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Experiment 2

The Addition of Vectors

In this experiment a force table is used experimentally to determine the magnitude and direction of a fourth force that is necessary to effect static equilibrium when three known forces act on a light ring. The reliability of the data is investigated, and the experimental values are compared to theoretical values.


According to Newton 's First Law of Motion, a particle is considered to be in static equilibrium when the vector sum of all the forces acting on the particle equals zero:
This is referred to as the First Condition of Equilibrium. A stationary particle corresponds to this situation. In two dimensions, (1) can be expressed as and That is, the sum of all the
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Clamp the fourth pulley at this angular position, pass the string over the pulley, and attach the fourth weight hanger.

5) Determine the mass that will achieve equilibrium by adding mass to the fourth weight hanger until the minimum amount necessary to center the ring is found. A method of accomplishing this is to hold the ring so that it is centered around the pin and add mass to the fourth weight hanger that is close to but less than the minimum mass needed to achieve equilibrium. When the ring is released, the ring will move away from the weight hanger. Center the ring again and add small increments of mass until the ring does not move. Record this value as m4min. Carefully continue to add mass until the maximum amount is found that will maintain the ring in its centered position. Record this value as m4max.

The best value of m4 is the average: 6) Use (4) to compute m4 and place this amount of mass on the fourth string. Check that the ring is centered.

7) Loosen the fourth clamp pulley and carefully move the clamp in a clockwise direction until the minimum angle is found that will maintain the ring in its centered position. Record this value as 4. Repeat in the
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