1 Name: ___________________ Date:_______________

Lab Partners:_______________________________________________

BALANCED TORQUES AND CENTER OF GRAVITY

Objectives: To study and understand the conditions for static equilibrium in a plane and to study the experimental concept of center of gravity.

Overview: In this lab you will examine the conditions for static equilibrium and explore the nature of Center of Gravity and Center of Mass. In addition you will explore the concepts of rotational and translational equilibrium and torque. Torque is defined as the product of force times distance and its units are Newton-meter or foot lbs.

Important Note #1: For this lab we will define Force to be solely the mass of the object in grams and distance to be in centimeters. This means that the units for torque, for this lab only, will be gram-centimeters, g.cm.

EXPERIMENT A: CONDITIONS NEEDED FOR EQUILIBRIUM

STEP 1: Set up the arrangement shown in the figure below to study the conditions for equilibrium.

STEP 2: Balance the meter stick system (i.e., with all the attachments) and record the balancing position as the position of the fulcrum.

STEP 3: Select two different size masses (more then 100 grams including the mass of the hanger) and using the string loops, suspend each one on either side of the fulcrum. Adjust the positions of each suspended mass until the meter stick is balanced once again. Record the masses used and their positions at the time when balance is achieved. Compute the clockwise and counter-clockwise torques and compute the percent difference. [Percent difference is defined as 100 times the difference in the two values of torque divided by one of the torque values]

Important Note #2. For all parts of this lab, your percent difference must be below 1%. If they are not redo the procedure.

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Put the answers to all questions that follow in the lab report.

QUESTION 1 a]. Does the condition for rotational equilibrium hold? b].What could account for the discrepancies?

QUESTION 2 a]. What would you have to do to the set-up to produce translation without rotation? b]. Figure out three ways to cause a rotational imbalance.

QUESTION 3: Is there more than one way to arrange the two weights and still achieve balance?

STEP 4: Now suspend two unequal masses [more then 100 grams] at different positions on one side of the fulcrum and one on the other side of the fulcrum.

Important Note #3: Don’t put the masses too close to the fulcrum.

Compute the clockwise and counter-clockwise torques and the percent difference and record the masses and positions once balance is achieved.

QUESTION 4: Does equilibrium depend on the number of forces pulling on either side of the fulcrum?

QUESTION 5: Does the condition for rotational equilibrium hold?

STEP 5: Use the arrangement in step 3 to balance the meter stick with one knownmass and another unknown mass. Record the positions and known mass.

QUESTION 6 a]. Is it possible to use the balancing system to calculate the unknown weight? b]. Explain how this might be done and compute the unknown weight.

EXPERIMENT B: WEIGHT OF THE BAR AND CENTER OF GRAVITY

STEP 6: Use the arrangement in Step 1 to balance the meter stick using one known mass (above 100 grams) on one end and no mass on the other end. You will have to move the fulcrum in order to balance the meter stick.

QUESTION 7: What do you think provides the torque on the end without a weight that balances the meter stick?

QUESTION 8: What position is this mysterious force located that balances out the meter stick?

STEP 7: Assume that the mass of the meter stick, W, is uniform. Use the conditions for equilibrium to compute the mass of the meter stick and compare this value to the measured mass of the meter stick. SHOW THIS COMPUTATION IN THE DATA PORTION OF YOUR REPORT.

STEP 8: Now tape a mass, such as a strip of lead, near one end of the meter stick. This arrangement will act as a loaded [non-uniform] meter stick. Find the mass of the loaded meter stick using a laboratory scale. Keep the load mass on the stick for the remainder of the experiment.

STEP 9: The center of gravity of this new loaded stick is at some arbitrary point C. Using the knife-edge once again, balance the meter stick and find the position of the fulcrum.

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STEP 10: Suspend a mass as shown in the figure and adjust the position of the knife edge until balance is achieved. Record all necessary information.

STEP 11: Determine the value of L, the moment arm of the mass W1, and find xcalculated , the moment arm of the loaded meter stick by balancing clockwise and counterclockwise torques. Determine xmeasured by measuring the distance between the new fulcrum and the center of gravity of the loaded meter stick.

The following problem is to be solved and included in your report in a section title Problems after the Conclusions section.

Problem: Find the center of gravity relative to the front axle of a van with 130 inch wheel base where the weight on the front tires is 2100 lb and the weight on the rear tires is 1800 lb. Keep your answer in inches and pounds and show your calculations.

4 RAW DATA

STEP Position of Fulcrum (cm)

Force (grams)

Position on Bar (cm)

Lever Arm (cm)

Clockwise Torque (g.cm)

Counter Clockwise Torque (cm)

Percent Difference

3

4

5

Unknown

5 Unknown Mass Calculated = ______

Unknown Mass by weighing ____________

Percent Difference

STEP 6: Position of the Fulcrum: ____

Position of

Lever Arm Torque of Lever arm of W calculated W measured Percent W1 of W1 W1 W Difference

STEP 8: Mass of the loaded meter stick, W2 : _________

STEP 9: Position of the center of gravity of the loaded meter stick: _____

STEP 10: Position of fulcrum ________ Weight W1 ______ Position W1 _____

Step 11 : L = _______ W1L = ____________ W2 = ________ (from Step 8)

xcalculated = ____________

xmeasured = ____________

Percent difference between xcalculated and xmeasured ________________