dragging the iOlab on the table), the coefficient of kinetic friction was the value of A in the linear equation, so 0.1245. For the second experiment (3 trials pushing the iOlab up a ramp), the average coefficient of kinetic friction of all three trials was calculated to be 0.028, which is significantly smaller than the coefficient obtained in the first experiment. A smaller coefficient of kinetic friction implies that there were less opposing forces on the iOlab in the second experiment, in comparison to the first. This may be caused by various differences between the two experiments, like the use of the wheels for the ramp experiment, or the gravity working for the iOlab when it was rolling down the ramp.