## Verify the rules for vector addition using a force table.

Physics 2011 Lab 2 Vectors /Lab Report/

Purpose: Verify the rules for vector addition using a force table.

Apparatus: Force table with pulleys, ring and strings attached, weight hangers, set of weights.

Theory: At equilibrium, according to Newton’s second law, all forces acting on the ring sum up to zero, 0 iT

 , where the tension force on the string is equal to the weight hangs on the string,

gmT ii  

. With the magnitude and direction known, iT 

is completely defined. Rearrange the

equilibrium condition, we obtain n ni

i TT 

 

, which can be used to verify the vector addition

rules by comparing the left side computed with vector addition rules to the right side.

Procedure: Variation of tension forces acting on the ring are obtained by changing the weight applied to the weight hangers and by moving the pulleys to different angles as indicated by the index marker.

A. Mount a pulley on the 0º mark on the force table and suspend a total of 200 grams on it. Mount a second pulley on the 90º make and suspend a total of 200 grams on it. Experimentally find the magnitude and position of a third force required to achieve equilibrium. At equilibrium, the ring moves to the center of the force table without touching the table and the center pin. (It can touch the top of the center pin.) Test the sensitivity of the apparatus by changing weight over the third pulley without obvious disruption from equilibrium. Record the maximum deviation.

B. Mount a pulley on the 20º mark on the force table and suspend a total of 300 grams on it. Mount a second pulley on the 170º mark and suspend a total of 200 grams on it. Experimentally find the magnitude and position of a third force required to achieve equilibrium. At equilibrium, the ring moves to the center of the force table without touching the table and the center pin. (It can touch the top of the center pin.) Test the sensitivity of the apparatus by changing weight over the third pulley without obvious disruption from equilibrium. Record the maximum deviation.

C. Mount a pulley on the 120º mark on the force table and suspend a total of 100 grams on it. Mount a second pulley on the 30º make and suspend a total of 100 grams on it. Mount a third pulley at 90º with 150 grams on it. Experimentally find the magnitude and position of a fourth force required to achieve equilibrium. At equilibrium, the ring will moves to the center of the force table without touching the table and the center pin. (It can touch the top of the center pin.) Test the sensitivity of the apparatus by changing weight and angle over the fourth pulley without obvious disruption from equilibrium. Record the maximum deviations for both the weights and the angles.

Analysis: 1. Sketch the vectors for each setup and show the vector addition graphically. This does not

need to be perfect, but try to get the scales for the vectors and the angles close to right. 2. Use the vector addition and subtraction rules to calculate the equilibrium force. Compare

the calculated force with the equilibrium force obtained experimentally. 3. Give the reasons for the deviations between the calculated values and experimentally

measured ones. Suggest ways to improve the sensitivity of the apparatus. 4. Find the % difference between the magnitude of the measured and calculated force in

each case.

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