Addition of Force Vectors

Lab Mmebers:

1. Ambar Gavidia

2. Jennifer Vallejos

3. Daniela

Lab Date Performance: 01/14/15

Purpose:

Introduce analytical and graphical techniques for vector addition. The objective is to measure the forces acting on an object in equilibrium and calculating their vector sums.

Apparatus:

Four pulleys are clamped to a force table, which is graduated from 0 to 360 degrees. A central stationary object is connected by strings to three different hangers, each loaded with different weights. It is assume that the string masses are negligible and disregarding friction at the pulleys, each horizontal force on the ring will equal the weight on the hanger (with the hanger’s weight included).

Fn=mn x g n=1,2,3 g=acceleration of gravity

Standard unit of force:

[m]=gr (gram mass) [F]=gmf (gram force) g=1 gmf / gr

1 gr of mass=1 gmf^(1) therefore, numerical values of mass and weight are identical.

In static equilibrium, the force vectors must cancel out. (sum)Fn=0

On the 2-Dimensional force table, each vector is expressed in rectangular components as : Fnx=Fn x cos 0n and Fny=Fn x sin 0n (n=1,2,3)

Then equation one requires that the components of the resultant force vector R be zero: Rx= (sum)Fnx=0 and Ry=(sum)Fny=0

Materials:

QT.

MATERIALS NEEDED

DRAWER #

1

Force table

N/A

3

Pulley

31

3

Hooks 50g

31

String

1

Ring

31

Mass set

33,34,35

Procedure:

1) Set up force table and bring the ring into equilibrium by using 3 different forces acting upon it.

2) Each force should be 200 gmf or more, AND they should be different from each other.

3) The pin needs to be at the center of the hole.

4) Each string has to point to the center of the table. The ring itself doesn’t have to center on the pin, but it shouldn’t touch it.

5) Clamp each pulley to the table and check that it turns freely with the string on in order to minimize friction.

6) Place one of the pulleys at 0 degrees.

7) Then one person in the lab group will gently pull on each of the 3 strings at the same time in order to center the ring.

8) Once the ring is centered different weights will be added to each clamp in order to maintain equilibrium without the person pulling on the strings.

9) The weights will be different for each clamp.

10) Stop adding weight once the ring is centered without anyone holding on the strings.

11) Organize a Data table to write down the degrees that show on the force table for each different string and the weights (including hook weight).

12) Finally do the calculations for each vector (Fx and Fy) and lastly write down the resultant force vector which is the sum of Fx and Fy for all 3 different forces on the experiment.

Data: (Use 2 significant digits)

n mn Fn

Degrees (n)

Units -> gr gmf degrees 1

45

45

0

2

67

67

241

3

60

60

101

Evaluation of Data:

n

Fx

Fy

Units

gmf