Activiay 5. You and de Fome Table You are standing in the center of a very large

Question

Activiay 5. You and de Fome Table You are standing in the center of a very large, y coordinate plane drawn in the center of an old gymnasium floor. A larg arrow pointing to your right represents the positive x-axis (at 0%, while a large arrow pointing ahead of you represents the positive y-axis (at 90%. You stand at the origin of this coordi nate system. You have three ropes tied around your waist, each one with a so-called friend at the other end ready to pull you in various directions. At the count of three, all three friends start pulling you with a steady force in a given direction. You are to describe what you feel as the object experiencing the forces After the experiment, you claim that it feels like a single force was acting on you in a direction in which no one was even pull ing you, but that it was a bit hard to tell, since you were being pulled away from the origin. You claim that it would be easier to experience the feeling of vector addition if that net force were equal to zero, so you wouldn't be pulled one way or the other The problem is that you aren't sure in what direction and with what magnitude a fourth rope should be pulled to make the new total force equal to zero. You have a sense of about where this new force should point, but exactly where and exactly how hard the rope should be pulled is certainty more difficult. You grab a pencil and paper and start solving the problem... You are supplied with a force table, which is a flat, circular hor izontal table top which has angles ticked off from 0 to 360 Pulleys can be attached to the side of the table at any degree mark desired, so that strings can be attached to an object at the center of the table top (representing you) and run over the pul leys to hanging masses which are used to supply the tension in the strings pulling the object in various directions with various forces. (The object in this case will be a ring centered on a post at the center of the table. The post is there to keep the from slipping off when the net force is not zero.) Your instruc tor will supply you with a list of three forces. Your challenge: Find the magnitude and direction of the equilibrant force that must be added to the other three forces to keep you from being pulled on way or the other (that is, to keep the ring centered on the post, but not in contact with it.

Explanation / Answer

F1 = 1.764*cos125i + 1.764sin125j

F1 = -1.01 i + 1.44 j

F2 = -2.45 j

F3 = 1.176 j

F4 = ?

Fnet = 0

F1 +F2 + F3 + F4 = 0

F4 = -(F1 +F2 +F3 )

F4 = -(-1.01i + 1.274 j)

F4 = 1.01 i - 1.274 j

F4 = sqrt(1.01^2 + 1.274^2) = 1.63 N

direction = tan^-1(1.274/1.01) = 308.4 degrees + x axis

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