Guiding Question:
What is the Mass of the Swinging Rubber Stopper?
Evidence:
Reasoning:
Ft, Tension force
Using the equation of the line from (Fig 1) the slope is given to be 45.24. The measured radius of
the string was 0.68 m. 0.68 รท45.24 = 0.00150๐๐ =15.0๐. Thus, calculated mass of the washer is 15g.
Weight (Fg)
0.42 N
0.78N
1.1 N
Time/Period
0.975s
0.707s
0.578s
Force of Gravity
V2
Ft =Fg: Since the system is not accelerating, the forces must be balanced therefore Ft = Fg
Fc = ๐๐ฃ2รท ๐ = ๐น๐ When rearranging for velocity squared this becomes: ๐ฃ2=(๐ รท ๐)โ
๐น๐. It is important to note that the mass in Fg is the mass at the bottom of the string pulling
the system down, while the mass listed simply as m is the mass of the washer. This means
they are different.
Looking at the data from part one (Fig. 2) it is possible to calculate the velocity from
the times measured using the formula ๐ฃ = (2๐๐)รท ๐. After squaring the calculated velocity
values, it is possible to graph the relationship between Fg and V2 linearly. Doing this gives us
a relation that is akin to the one shown in Fig 1. The formula for a linear equation is ๐ฆ = ๐๐ฅ +
๐. If this were to be rewritten as a formula with relevant variables it would become the
familiar ๐ฃ2=(๐ รท ๐)โ ๐น๐ + ๐ต . (Note: B does not represent a real variable, it was just the
y intercept for this relationship.) Since m, or slope equals (๐ รท ๐) it is possible to take a
numerical value for slope from the graph and rearrange the equation to solve for mass. This
becomes (๐ รท ๐ ๐๐๐๐)= ๐.
Force of Gravity, or Fg
Figure 2
Figure 1
๐ฆ = 45.24๐ฅ + 2.196
