homework

R

mp

m1

m2

Physics 161 Lab 4, Atwood’s Machine Part 1: Calibration

Objective To determine the acceleration due to gravity using Atwood’s Machine by varying experimental parameters and taking measurements of each experimental run and doing calculations on the data collected. In most, if not all, experimental sciences (and physics is no exception) the first round of experimentation does not yield perfect and exact results. There are often combinations of experimental parameters that yield the best results. There are also sources of random and systematic error that can be discovered through careful measurement and calculations using collected data. In this exercise you will be using an Atwood’s machine (a detailed explanation of this experiment is in the Introduction section below). In this two part lab you will find the best set of experimental parameters to calculate the most accurate value of the gravitational acceleration of Earth, 9.8 m/s2.

Turn in There is no preliminary survey for this lab. The lab exercise for this lab will be due in one week after posting. The lab exercise can be accessed on Canvas by clicking the “Assignments” link on the front page. Background The Atwood’s machine consists of a string draped over a pulley with a radius, R, as shown in the schematic to the right. There is a mass attached to each end of the string (m1 and m2). The pulley also has an associated mass, mp. The string also has mass but if it is very small compared to the masses attached to the string then the string mass can be ignored and good experimental results can still be attained. Suppose the masses attached to the string are held in place and then released. If the masses are unequal then the system will accelerate. We know from Newton’s 2nd Law that objects being acted on by unbalanced forces will accelerate. This means that one of the masses will travel upwards a certain distance and the other mass will drop a given distance (provided the string is not stretchy). We also know that if we know that if an object has constant acceleration, we can determine that acceleration from distance traveled and the time it takes to travel that distance.

Task: Using different masses for m1 and m2 and different travel distances, collect distance and time data from each experimental run. Look at the video titled “Atwoods Video” on the Panopto Recordings link on the PHYS 161 Canvas front page for some tips on how to set up the experiment. Collect data from 10 different experimental parameter configurations, in other words, take measurements from ten different combinations of masses and travel distances. After considering these questions, calculate numerical values for gravitational acceleration. It is ok, if you do not have values of 9.8 m/s2 exactly.

Rarely do experiments work perfectly the first time. However, it is important to think about what the results mean in terms of the physics involved and how the measurements were taken and how adjustments to the experiment can be made to get better results.

STOP & THINK

- What are the forces acting on the hanging masses, m1 and m2, as they accelerate? - How will you use distance and time to determine the rate of acceleration of the masses? - Using the forces acting on the hanging masses and the rate of acceleration for the masses, can

you derive an equation for the Earth’s gravitational acceleration ‘g’? - What could be the advantages of collecting data from a system that accelerates rapidly? - What could be the advantages of collecting data from a system that accelerates slowly? - What influence does the pulley and its mass have on the experimental results?