Physics I - Newton's 2nd Law Lab Report

Physics I – Newton’s 2 nd Law Lab Student: Havana Perez Partners: Medha Namala and Julie Coronel Section 024 Lab Date: 10/06/23 Due date: 10/19/23

Objective: The objective of this experiment was to verify Newton’s 2 nd Law through a series of tests as it was applied to various systems. The measured acceleration from each trial should be equal to Force ( N ) Mass ( kg ) if Newton’s 2 nd Law is proven to be true through this experiment. Description: In this laboratory experiment investigating Newton’s Second Law, we utilized several pieces of equipment, including Capstone software, motion and force sensors, various weights, gliders on an air track, a photogate, a pulley, and a picket fence. The pulley served to record position, linear speed, and linear acceleration, while the sensors measured force, acceleration, velocity, and position. We conducted trials using 40g and 70g masses in conjunction with the glider, and subsequently, we compared the results of each combination. Theory: The physics principle being studied and tested in this experiment is Newton’s 2 nd Law, described as F=(m)(a) . F is the force in newtons, m is the mass in kilograms, and a is the acceleration in m/s 2 . The Force is also the sum of all of the forces acting in the system, known as the net force. Newton’s gravitational law that gives the gravitational force F G between m and M is set forth by F G = G m M R 2 = mg . R is the radius, G is Newton’s gravitational constant, and g is the acceleration due to gravity, given by g = GM R 2 = ¿ 9.81 m/s 2 . The weight of an object in newtons (N) is equal to the mass of the object in kg x 9.81 m/s 2 . In this experiment there are two bodies of mass in the system along with the force of Tension (T) acting on the strings holding up the weights. The relevant equations for this system would be: 1. ( m 1 g ) − T = ( m 1 a ) 2. T = ( m 2 a ) 3. ( m 1 g ) − ( m 2 a ) = ( m 1 a ) = F 4. m 1 ×g m 1 + m 2 = a Procedure: a. Part 3) Does F = ma: i. Measuring the net force, mass, and acceleration using a force sensor and a motion sensor. ii. Program the motion and force sensor properly with Capstone. iii. Calibrate the force sensor by running the Capstone program while suspending the force sensor from a horizontal rod. iv. Hang a 0.5 kg mass on the force sensor, then add 2 0.2 kg masses.

b. What happens when F=0 in each graph? i. When F=0, the acceleration is also=0, due to F=ma. This also means that when the object is changing directions, the velocity will change signs because it has reached its maximum or minimum . c. Part 4) Calculate the Average & S.D. of acceleration for each combination: Table 1. Large glider (28.7 cm; 0.454 kg): Trial Experimental Acceleration (m/s 2 ) with 40g used Experimental Acceleration (m/s 2 ) with 70g used 1 0.755±9.7x10 -4 0.947±0.096 2 0.756±0.0016 1.26±0.0021 3 0.749±0.0020 1.25±0.0027 4 0.754±0.0015 1.15±0.0098 5 0.748±0.0017 1.16±0.0033 Average 0.752 1.15 Standard Deviation 0.00326 0.113

Table 2. Small glider (18.7 cm; 0.306 kg): Trial Experimental Acceleration (m/s 2 ) with 40g used Experimental Acceleration (m/s 2 ) with 70g used 1 0.267±9.4x10 -4 0.473±0.090 2 0.343±0.00326 0.533±0.113 3 0.341±0.00320 0.583±0.0033 4 0.322±0.00272 0.575±0.0098 5 0.374±0.0017 0.581±0.0030 Average 0.329 0.549 Standard Deviation 0.0395 0.0471 d. By using the slope of the velocity curve measured by Capstone, the experimental acceleration can be calculated: Large Glider: 40 gmasstheoreticalacceleration : a = m 1 ( g ) ( m 1 + m 2 ) = 0.040 kg ( 9.81 m s 2 ) ( 0.040 kg + 0.454 kg ) = ¿ 0.793 m/s 2 70 g masstheoretical acceleration : a = m 1 ( g ) ( m 1 + m 2 ) = 0.070 kg ( 9.81 m s 2 ) ( 0.070 kg + 0.454 kg ) = ¿ 1.31 m/s 2 Small Glider:

