GOAL: To investigate the relationship between force, acceleration, and mass.

INTRODUCTION: A glider of mass m_G on a level air track is attached (via recording tape) to a mass m_H that hangs over the end of the air track. When the air is turned on, the tape slides with minimal friction over the air pulley; the hanging weight therefore accelerates the entire system (hanging mass + glider mass). The acceleration of the system will be measured with the picket fence method used in lab A5. The picket fence is taped to the top of the glider, and a photogate is positioned in the path of the fence.
 
 

Some lab groups will vary the total mass of the system (m_H + m_G) while keeping the accelerating force (the weight of the hanging mass, m_Hg) constant. The other lab groups will vary the accelerating force, while keeping the total mass of the system constant. Each group will plot the dependent variable (acceleration) vs. the independent variable (the quantity that was varied) in order to determine the type of relationship between the variables.

PRELAB: Do the following in your lab book before coming to lab.

1) Write a formula for the acceleration of the system in terms of m_H, m_G, and g. Explain why you

think your formula is correct.

2) What mathematical relationship (e.g., direct, inverse, quadratic, ...) should there be between

the acceleration of the system and the net accelerating force (m_Hg)?

3) What mathematical relationship (e.g., direct, inverse, quadratic, ...) should there be between

the acceleration of the system and the total mass (m_H + m_G) of the system?

4) Prepare your data table in your lab journal. (See Method section below.)

METHOD: The air track should be level. Tie 0.100 kg of mass [if your variable is net force, this 0.100-kg mass should be in the form of five 0.020-kg masses; if your variable is system mass, this 0.100-kg mass should be in the form of a single 0.100-kg mass] onto the recording tape (this will be the hanging mass) and put a box containing styrofoam on the floor below it. Position the photogate so that all the pickets will pass unobstructed through the gate before the hanging mass strikes the box. For each run, stop the glider before it hits the end of the air track. At some point in the lab, measure the mass of the glider, including the picket fence, and record it in the Data section of your report. Carry out the procedure for the independent variable that your group is assigned.

All groups begin by taking 3 separate measurements of the acceleration. The software and the instructions for its use are the same as for lab A5. In a table with clearly-labeled columns, record the value of the acceleration and its uncertainty for each trial. Add a fourth column for the average acceleration of the three trials. Appropriate SI units should be used for all quantities.

If your variable is the net force, then

If your variable is the system mass, keep the 0.100 kg hanging mass constant. Tape 0.050 kg to the glider on the center of one side of the glider. Again make 3 measurements of the acceleration. Repeat this process (taping an additional 0.050 kg to the glider and measuring the acceleration 3 times) three more times. Distribute the taped masses uniformly (so that the glider remains balanced) during each new run.

ANALYSIS: Graph your data (independent variable on the horizontal; dependent (the accelerations), on the vertical).

a) If your variable is the net force, explain why there should be a linear relationship between the

acceleration and the net force.

If your variable is the system mass, explain why there should be a linear relationship between the acceleration and (m_H + m_G)^-1. These groups will have to re-express their independent variable to obtain a linear relationship. Ask if you don’t know how.

b) After reexpressing your independent variable (if necessary), carry out a linear fit to your data.

Sketch the graph of your data and the best-fit line in your lab book. Write the fit parameters

below the graph. Make sure that all numbers have appropriate units.

c) Write down the math equation describing the fit and the appropriate physics equation. Write a

translation table between the variables in the two equations.

4. Based on the equation you wrote for the acceleration in the Prelab and your translation table, what should the expected slope and the expected intercept have been? Find numerical values for the expected slope and expected intercept. Find the % differences between the

quantity is zero, there is no need to find the percent difference between expected and

measured values (why not ?).