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Leighton Thompson

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Physics 001-09

Vector Force Table

Objective:

The objective of this experiment is to study vectors and compare experimental results with graphical and analytical calculations by finding a resultant force that balances out the given force so that the system will be equilibrium.

Apparatus:

Force table, weight holders, set of masses, rulers, protractors, spirit levels.

Theory:

Vectors A and B can be added graphically by drawing them to scale and aligning them head to tail. The vector that connects them is the resultant, vector R.

The components (Ax and Ay) of a vector A can be calculated by projecting the length of A onto the coordinate axes as shown in figure 1. The components can be obtained by using the following equations

Ax = l A l cos θA

Ay = l A l sinθA

The sign of a component gives its direction along the x or y axis. Conversely, from the components, the magnitude l A l and direction θ of the vector can be calculated using following:

lAl = √Ax 2+ Ay2

To add vectors analytically, they must be in component form. The components of a vector sum of two vectors A and B yields the components of a new vector, called a resultant vector and will be denotated by R. The components of R can be calculated by:

Rx = Ax + Bx

Ry= Ay + By

I

Procedure:

Place the force table on a flat surface.

Using the spirit level, make sure the force table is level, then cut 3 pieces of string 12 to 15 inches long. Tie a loop at the end of each piece of string, and attach the other end of the string to the ring.

Place the ring in the center of the force table then put the strings over the pulleys that are attached to the force table.

Get three mass holders, for vector A, add mass to one mass holder until the entire setup is 20 to 30g. Place this mass on the end of one of the strings looped over a pulley and set the pulley at an angle of 630. For vector, to the second mass holder, add 41g. Place this mass on the end of one of the strings looped over a pulley and set the pully at an angle of 154 0. For vector C, attach the last mass holder to the last string. Add mass to the system until equilibrium is reached.

Record the values for mass and angle for vectors A, B and C in Table 1. Record the values for mass and angle of vectors A and B. Use the formulas to calculate the mass of x component and y components of vectors A and B, and calculate the mass, force, components and angle for vector C.

Draw the vectors A, B and their corresponding components to scale in each space provided. Also draw the complete system of vectors A, B and C together.

Compare the experimental results for mass and angle measure of vector C with the analytical calculations. Determine the percentage error.

Calculation and Results

A

B

C

Mass (g)

25.0g

41.1g

48.1g

Θ(0)

63

154

305

A

B

C

Force (N)

245.0 N

402.8N

471.4N

X - component

111.2 N

-362.0 N

270.4 N

Y - component

218.3 N

176.6 N

-386.1 N

CONCLUSION

The addition of two vectors (A,B) is equivalent to th e resultant vector. This was seen in this experiment when the vectors in the force table reached equilibrium.