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Report for Experiment #11

Testing Newton’s Second Law

On the Moon

Abstract

In this experiment, we tested Newton’s second law and determined the acceleration due to gravity on the Moon. We used a frictionless air table equipped with a spark timer, and studied the motion of a puck

attached to a vertically hanging weight. In both setups that we tested, the puck’s acceleration changed linearly with the mass of hanging weight as expected from Newton’s second law, but in one case, the  measured gmoon value was not consistent with the known value within the uncertainty.

Introduction

An object which is acted upon a non-zero total force undergoes an acceleration in the direction of the force. The relation between the acceleration of the object and the net force acting on it is given by

Newton’s second law [1], which can be expressed as

where net is the net force, m is the object’s mass and denotes the object’s acceleration. As an example, for the case of free fall on Earth, net  is equal to the object's weight and Newton’s second law reads

From this we can conclude that the object falls on Earth at a constant rate a = g = 9.81 m/S2 .

The goal of this experiment was to test Newton’s second law on the Moon by studying the motion of a puck attached to hanging weights on a frictionless air table, and to measure the acceleration due to

Moon’s gravity gmoon . In the first investigation, the motion of the puck pulled by three different weights   was analyzed. The position of the puck was measured periodically, and the velocity and acceleration were determined. The accelerations were compared to the mass of the system to test Newton’s second law and   to determine gmoon . The second investigation involved the same procedure, but the mass of the puck was  doubled by adding extra weights to it. A similar analysis was performed and a second measured value of   gmoon was obtained.

Investigation 1

The setup consists of pucks that float on a flat glass surface table using compressed air [2]. The motion of the pucks can be tracked from dots that are periodically marked by a spark timer on a white   paper placed under the pucks. A sheet of carbon paper placed under the white paper provides the

electrical connection between the pucks and the spark timer. A pulley hooked up to the side of the table allows a puck to be attached to a vertically moving mass hanger.

Before data were collected, the air table was leveled by adjusting its three adjustable legs. The

spark timer was set to 10 Hz so that, when the circuit was closed by pressing the associated switch pedal, sparks were generated every 0. 1 S. The mass of the puck was measured to be mp  = 550 g. For the first    trial, a mass of mw  = 200 g was used as the hanging weight.

Data were collected by pressing down the spark timer pedal and then releasing the puck. The

puck slid along the air table, generating sparks at fixed time intervals. When the puck reached the end of the table, the pedal was released and the white paper was removed and inspected. After skipping the first few dots, ten consecutive dots for which the puck was in a smooth motion were labeled 1-10. The

displacement between each set of three adjacent dots, Δx, was measured with a ruler and recorded.

Displacement #1, for example, was the distance between dots 1 and 3, while displacement #2 was the

distance between dots 2 and 4 (and so on). The instrumental uncertainty in these measurements, δΔx =   0.3 cm, was assessed based on the radius of the spark timer dots. The time interval between each pair of adjacent dots, Δt = 0. 1 S, was also noted. The relative uncertainty δΔt/Δt = 0.2% was provided by lab personnel. After these values were gathered and recorded for the 200 g trial, the process was repeated    two more times with hanging masses of 400 and 800 g, respectively. The resulting data are provided in  Table 1 below.

In order to determine the acceleration of the puck, the velocity had to be calculated from the raw displacement and time data at various points. Because each displacement Δx was defined over two time  intervals Δt, the average velocity v during each displacement was calculated as:

The average velocities for each displacement interval were assumed to take place at the middle of each associated time interval. In other words, for the first v value, corresponding time was 0. 1 s, for the second one, t was 0.2 s and so on. The derived v, δv and t values are also included in Table 1.

To calculate the acceleration, a plot of the average velocities vs. time plot was created (see Fig. 1 below). The data points were input into the IPL straight-line fit calculator [3] to determine the slopes, a,   and their uncertainties, δa. The resulting values are provided in Table 2 below.

As previously discussed, Newton’s second law states that the sum of all forces on an object is    equal to the product of its mass and acceleration. If we denote the mass of the hanging weight and puck  as, respectively, mw and mp , then Eq. (1) can be used to describe the acceleration of the entire puck &   hanging mass assembly, F =  (mw + mp )a. The force on this assembly is just the gravitational force on the hanging mass, given by F = mw gmoon . The combination of these two equations gives:

Questions

Answers to the questions at the end of the lab.

Acknowledgements

I would like to thank my lab partner, Buzz Aldrin, for his assistance during the Moon landing,

and our TA, Michael Collins, for waiting to rendezvous with us in the Command Module orbiting around the Moon while we collected data on the Moon’s surface. Special thanks go to NASA for funding this

experiment.

References

[1] H. Young and R. Freedman, University Physics, p 111, Pearson Education, 14th  edition.

[2] Hyde, Batishchev, and Altunkaynak, Introductory Physics Laboratory, pp 411-415, Hayden-McNeil, 2017.

[3] IPL Straight Line Fit Calculator, http://www.northeastern.edu/ipl/data-analysis/straight-line-fit/