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Experiment 2

Resultant and Equilibrant Forces

I. AbstractUsing a force table, we mounted a ring to serve as the object forces act on. We then attached three strings around the ring and to each end of the strings designated a pulley with corresponding weight holders situated in different directions. We proceeded to balance the weights each weight holder had to obtain equilibrium with the ring stable in the center and thereby obtaining a specific magnitude and direction for each of the three concurrent forces. With all three forces determined, we derived the experimental resultant forces by computing for the negative vector of any one of the three forces given the two other forces. Upon calculating the experimental resultant forces, we were able to solve for their corresponding equilibrant forces by computing for the negative vectors of the said resultant forces. Finally, we came up with the computed resultant forces of the three given concurrent forces by using the component method.

II. Guide Questions1. Differentiate the resultant and the equilibrant of two forces.2. If three concurrent forces are in equilibrium, what is the relation between

any one of the three forces and the resultant of the other two forces?3. If two forces with the same magnitude were exactly in the same opposite

directions, what is the magnitude and direction of their resultant? What is the magnitude and direction of their equilibrant?

4. Use the component method to find the magnitude and direction of the resultant of the following forces:

Given x-component y-component

A = 2000 N at 0°B = 1500 N at 60°C = 1000 N at 150°D = 3800 N at 225°

2000.00000750.00000

-866.02540-2687.00577

0.000001299.03811

500.00000-2687.99577

-803.03117 -887.96766

5. A body weighing 100 N is suspended by a rope. A second rope attached to the body is drawn aside horizontally until the suspended rope makes an angle of 30° with the vertical. Find the tension in each rope.

III. Answers to Guide Questions1. A resultant force would cause a stationary object to start moving or an object moving with a given velocity to speed up or slow down or change direction such that the velocity of the object changes. It is usually computed by the component method given two or more known forces. If a resultant force acts on an object then that object can be brought into equilibrium by applying an additional force that exactly balances this resultant. Such a force is called the equilibrant force and is equal in magnitude but opposite in direction to the original resultant force acting on the object. Therefore, the equilibrant force is the negative vector of the resultant force.

2. Any one of the three forces is the negative vector of the resultant of the other two forces meaning they possess the same magnitude but are opposite in direction and vice-versa.

3. If two forces are equal and directly opposite, then they entirely cancel each other out. The result is zero force. In this case, the resultant and equilibrant are both zero. In other words, the resultant and equilibrant are the "zero vector."

4. Resultant force = √(-803.03117)2 + (-887.96766)2

= 1197.22413 NΦ = tan-1 | -887.96766/-803.03117|

= 47.9° ~ QIII = 47.9° + 180° = 227.9°

5. Let the tension in the suspended rope be T1 & T2 in the horizontal rope. By balancing the forces in x & y-axis,

Given x-component y-component

T1 = T1 at 120°T2 = T2 at 0°Weight = 100 N

T1cos120° = -0.5T1 T2cos0° = T2

0

T1sin120° = 0.86603T1

T2sin0° = 0-100N

ΣFy = 0T1sin120° + T2sin0° + -100N = 0T1sin120° = 100NT1 = 100N sin120° = 115.47005 N

ΣFx=0T1cos120° - T2cos0° + 0 = 0T1cos120° = T2cos0°115.47005cos120° = T2cos0°T2 = 115.47005cos120°

cos0° = 57.735025 N