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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.
Theory
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 x-components of the forces and the sum of all the y-components of the forces must both be equal to zero.
Apparatus
o force table (including four clamp pulleys, centering pin, and ring with strings attached) o four weight hangers o assortment of slotted weights o bubble level
Procedure
1) Use the bubble level and adjust the screws on the feet of the force table until the surface of the table is level.
2) Place three pulleys at their appropriate angular positions according to Table 1.
3) Place the ring over the centering pin and pass three strings over the pulleys. From the strings, hang the amount of mass corresponding to your group number in Table 1. Do not permit the masses to swing. The line of each string should pass through the center of the ring.
Table 1. Masses and corresponding angles that will be used by each group. The value of the mass represents the total mass (includes the weight hanger).
group number String 1
String 2
String 3
m1(g)
1(deg)
m2(g)
2(deg)
m3(g)
3(deg)
1
150
30
200
135
140
200
2
150
30
250
140
100
250
3
200
30
150
110
250
210
4
200
30
250
135
140
200
5
150
60
200
150
180
200
6
150
60
250
110
180
250
7
200
60
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.
Theory
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 x-components of the forces and the sum of all the y-components of the forces must both be equal to zero.
Apparatus
o force table (including four clamp pulleys, centering pin, and ring with strings attached) o four weight hangers o assortment of slotted weights o bubble level
Procedure
1) Use the bubble level and adjust the screws on the feet of the force table until the surface of the table is level.
2) Place three pulleys at their appropriate angular positions according to Table 1.
3) Place the ring over the centering pin and pass three strings over the pulleys. From the strings, hang the amount of mass corresponding to your group number in Table 1. Do not permit the masses to swing. The line of each string should pass through the center of the ring.
Table 1. Masses and corresponding angles that will be used by each group. The value of the mass represents the total mass (includes the weight hanger).
group number String 1
String 2
String 3
m1(g)
1(deg)
m2(g)
2(deg)
m3(g)
3(deg)
1
150
30
200
135
140
200
2
150
30
250
140
100
250
3
200
30
150
110
250
210
4
200
30
250
135
140
200
5
150
60
200
150
180
200
6
150
60
250
110
180
250
7
200
60