EXPERIMENT 4 ADDITION OF FORCES AND VECTORS Objective: The purpose of this exper

Question

EXPERIMENT 4 ADDITION OF FORCES AND VECTORS Objective: The purpose of this experiment is to practice the addition of vectors graphically and analytically and to compare the results obtained by these two methods. Apparatus: o force table with pulleys, metal ring, string, mass hangers, masses, ruler, protractor The force table provides a means for applying known forces at one or more points and in various directions in the horizontal plane. The forces are the tensions in strings which pass over attached to the rim of the circular table and from which masses hung Terminology: Objects called "weights" have both a mass measured in kilograms (or grams) and a weight measured in Newtons (or pounds). Weight is a measure offorce (W mg) NOT a measurement of mass. In the SI (metric) system, weights are sometimes designated by their mass. For example, a 100 gram "weight" is referred to by its mass of 100 grams Theory: If several forces act on a body, the vector sum of these forces governs the motion of the body. According to Newton's 1st Law of Motion the body will remain at rest (if originally at rest) or will move with a constant velocity (if originally in motion) if the vector sum of all forces acting on it is zero (the vector sum is called the resultant force). The body is then said to in translational equilibrium. 24

Explanation / Answer

Part 1: Our data:

a: 200grams, 0°
b: 100grams, 55°
c: 200grams, 135°

Our scale: 1cm = 20 grams

The magnitudes (length) of vectors:

a: 200grams x (1cm/20grams) =10cm
b: 100grams x (1cm/20grams) = 5cm
c: 200grams x (1cm/20grams) =10cm

Vector diagram:

We find "d" is the resulant force. Then we use ruler and protractor to determine the magnitude (length) and direction (angle) of "d".

The magnitude (length) of "d": 12.5 cm (equal to 250 grams)
The direction (angle) of "d": 62°

Part 2:

Vector components:

a: Ax=10 × cos(0°) =10
Ay=10 × sin(0°) =0
a= 10i + 0j

b: Bx=5 × cos(55°) =2.87
By=5 × sin(55°) =4.1
b= 2.87i + 4.1j

c: Cx=10 × cos(135°) =-7.07
Cy=10 × sin(135°) =7.07
c= -7.07i + 7.07j

d: Dx= Ax+Bx+Cx =20+5.74-14.14 =5.8
Dy= Ay+By+Cy =0+4.1+7.07 =11.17
c= 5.8i + 11.17j

The magnitude (length) of "d": (5.8^2+11.17^2) = 12.59cm (equal to 251.7 grams)
The direction (angle) of "d": arctan(11.17/5.8) 62.6°

Part 3:

Mount three pulleys on the edge of force table at the angles. Attach strings to the center ring so that they each run over the pulley and attach to a mass holder. Hang the appropriate masses on each string.

Conclusion:

When we place a mass on fourth holder equal to the magnitude of the resultant, the ring turns to equilibrium. That means the force of the fourth mass is equal to the resultant force of the first three masses.

This experiment proved that force has direction, and a resultant force consists several vector forces.

a: 200grams, 0°
b: 100grams, 55°
c: 200grams, 135°

At this moment, the ring is not equilibrium.

Set up a fourth pulley and mass holder at 180 degrees opposite from the angle you calculated for the resultant of the first three vectors.

d: 251.7 grams; 62.6°+180° =242.6°

When we place a mass on fourth holder equal to the magnitude of the resultant, the ring turns to equilibrium.

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