PhysicsLAB: Mass of a Paper Clip

The purpose of this lab is to use the principles of rotational equilibrium to determine the mass of a single paperclip.

Procedure:

Use a triple beam balance to mass a meter stick. Be certain that its center of gravity is in the center of the pan and that the length of the stick is oriented perpendicular to the beams. Record its mass in kg.

Measure the mass of your 5 washers. Record their mass in kg.

Balance the meter stick on the bridge. Record position of knife edge in cm.

Bend two paper clips to hold the five washers and the balancing clips.

Place the clip that is to hold all 5 washers exactly 10 cm from the knife-edge--NEVER move it! Record its location in cm.

Through a combination of moving the balancing clip hanger and varying the number of clips, find ten (10) different locations that balance the five washers. Fill in the following chart on notebook paper as you proceed through the lab.

Note that you do not need to include the hanging clips in your totals since they cancel each other out.

	# of clips	Position of clips	Moment arm of clips	Reciprocal of moment arm
TRIAL	N		L_⊥	1 / L_⊥
		(cm)	(m)	(1/m)
1
2
3
4
5
6
7
8
9
10

Using EXCEL, plot a graph of # clips vs 1/moment arm. Save your file as lastnamelastnametorque to your period's folder. Before printing your graph, be sure that all of the information has been filled out in the blanks located in the upper right-hand corner.

Refer to the following information for the next five questions.

Offset the knife-edge 6 cm from its location in Step I and use paper clips to bring your beam back into equilibrium. Record the new knife-edge position, number of paper clips (counting the hanger) and the position of the clips in the chart below. Then calculate the moment arms for the meter stick and clips.

number of clips, N, to bring the meter stick back into equilibrium

position of clips (cm)

new knife-edge position (cm)

moment arm of paper clips (cm)

moment arm of meter stick's center of gravity (cm)

Refer to the following information for the next two questions.

Conclusion #1: We will now use data analysis techniques to determine the mass of a single paper clip. To begin, we need to write the theoretical equation that models the data you graphed.

In your lab the paper clips provided the clockwise (cw) torque and the washers provided the balancing counter-clockwise (ccw) torque, so our initial equation would be

N(m_clipg)L = M_washersg(0.10)

Since your EXCEL graph is titled N vs (1/L) you need to solve the equation given above for N. That is, you need to rewrite it in a form that parallels the generic equation of a line: y = mx + b.

N(m_clipg)L = M_washersg(0.10)

will become

N = (coefficient)(1/L)

The expression making up the coefficient of (1/L) represents the slope of your EXCEL line.

Solve for the mass of a single clip, m_clip. by setting the coefficient of (1/L) equal to the numerical slope of your experimental data provided by EXCEL.

Refer to the following information for the next question.

Conclusion #2: We will now use your data from Step VII to obtain a second value for the mass of a single paper clip.

In this section of your lab the weight of the meter stick provided the clockwise (cw) torque and the paper clips provided the balancing counter-clockwise (ccw) torque, so our initial equation would be

M_stickg(0.06) = Nm_clipgL

Note that N must also include the hanging clip since the meter stick's center of gravity does not have a corresponding clip to cancel out its weight.

Solve the equation given above for the mass of a single paper clip.

Error Analysis: Compare the two values for the mass of a single paper clip by calculating a percentage difference between the values found in your two conclusions.

After submitting your lab results, turn in a copy of your data table (Step VI), your EXCEL graph and all of your calculations for conclusion I, conclusion II, and your error analysis.