Pan B: Moving in a horizontal circle
Calculate given the masses of the swinging and hanging objects. Combine this with the results from the third video. Does it seem reasonable?
Theory: This is a side view of the Experiment, showing the forces acting on the hanging mass in equilibrium.
The third video includes 40 revolutions of the swinging mass for three different values of L: 0.75, 1.0, and 1.25. Note that these three values are referred to as "radius" in the video but strictly speaking, they are the length of the string. But since we have the angle θ, we might as well do a bit of trigonometry and calculate the actual radius.
Mass of swinging mass and mass of hanging mass, length of string from top of tube to swinging mass.
Calculate the following table using the third video as the time for 40 revolutions:
Period (T)
Radius (r)
Speed (v)
Tension
Weight
Plotting the Data
Use whatever software you choose to plot speed squared (v²) vs radius (r) and find the best-fit line to the data. Paste the graph below (it should include the individual data points and the best-fit line) and write down the equation for your best-fit line.
Write down Newton's Second Law for the swinging mass in the radial and vertical directions, including the expression for centripetal acceleration.
Radial direction:
Vertical direction:
By using the equations above, find the relationship between speed and radius. You should find that v² is proportional to r, that is v² = Cr, where C is a proportionality constant. Using the fact that the tension equals the weight of the hanging mass, write C in terms of the masses and gravitational acceleration g.
Comparing Data and Theory
Compare the value of the slope for the line above to the value for the slope given by the formula for the proportionality constant. Calculate the percent relative error.
Data and Calculation:
Note that for any value of L, θ is the same since sin θ = m/M.