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Lab 1 Feb.27: Finding a relationship between mass and period for an inertial balance.

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Physics 4A, Lab 1:
Author: Jiarong Song (Nina), Joel
Date of Lab: Feb 27

Purpose Statement:   To determine the inertial mass of an unknown object by using the relationship between mass and period on an inertial balance, and using this model to determing the unknown masses of some other objects.

Procedure:
Use a C-clamp to secure the inertial balance to the tabletop. Put a thin piece of masking tape on the end of the inertial balance. Set up a photogate so the when the balance is oscillating the tape completely passes through the photogate.
Hit collect and pull back the release the inertial balance the computer starts measuring a reasonable period. Record the period with no mass in the tray first. Adding 100g each time and record the data in table.

Measured data:

Mass in balance (g)
Period (sec.)
Mass in balance (g)
Period (sec.)
0
0.283
500
0.547
100
0.346
600
0.597
200
0.401
700
0.637
300
0.452
800
0.684
400
0.499

Next, we use the same method to collect the data from two random items. 
Items
Period (sec.)
iphone
0.379
tape holder
0.629

Calculated results/ Graphs of data:
Guess the value of the M tray and input the data from the first data collection. The result is a curved graph. We need to continue to guess on the mass of the tray until we get a straight line, the straighter the line is, the more accurate the value of M tray becomes. 

First consider the equation:
T=A(M added+ M tray)^n
Linearize the curve by taking the natural log of the equation, we get:
ln(T) = n* ln (M added + M tray) + ln A.















Find the range of the M tray to be 0.280 kg - 0.325 kg. Use this range and the data of the slope (m) and y-intercept (b) on the graph to find the two equations that uses the low and high value of the tray.

 






Summary: 
The purpose of inertial balance lab is to find the relationship between the mass and period of the inertial balance. After setting up the balance, photogate. we collect the data by measuring the period of the balance with various masses. Then we measure the period of two items with unknown mass. We begin the formulation of the equations with T= A(M added +M tray)^n. We take the natural log of both sides to linearize the equation, in order to find A and n. After we have the value for A and n, we input different value for the M tray until we get a correlation value at 0.9999. We then use the range of the M tray to write the two equations, one for the lowest value of M tray (0.280 kg) and one for the highest value of the M tray (0.325 kg). After finding the two equations for the period of the balance, we uses the periods of the two objects with unknown mass to test our equations. The result is that the mass for the same object is close to each other whether we use the high or low equation. 

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