a. Part 4: Newton’s 2nd Law Applied To A System Large Glider: Percent error for 40g mass: 0.793 m s 2 − 0.752 m s 2 0.793 m s 2 × 100% = 5.17% Percent error for 70g mass: 1.31 m s 2 − 1.15 m s 2 1.31 m s 2 × 100% = ¿ 12.21% Small Glider: Percent error for 40g mass: 1.13 m s 2 − 0.329 m s 2 1.13 m s 2 × 100% = ¿ 70.88% Percent error for 70g mass: 1.98 m s 2 − 0.549 m s 2 1.98 m s 2 × 100% = ¿ 72.27% b. Part 5: The Acceleration of Gravity, g Percent error: 9.81 m s 2 − 9.80 m s 2 9.81 m s 2 × 100% = 0.102% c. For part 4, a potential source of error was the presence of friction between the air track and the glider, as well as between the pulley and the string. Additionally, although we assumed the pulley to be massless and frictionless, it was not truly massless. These factors contributed to a systematic error, resulting in a slower experimental acceleration. In part 5, we encountered a slight air resistance when the picket fence was dropped through the sensor. Lab Questions:

a. For comparison with the acceleration, it is more convenient to change the sign and enter the weight as a positive quantity. Why should you enter a negative number? Explain. I. You should enter a negative number for the weight so that the force and acceleration graphs can be consistent. Acceleration is a negative quantity (-9.8 m/s2) so if you were to enter the weight as a positive quantity, the two graphs would be inconsistent and would be recorded as going in opposite directions. b. Compare the graph for force with the graph for acceleration. Does the curve for force pretty much duplicate the shape of the curve for acceleration? I. When examining the set of graphs from Part 3, the force graph follows the trends observed in the shape of the acceleration curve. This correlation is expected because force, F, is proportional to acceleration, a, as defined by F=ma. While considering the mass, m, the graphs should exhibit similar patterns. c. What is occurring at the zero crossing for velocity, acceleration, and force? Explain in detail. I. At the zero crossing for velocity, a change in direction occurs, as indicated by the object moving in a direction labeled as positive by the sensor, followed by a motion in the opposite direction labeled as negative. At the zero crossing for acceleration, the velocity of the object remains unaltered. At the zero crossing for force, it's also when the acceleration crosses zero because force and acceleration are directly related. d. If you made the same motion with the force sensor but at a different distance from the motion sensor, which of your 4 graphs would differ from the ones you actually took? Explain. I. Among the four graphs, the position graph would diverge from the collected data. The other values in the acceleration, velocity, and force graphs depend on the slope of the position graph, not the absolute position of the object concerning the motion sensors e. Compare your results to the theoretical values. How well do they agree? What are possible reasons for any disagreement? I. I n our trials from part 4, we observed a percent error of 5.17% for the 40g mass and 12.21% for the 70g mass in the case of the large glider. For the small glider, we noted a 70.88% percent error for the 40g mass and 72.27% for the 70g mass. II. The percent error for the large glider is significantly smaller between the theoretical value (0.793 m/s²) and the average of my experimental values for the 40g mass (0.752 m/s²) compared to the theoretical value (1.31 m/s²) and the average of my experimental values for the 70g mass (1.15 m/s²). III. Similarly, for the small glider, the percent error is considerably smaller between the theoretical value (1.13 m/s²) and the average of my experimental values for the 40g mass (0.329 m/s²) compared to the theoretical value (1.98 m/s²) and the average of my experimental values for the 70g mass (0.549 m/s²). These discrepancies can largely be attributed to the presence of friction between the

relationship between acceleration and force through this experiment. The percent error observed for the 40g and 70g masses in Part 4 is likely attributed to the presence of friction within the system and the mass of the pulley. Despite our experiment assuming friction lessness and a massless pulley, these factors influenced the results. Additionally, although minimal, the percent error in our experimental acceleration can be attributed to air resistance. This experiment also successfully reinforced our understanding of the relationships between position, acceleration, force, and velocity. The graphical representations allowed us to discern when the values crossed the x-axis and what significance these crossings held for each parameter. In conclusion, each part of this experiment served to corroborate Newton's 2nd Law and test the theoretical value of g."