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The Modified Atwood Machine: Using Newton's Second Law

A cart of mass m₁ is connected to a mass m₂ by an ideal string passing over an ideal pulley, as shown. The friction on the horizontal surface is negligible. First make predictions for the cases below, then draw free body diagrams and predict the result based on the diagram! You will make observations as described on the reverse side.

Case 1: You put your hand on the cart of mass m₁ and hold it at rest.

(i) What is the direction of the acceleration of m₁, left, right or a=0?

Prediction--left, right, zero	Observation--Direction and value (with uncertainty)

(ii) Compare the string tension to the force of gravity on mass m₂ is T >m₂g , T =m₂g , or T < m₂g?

Initial Prediction

Based on Free Body Diagram

Observation--Direction and value (with uncertainty)

m₂g =

T =

Case 2. Starting from the situation in case 1, you quickly remove your hand.

(i) After you remove your hand, what is the direction of the acceleration of m₁?

Prediction: left, right, zero	Observation--Direction and value (with uncertainty)

(ii) After you remove your hand, compare the tension in the string to the force of gravity on mass m₂, left, right or a=0?

Initial Prediction	Based on Free Body Diagram	Observation--Direction and value (with uncertainty)

Case 3. Starting from the situation in case 1, you now push m₁ so that it begins to move to the left.

(i) What is the direction of the acceleration of m₁, in the early part of your push, while your hand is pushing,

Prediction left, right, zero	Observation--Direction and value (with uncertainty)

(ii) Compare the tension in the string to the force of gravity on mass m₂ while your hand is pushing,

Initial Prediction	Based on Free Body Diagram	Observation--Direction and value (with uncertainty)

Case 4 Repeat Case 3, but now consider the motion after the cart leaves your hand. Compare the results for (a) motion of m₂ upwards to (b) motion of m₂ downwards

Prediction for acceleration left, right, zero		Observation--Direction and value (with uncertainty)
(a)
(b)
Prediction for tension	Based on Free Body Diagram		Observation--Direction and value (with uncertainty)
(a)
(b)

Observation

Set-up a track with a cart and level the track as best you can. The cart should have a force sensor mounted to it along with a single massive bar with an electronic accelerometer taped to it. The arrow of the accelerometer should point in the direction that the cart will move. Connect a string to the hook on the force sensor, pass it over a pulley and attach it to a mass hanger with attached mass totaling 200 g.

Connect the sensors to the Lab-Pro (accelerometer in Ch 1, force sensor in Ch 2), and the Labpro to the computer. Drag the program F300QualitativeAtwood.xmbl from the server to My Documents and open it. Be sure the force sensor switch is on the 10 N setting. Calibrate the force sensor and the accelerometer as described below. Zero the sensors when there is no applied force and no acceleration.

Make measurements to check your predictions for the four cases. First make qualitative measurements (direction of acceleration, size of tension compared to m₂ g) then record actual averages as indicated below by using the STAT icon (Statistics under the Examine menu). First drag across a region of interest, then click on the icon. Record the mean and standard deviation (std dev) of the results, using the appropriate number of significant figures.

Analysis

Compare your predictions to the measurements. Resolve any differences.

In Case 1, did the value of the acceleration match the prediction?

In Case 1, did the tension have its expected value?

Compare the values of the acceleration in Cases 2, 4a, and 4b. Are they equal?

Compare the tensions in Cases 2, 4a, and 4b. Are they equal?

Compare the accelerations in Case 3 and Case 2. Is the result what you would expect?

Compare the tensions in Case 3 and Case 2. Is the result what you would expect?

Calibration: Under the Experiment menu, Calibrate, and choose the sensor.

Force sensor: Hold the sensor vertically with no mass attached so that the force is zero, and enter that value. Then hang a mass of about 500 grams (remember to include the mass of the hanger!) and enter the weight of the hanging mass. Recall that W = m g.

Accelerometer: Hold the accelerometer so arrow points vertically up, and enter the gravitational acceleration of +9.8 m/s². Reverse the accelerometer so that the arrow points down. Enter -9.8 m/s².