Name ______Date ______
Algebra 2 with TrigonometryMr. Yates
Quadratic Physics: Pendula
A pendulum swings back and forth keeping quite regular time; this was the basis for the first mechanical clocks. The amount of time it takes to complete one full swing (from one high point back to the same point) is called the pendulum’s period, denoted by T for time. We wish to compare different lengths (L) of pendula and their associated periods.
1)Data recording should be done in pairs.
2)Cut a length of string slightly more than five feet long.
3)Tie one end around a washer or other weight.
4)Use a marker to record distances from the washer’s edge of 6”, 12”, 18”,…, up to 60”.
5)Practice swinging the pendulum at different lengths by holding your finger at the mark.
6)If you are waiting for the stopwatch, solve the quadratic equations on back.
7)Use the stopwatch to record the time it takes the pendulum to swing three periods. Check with Mr. Yates to make sure you are counting swings correctly. Make three trials (of three swings each) per length.
8)Record these data in the attached table and graph.
9)Enter these data into graphing calculator lists L1 and L2.
10)Adjust your window and display the data in a scatterplot.
11)Get back to those quadratic queries on the back of this sheet.
While waiting to use the stop watch (or afterwards)warm yourself up for some quirky quadratics by solving these equations:
a)solve for x: 7(x – 2)2 – 343 = 0
b)solve for y: 2(y + 1)2 – 10 = 0
c)solve for W: 3(W + 5)2 – 19 = 5
d)solve for Q: -3(Q + )2 + 300 = 0
e)solve for s:
f)solve for T:
Name ______Date ______
Algebra 2 with TrigonometryMr. Yates
Quadratic Physics: Pendula Part 2
A pendulum swings back and forth keeping quite regular time; this was the basis for the first mechanical clocks. The amount of time it takes to complete one full swing (from one high point back to the same point) is called the pendulum’s period, denoted by T for time. We wish to compare different lengths (L) of pendula and their associated periods.
1)Make sure you complete the quadratic equations warm-up from yesterday.
2)On your graphing calculators, enter (STATEdit) the string length data in L1 and the time for one period in L2.
3)Adjust your window range so the x-values and y-values are appropriate to show the data, then create a scatter plot of L1 vs. L2.
4)Use your calculator to perform a quadratic regression of L1 vs. L2 (QuadReg L1,L2). State the quadratic regression equation: ______. Graph this in Y1. Is it a good fit? Why or why not?
5)Change your window range and scatter plot to show L2 vs. L1.
6)Use your calculator to perform a quadratic regression of L2 vs. L1 (QuadReg L2, L1). State the quadratic regression equation: ______. Graph this in Y1. Is it a good fit? Why or why not?
7)Express the better model using the variables L (length) and T (period time)
8)If your pendulum has a period of 1.5 seconds, estimate its length. Does this fit with your data?
9)If your pendulum has a period of 2 seconds, estimate its length.
10)If your pendulum has a period of 20 seconds, estimate its length.
11)If your pendulum has a length of 10 inches, what do you estimate its period to be? Does this fit with your data?
12)If your pendulum has a length of 32 inches, estimate its period.
13)If your pendulum has a length of 1200 inches, estimate its period.
14)The theoretical formula for a pendulum’s period, measured in seconds, is: . What value should we use for g?
15)Calculate the theoretical values of T by adding a column to our data table. How do your average data values compare with the theory?
16)Looking on Mr. Yates’s website (start at name at least one big idea explored in this lab.
17)Extra credit 1 (ten points): re-create your scatter plot in Microsoft Excel!
18)Extra credit 2 (five points): solve the theoretical pendulum formula for L.
Rubric:
10 points each for:
- Quadratic warm-up
- Data recorded
- Averages recorded
- Scatter plot drawn
- Theoretical values recorded
5 points each for:
- Questions 4, 6, 7, 8, 9, 10, 11, 12, 13, 16 on this page