# Using Newton's Second Law: acceleration

Set up a modified Atwood's machine of your own.

First, gather a cart, a force sensor with hook, plus a pair of mass bars. We aren't going to connect the force sensor to the computer, we're just using it to increase the mass of our cart.

Put a track on the table and attach a pulley to one end. Get one of the blue mini-mass sets from the shelf and figure out how to assemble a hanging mass of 15 grams. Attach this hanging mass to a long piece of string, so that it can pull the cart from one end of the track almost to the other end.

Verify that you can cause the cart to roll smoothly from a standing start over a distance of at least 60 or 70 cm. Make sure that the track is level -- use pieces of paper to prop up one end if necessary.

#### Prediction

Measure the mass of the cart plus force sensor plus weights. Draw a free-body diagram of the cart, and write out the equation for its motion along the track. You should end up with one equation and two unknowns.

Measure the mass of the hanging weight. Draw a free-body diagram of the weight, and write out the equation for its motion as it falls. Again, you should end up with one equation and two unknowns.

Using your mathematical skills, combine these into two equations for two unknowns. Solve to find the acceleration of the cart.

#### Confirmation (we hope!)

Using a stopwatch, measure the time it takes the cart to slide by 20, 30, 40, 50 and 60 cm. Make at least three trials at each distance, and write a neat table with all your measurements. Give each person a chance to use the watch -- do the results change when different people use it?

Make a graph of your measurements. Place time squared on the horizontal axis, and distance moved on the vertical axis. Fit a straight line to the data, and compute its slope. Also compute the uncertainty in this slope.

What are the units of the slope? What does the slope represent?

#### Analysis

Compare the acceleration you calculated from Newton's Second Law to the acceleration you determined from your graph. Do the two agree within the uncertainties? If not, can you explain the difference?

Submit your table of measurements, the graph, and a copy of all your calculations. Answer all the questions you see on this instruction sheet. Staple it all together and place into the folder on your table.

#### If you have time ....

What if there were friction in your system? Make a new free-body diagram of the cart which shows a force of friction: call it Ff. Using this force, once again set up two equations and two unknowns. Solve for the acceleration of the cart; your equation should now have a term of Ff in it.

Can you figure out how to determine this value of Ff from your measurements? If so, do it. If not, ask an instructor. In either case, figure out the force of friction and its uncertainty. Is the force of friction significantly different from zero?