Physics I - Newton's 2nd Law Lab Report

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New York University *

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Physics

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Dec 6, 2023

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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.

v. If completed properly, the force sensor has been calibrated to read zero when the 0.5 kg mass is at rest. vi. Then set up a force, position, velocity, and acceleration graph. With the motion sensor on the floor, record as you move the force sensor with the 0.5 kg mass attached up and down 5 times in a vertical line above the motion sensor. b. Part 4) Newton’s 2 nd Law Applied to a System: i. Note: data must be collected for both the small and large gliders, for a total of 5 trials per glider. ii. Run this experiment with the assumption that the pulley is massless and frictionless. iii. Restart the Capstone software for this portion of the experiment. iv. Level the air track, attach one end of the string to the large glider and a 40g mass to the other end. v. Make sure that the string is horizontal and passes over the pulley, through the groove at the end of the air track. vi. Click Record as you draw the glider back on the air track as far back as possible without hitting the hanging masses on the table clamp and click Stop right before the glider hits the end of the air track. vii. Repeat with a 70g mass. c. Part 5) The Acceleration of gravity, g: i. Using a picket fence, the acceleration is measured and compared to g. ii. Restart the Capstone program. iii. Hold the picket fence just above the photogate, click Record as you let go of the picket fence and it passes through the photogate sensor, then click Stop. iv. Now you can determine the acceleration of the picket fence. Data And Calculations: a. Part 3) best “stack” of graphs:

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

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