edited PHYS Lab#4

Lab #4: Newton’s Second Law PHYS-UA11

Objective and Description In this experiment, students are able to further their familiarity with the Capstone interface. Object from previous experiments, such as the motion sensor, air track, glider, and weights were used once again. In addition, students also used a force sensor, photogate sensor, smart pulley, and a picket fence. Through the use of these objects in three different parts, students are able to compare their experimental values for acceleration to the theoretical one that can be calculated. In doing so, the validity of Newton’s Second Law can be analyzed in a physical sense. Theory According to Newton’s second law of motion, an object’s acceleration is dependent upon the mass of an object and the sum of all forces acting upon that mass, referred to as the net force. In other words, F=ma This statement is further expanded to demonstrate that the only force acting on a falling object is acceleration due to gravity. a=g= 9.81m/s 2 Procedure My partner and I followed the procedure fairly closely to that expressed in the write-up. In the first part, it was helpful to attach an index card with tape to the bottom of the hanging mass to be moved up and down. This enabled the motion sensor to get a more accurate read, since it does so based off sound waves bouncing back towards it. In the second part of the experiment, I found it necessary to stop the glider before it hit the end of the track while my partner simultaneously hit the stop button. If the glider was allowed to hit the end of the track, this often resulting in the string coming loose from the pulley and the hanging weight falling off the force sensor.

Figure 2. Free body diagram when m 1 is in free fall with friction. Hanging Mass Run #, Acceleration (m/s 2 ) 1 2 3 4 5 6 40g m=0.781 0.78 𝑎 = m=0.782 0.78 𝑎 = m=0.782 0.79 𝑎 = m=0.770 0.77 𝑎 = m=0.779 0.78 𝑎 = m=0.783 0.78 𝑎 = 50g m=0.961 0.96 𝑎 = m=0.959 0.97 𝑎 = m=0.957 0.96 𝑎 = m=0.961 0.96 𝑎 = m=0.959 0.96 𝑎 = m=0.959 0.95 𝑎 = 70g m=1.29 1.29 𝑎 = m=1.29 1.28 𝑎 = m=1.30 1.30 𝑎 = m=1.29 1.30 𝑎 = m=1.29 1.30 𝑎 = m=1.30 1.30 𝑎 = Table 1. The acceleration is provided both from the slope of the velocity graph as well as the mean of the acceleration graph. Theoretical Accelerations ( ) 𝑎 = 𝑚 1 𝑔 (𝑚 1 )+(𝑚 2 ) m 1 =40g, m 2 =452.1g m 1 =50g, m 2 =452.1g, m 1 =70g, m 2 =452.1g 𝑎 = 40•9.81 (40)+(452.1) =0.797 𝑎 = 50•9.81 (50)+(452.1) =0.977 𝑎 = 70•9.81 (70)+(452.1) =1.315 Table 2. Section 5 Run # 1 2 3 4 5 6 7 a (m/s 2 ) m=9.81 9.86 𝑎 = m=9.5 9.57 𝑎 = m=9.6 9.67 𝑎 = m=9.68 9.65 𝑎 = m=9.71 9.64 𝑎 = m=9.72 9.70 𝑎 = m=10.1 10.2 𝑎 =

Table 3. The acceleration is provided both from the slope of the velocity graph as well as the mean of the acceleration graph. Questions 1. Why should you enter a negative number when calibrating the force? Explain. Depending upon whether you enter a positive or negative value, while the graphs of acceleration and force are the same, they will either be 180º in phase or out of phase. 2. Does the curve for force pretty much duplicate the shape of the curve for acceleration? As previously mentioned, while the graphs are the same, for my partner and I, since we entered a negative value, our graphs are 180º out of phase. Other than that, each place that F=0, a=0. 3. What is occurring at the zero crossing for velocity, acceleration and force? Explain in detail. *see analysis under Figure 1. 4. If you made the same motion with the force sensor but at a different distance from the motion sensor, which of your four graphs would differ from the ones you actually took? Explain. When my partner and I performed the same motion of part one but started closer to the sensor, the only graph that changed was the position graph. The other graphs were the same as those of the different starting position. 5. What are all the units of force? Force is typically measured in Newtons (N), which has the SI units of kg•m/s 2 . In the CGS system, force is measured in Dynes, or g•cm/s 2 . In the FPS system, force is measured in pounds (lb), or slug•ft/s 2 . 6. Is mass gravity dependant? It is significant to distinguish the difference between weight and mass. It is commonly known that a person would not weigh the same on the moon as they do on Earth because weight is dependant on gravity. This is because weight is measured by the force of gravity pulling on on object. Mass, on the

m 1 =70g, m 2 =452.1g m=1.29 2.22•10 -5 1.315 Table 4. Section 5 Average Acceleration (m/s 2 ) Standard Deviation Theoretical 9.73 1.75•10 -1 9.81 m/s 2 In both parts, the low standard deviation displays consistency in the data collection. In both cases, the experimental data were also found to be slightly lower than the theoretical. This could be explained by the presence of air friction, which was ignored. Despite being lower, they are still fairly similar. Conclusion Through the use of the Capstone database and various apparatus, it can be seen that Newton’s Second Law does hold up in a physical sense. Resources Halliday, David, Robert Resnick, Jearl Walker. Fundamentals of Physics, 11th Edition. Wiley, 05/2018. VitalBook file. Experiment #4: Newton’s 2nd Law lab manual, NYU Physics department, https://physics.nyu.edu/~physlab/GenPhysI_PhysII/Final%20Draft%20of%20General%20Physic s%20I%20write%20ups/Newton's-2nd-law-09-30-2016.pdf