Using a tilted Atwood's machine

The goal of today's experiment is for you to determine

• the local acceleration due to gravity, g
• the coefficient of static friction between fabric and track
• the coefficient of kinetic friction between fabric and track

Clean your track gently with a damp paper towel, then dry it off. Place a "friction block" on the track so that wide face of the block covered in fabric lies on the track. Connect this block to a hanging mass via a pulley.

Add mass to the block so that its total mass is about 225 grams; try to use as many of the small weights in the set as you can, so that there are plenty of 1-gram and 2-gram pieces placed on top of the block. Add weights to the hanger so that its total mass is about 100 grams.

Now, tilt the entire track until you find the angle theta at which the block just barely does NOT slide up along the track. Do not use the protractor to measure this angle. Place stuff around the track so that it doesn't slide or move. You will need to keep the angle constant for the rest of the experiment.

1. You should be able to determine the coefficient of static friction between the block and the track with this information.

Need some clues?

• Clues for finding the coefficient of static friction

The next goal is to find the coefficient of kinetic friction, which must involve motion. Here's the idea: transfer mass from the block to the hanger, just 1 grams or 2 grams each time. At first, the block may not move; then, it may slide a little way, and then slow down and stop. Keep transferring mass. Eventually, you should reach a point at which the block slides slowly but smoothly up the ramp, accelerating as it goes. Call this your starting point.

Measure the time it takes the block to slide a distance of L = 70 cm up the ramp. Make several trials so you get some idea for the uncertainty in this measurement.

Now, transfer little bits of mass at a time from block to hanger, and each time measure the time for the block to slide up the ramp. Make a table of your measurements.

Eventually, the block will slide so fast that you can't measure the time very well. Stop the experiment when that happens. You should have good measurements for at least 4 or 5 different values of hanging mass m₂; if you have more values, that's even better.

2. You should be able to determine the coefficient of kinetic friction between the block and the track, and the value of the local gravitational acceleration "g", with this information.

Need some clues?

• The analysis for a horizontal Atwood's machine with friction

Each student must submit his own lab report at the start of our next class. The lab report must contain

• title, name, date
• brief description of the procedure
• picture(s) of the setup
• table(s) of all measurements, including units
• sample equations showing calculations (just provide one example for each type of calculation)
• a graph showing acceleration plotted against the hanging mass
• derived values of
  • (a limit on) the coefficient of static friction
  • the coefficient of kinetic friction, with uncertainty
  • the local acceleration due to gravity, "g", with uncertainty
• comments on the values you derived; for example, does your value of "g" agree with the usual value within the experimental uncertainties?

I will judge each report on a number of criteria, which include grammar, spelling, and neatness.