Experiment: Newton's Laws of Motion and the Atwood Machine

Experiment: Newton's Laws of Motion and the Atwood Machine

Introduction:

Refer to the following figure of the two connected objects. The weight (force due to gravity, mH g) of the hanging mass causes the acceleration of both masses (mc+mH) since they are connected by a string. Using force diagrams, Newton's second law and ignoring friction, you should be able to find an expression for the acceleration of the mass system (both masses). DO THIS BEFORE COMING TO LAB.

In lab you will set up this track system with car and hanging mass, and measure the acceleration of the system (ameas). Then compare the measured acceleration to the results from Newton's second law (atheory).

Procedures:

1. Arrange your track so that it is level and attach a pulley to the end of the track as indicated in the figure. The string must be just long enough so that the cart hits the end of the track just before (as) the hanging mass reaches the floor. That way both the objects that are tied together will accelerate for the entire trip. Use the photogate to measure the final speed of the car (AS) just when the hanging mass hits the floor Make sure that your string is not rubbing on anything.

2. Start with a total hanging mass of 50g, and with two of the black heavy bars on top of the cart (the cart has a mass of 500g, and each black bar does also, so total cart is 1500g).

3. Pull the cart back and note the starting position.

4. Release the cart and measure the final speed using the photogate.

5. Repeat several times.

6. Do steps 1-5 again but with a hanging mass of 100g.

Analysis:

1. For each set of runs use photogate time and size of your black block mass (used as a flag) to determine vf.

2. Use the appropriate kinematic equation to determine the measured acceleration for the 50g hanging mass, and again for the 100g hanging mass.

3. Now find the theoretical acceleration using Newton's second law.

4. For each result what is the percent difference (absolute value of difference between the theory and measurement/(theory) all x100%).

5. For your measured accelerations, consider the formula you used to calculate ameas. Determine a percent uncertainty in your distance, and time measurements. Use the percent uncertainties to determine uncertainty in acceleration using the rules developed in the first lab.