Keeping in Balance

Purpose: Use the concepts of torque to determine the mass of an unknown object.

Discussion: Torque is a force that causes a body to rotate. Similar to the the idea that a NET force causes and object to accelerate in a straight line a NET torque causes a body to rotate about an axis. The main difference between torque and force is that WHERE you place the force becomes important and the distance to the rotational axis is known as the lever arm.

Hypothesis: To cause a body to rotate, there must be a ______________ applied at a _________________ from the rotational axis. The bigger/smaller the force and the bigger/smaller the lever arm, the more torque there will be causing the object to move into equilibrium/nonequilibrium. The mass of an unknown object can therefore be determined by balancing a meterstick and calculating the equal ______________.

Materials:

Procedure:

Part I--

  1. Balance the meterstick horizontally with nothing hanging from it. (Hopefully this is at th 50 cm mark)
  2. Using the slider, attach an unknown mass at the 90-cm mark of the meterstick. Place a known mass on the other side to balance the meterstick. Record the mass and position of both the known and known masses used to balance the meterstick.
  3. Calculate your lever arm for both objects. (The distance from the fulcrum to the object)
  4. Calculate the torque for the known mass.
  5. Set the unknown mass' torque equal to the known mass' torque and determine the mass of the unknown object.
  6. Measure the mass of the unknown object and record.
  7. Calculate your percent relative error.

Part II--

  1. Place the fulcrum exactly on the 85-cm mark. Balance the meterstick using a single mass hung between the 85-cm and 100-cm marks. Record the mass used and position.
  2. Draw a Free Body Diagram of your meterstick system. (Remember that the mass of the meterstick acts at it's center). Label the fulcrum and forces. Show the lever arms and write in the distances. (Remember this should be from the pivot point NOT the 50 cm mark)
  3. Calculate the two torques for the forces in your diagram.
  4. Determine the mass of the meter stick by setting your torques equal to each other (since it is not spinning)
  5. Mass your meter stick and record.
  6. Calculate your percent relative error.

DATA:

Part I:

known mass: ____ kg, lever arm for known mass: _______ m

distance from fulcrum to unknown mass ________ m

Torque of known mass (5 -steps) Mass of unknown (5 -steps)
. .

Actual mass of unknown object _____ kg

% relative error: (Show calc:) __________

Part II

mass ______ kg, lever arm for known mass: _______ m

lever arm for meter stick's center of mass: _________ m

Drawing showing F's and fulcrum and lever arms.
Torque of known mass (5 -steps) Mass of meterstick (5 -steps)
. .

Actual mass of meterstick: _________ kg

% relative error: (Show calculation):

Questions:

  1. Where is the mas of the meterstick effectively located?
  2. How does lever arm affect torque?
  3. How does the mass hanging affect torque?
  4. How would a mass hanging at the fulcrum affect the torque on the meterstick?