(Sample Lab Report)

The Force Table Physics 221 Section 001

September 22, 2006 Kyle Schmitt

Tony the Tiger

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Purpose/Theory The purpose of this experiment is to verify vector addition. According to Newton’s second law, an object that is not accelerating must have no net force, i.e. the sum of the vectors of the forces on that object must be zero. The method for vector addition includes finding the orthogonal components of each vector and adding so that the components of the resultant vector R is related to the components of the individual vectors A, B, etc., in the following way:

Rx = Ax + Bx + ... + Nx Ry = Ay + By + ... + Ny,

where N is the total number of forces acting on the object. The magnitude of the resultant vector is

22yx RR +=R ,

and the angle θ between the vector R and the x-axis is

)(tan 1

x

y

RR−=θ .

The equilibrant vector is the vector E which when added to R returns zero (Parks 35-38). Procedure Three masses were used to exert measurable forces on a ring at the center of the force table. They were placed at measurable angles so that the components of the force vectors could be calculated. A forth mass was placed so that the net force on the ring was zero, i.e. the ring was centered on the table. Data The forces applied to the ring and the calculated and measured equilibrant forces are presented in Table 1.

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Forces Magnitude Angle X Component Y Component Force #1 400 30 346.4101615 200

Force #2 200 -60 100 -173.2050808 Force #3 300 135 -212.1320344 212.1320344 Sum of Components 234.2781272 238.9269536 Resultant Force R 334.62267 45.56 Equilibrant Force E 334.62267 225.6 Measured Force 350 227 % Difference 4% 1% Force #1 400 45 282.8427125 282.8427125 Force #2 200 -45 141.4213562 -141.4213562 Force #3 500 270 -9.18861E-14 -500 Sum of Components 424.2640687 -358.5786438 Resultant Force R 555.49855 -40.2 Equilibrant Force E 555.49855 139.8 Measured Force 550 140 % Difference 1% 0% Force #1 350 20 328.8924173 119.7070502 Force #2 200 315 141.4213562 -141.4213562 Force #3 500 250 -171.0100717 -469.8463104 Sum of Components 299.3037018 -491.5606165 Resultant Force R 575.51242 -58.66 Equilibrant Force E 575.51242 121.3 Measured Force 570 118 % Difference 1% 3% Force #1 300 25 271.8923361 126.7854785 Force #2 200 310 128.5575219 -153.2088886 Force #3 250 200 -234.9231552 -85.50503583 Sum of Components 165.5267029 -111.9284459 Resultant Force R 199.81758 -34.07 Equilibrant Force E 199.81758 145.9 Measured Force 200 143 % Difference 0% 2%

Table 1_________________________________________________________

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Results/Conclusions The results of this experiment are presented in Table 1. All of the measured forces are within 4 percent difference of the calculated forces, so it can be concluded that this method of calculating vector addition is accurate. Questions This section is self explanatory, and I won’t give you the answers to the questions ☺ Write the question and the answer, or just the answer if it is worded well enough that I can tell what the question is. “Yes” or “no” isn’t enough, but “Our measurements were within 4% difference, so the apparatus was reasonably accurate.” is. It took me about an hour to write this lab report... the reports are a significant percentage of your overall grade so do a good job. Works Cited Parks, James E. Selected Introductory Physics Experiments. Knoxville: Thomson

Custom Publishing, 2002.