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Part B: Mass swinging in a horizontal circle Theory Here is a side view of the experiment, showing the forces acting on the swinging mass. Note that because the hanging mass stays in equilibrium, T = mµg. m=mass of swinging mass mu = mass of hanging mass L= length of string from top of tube to swinging mass r= radius of circular motion Side View Tension T Weight W m 1. Write down Newton's Second Law for the swinging mass in the radial and vertical directions, including the expression for centripetal acceleration.

Part B: Mass swinging in a horizontal circle Theory Here is a side view of the experiment, showing the forces acting on the swinging mass. Note that because the hanging mass stays in equilibrium, T = mµg. m=mass of swinging mass mu = mass of hanging mass L= length of string from top of tube to swinging mass r= radius of circular motion Side View Tension T Weight W m 1. Write down Newton's Second Law for the swinging mass in the radial and vertical directions, including the expression for centripetal acceleration.

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Part B: Mass swinging in a horizontal circle Calculate 0 given the masses of the swinging and hanging objects (provided in second video). Compare this value to an image from the third video. Does it seem reasonable? Theory Here is a side view of the experiment, showing the forces acting on the swinging mass. Note that because the hanging mass stays in equilibrium, T = mµg. 4. The third video includes 40 revolutions of the swinging mass for three different values of L: 50, 75, and 100 cm. Note that these three values were referred to as "radii" in the video, but strictly speaking they are L, not r. We could approximater with L as they are close to one another, but since we have the angle 0, we might as well do a bit of trigonometry and calculate the actual radii. m=mass of swinging mass mu = mass of hanging mass L= length of string from top of tube to swinging mass r=radius of circular motion Complete the following table. Use the third video to measure the times for 40 revolutions. Time for 40 revolutions (s) v² (m²/s*) Side View L (m) r (m) Period (s) v (m/s) 0.500 Tension T 0.750 1.000 Weight W Plotting the Data 5. Use whatever software you choose to plot speed squared vs radius, 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. 1. Write down Newton's Second Law for the swinging mass in the radial and vertical directions, including the expression for centripetal acceleration. Radial direction: Comparing Data and Theory 6. Compare the value of the slope for the line above to the value for the slope given by the formula for the proportionality constant C from number 2. Calculate the percent relative error between these values. Vertical direction: 2. By using the equations above, find the relationship between speed and radius. You should find that v? is proportional to r, that is v2 = Cr, where C is a proportionality constant. Using the fact that T2 = T? + T2, write C as a function of the two masses and the gravitational acceleration g. Data and Calculations 3. Note that for any value of L, 0 is the same since Tz sin 0 = T mg m
Transcribed Image Text:Part B: Mass swinging in a horizontal circle Calculate 0 given the masses of the swinging and hanging objects (provided in second video). Compare this value to an image from the third video. Does it seem reasonable? Theory Here is a side view of the experiment, showing the forces acting on the swinging mass. Note that because the hanging mass stays in equilibrium, T = mµg. 4. The third video includes 40 revolutions of the swinging mass for three different values of L: 50, 75, and 100 cm. Note that these three values were referred to as "radii" in the video, but strictly speaking they are L, not r. We could approximater with L as they are close to one another, but since we have the angle 0, we might as well do a bit of trigonometry and calculate the actual radii. m=mass of swinging mass mu = mass of hanging mass L= length of string from top of tube to swinging mass r=radius of circular motion Complete the following table. Use the third video to measure the times for 40 revolutions. Time for 40 revolutions (s) v² (m²/s*) Side View L (m) r (m) Period (s) v (m/s) 0.500 Tension T 0.750 1.000 Weight W Plotting the Data 5. Use whatever software you choose to plot speed squared vs radius, 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. 1. Write down Newton's Second Law for the swinging mass in the radial and vertical directions, including the expression for centripetal acceleration. Radial direction: Comparing Data and Theory 6. Compare the value of the slope for the line above to the value for the slope given by the formula for the proportionality constant C from number 2. Calculate the percent relative error between these values. Vertical direction: 2. By using the equations above, find the relationship between speed and radius. You should find that v? is proportional to r, that is v2 = Cr, where C is a proportionality constant. Using the fact that T2 = T? + T2, write C as a function of the two masses and the gravitational acceleration g. Data and Calculations 3. Note that for any value of L, 0 is the same since Tz sin 0 = T mg m
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