Pulleys and Ramps
Exp 1: The Atwood Machine Exp 2: The Cart on a Ramp Answer Sheet
For this experiment, you will need
- 1 Ring Stand
- 1 Right Angle Clamp
- 1 Metal Rod
- 1 Meter Stick
- 1 Pulley
- String
- Assorted Masses (50g, 100g, 200g)
- Camera
Hover your mouse over a piece of equipment to see it displayed here.
Use the right-angle clamps to connect the metal rod to the ring stand. Fasten the pulley to the metal rod with the wheel facing down.
Measure out about 120cm of string, then tie a loop onto each end. To tie a loop:
- Fold one end of the string inward by 10cm, forming a narrow loop.
- Tie the loop into a simple knot.
Thread the string through the pulley, over the top of the wheel.
Hook the 200g mass onto one of the loops and rest it on the table. Hook the 100 gram mass onto the other loop, then attach the 50g mass to the 100 gram mass. The 100+50 gram masses should be hanging some distance above the table, close to the pulley wheel.
You have now constructed the atwood machine.
Lean the meter stick against the metal rod, next to the pulley.
Raise the 200g mass off the table until the 150g mass is just barely above the surface of the table.
Using your phone's camera, record the motion of the 200g mass as you let it fall. Be sure that the camera is held steady, and that the entire meter stick is in frame. For best results, the camera should be as far away from the atwood machine as reasonably possible.
Next, use the motion tracer app below to analyze the motion of the 200g mass.
Motion Tracer
Upload your video footage here:
Calibration
Follow the instructions to calibrate the length of the vertical meter stick shown in the image below.
When you are done, a colored line will be visible running the length of the meter stick and you will have the option to confirm the calibration.
Do not confirm the calibration until you are satisfied that it is good enough. You will not be able to change it later.
Trimming
The next step is to determine the appropriate timeframe for analyzing the weight's motion.
We are only interested in the weight's motion while it is falling.
Use the navigation buttons to move through the video frame by frame.
Set the starting point as the first frame after you release the weight.
Set the ending point as the last frame before the weight hits the floor.
When you are finished, hit the Confirm button. You will not be able to make changes later.
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Start:
End:
Data Collection
The final step is to record the position of the weight at each moment in time.
Click on the weight in each frame in order to mark its position.
Use the navigation buttons to correct any mistakes you may make.
Your data does not need to be perfect.
When you are satisfied with the data you have collected, hit the Confirm button. You will not be able to make changes later.
Data Conversions
The computer now has nearly enough information to create a data file.
The origin of our coordinate system, (the point where y=0), can be chosen arbitrarily, so we let the origin be the location of the first data point.
We can also let time be 0 at the first data point.
Lengths in meters are measured by converting from lengths in pixels based on the length in pixels of the meter stick.
The time in seconds can be determined by knowing that we sampled the video at frames per second, so each frame cooresponds to 1/ of a second.
Downloads
Download the data file to use in the next part.
Analysis
The predicted acceleration of an Atwood machine is given by
$$a = \left(\frac{m_2 - m_1}{m_2 + m_1}\right)g$$
Where \(m_1\) is the smaller mass, \(m_2\) is the larger mass, and \(g = 9.8\) m/s\(^2\) is the gravitational acceleration.
Calculate the predicted acceleration \(a\) based on the masses used in this experiment. (Question 1.A)
Open your data file in Excel, and make a scatter plot of position \(y\) vs time \(t\).
The equation of motion for an atwood machine undergoing constant uniform acceleration is given by
$$y = \frac{1}{2}at^2 + v_0 t + y_0$$
Perform a quadratic (polynomial order 2) fit and use the trendline equation to find the measured acceleration \(a\). (Question 1.B)
When you are finished, call over the instructor to check your work.
For this experiment, you will need
- 1 Track
- 1 Vernier Sensor Cart
- 5 Bricks
- 1 Meter Stick
- Vernier Graphical Analysis Software
Hover your mouse over a piece of equipment to see it displayed here.
Setting Up Graphical Analysis
Download Vernier Graphical Analysis onto your laptop or smartphone to interface with the sensor cart.
Hold down the power button on the sensor cart to turn it on.
Open Graphical Analysis, and select Sensor Data Collection from the splash screen.
Select your sensor cart from the Sensors menu and press Connect. The serial number should be printed on the cart, next to the power button. Once your cart is selected, press Done.
Lay out one brick on the table and use it to prop up one end of the ramp. Measure the height of ramp at the 100cm mark in Table 2.A. Additionally, calculate the sine of the angle of incidence $$\sin{\theta} = h/L$$ where \(h\) is the height, and \(L\) is the length of the ramp at the 100 cm mark.
Place the cart at the top of the ramp. Hit the Collect button and release the cart to record the cart's motion.
Click and drag on the Position graph to select the first parabola on your graph. From the menu that appears, select Apply Curve Fit then choose Quadratic, and apply.
The equation of motion for a cart on a ramp undergoing constant uniform acceleration is given by
$$y = \frac{1}{2}at^2 + v_0 t + y_0$$
Use the curve fit equation to find the acceleration \(a\) of the cart, and record your result in Table 2.A.
When you are finished, call over the instructor to check your work.
Repeat your measurements for 2, 3, 4, and 5 bricks.
Using your data from Table 2.A, plot acceleration \(a\) vs \(\sin \theta\) in Excel, and perform a linear fit.
Record the slope of your line as the gravitational acceleration \(g\). (Question 2.B)
When you are finished, call over the instructor to check your work.
Answer Sheet: atwood_answer_sheet.pdf