three people located at a b and c pull on ropes tied to ring find ihe magnitude and direction of

1. We have three forces acting on the ring: F1, F2, and F3. We are given the magnitudes of F1 an

Three people located at a b and c pull on ropes tied to ring...

Three people located at A, B, and C pull on ropes tied to a ring: Find the magnitude and direction of the force with which the person at C must pull so that no one moves (the system is in equilibrium). Given: F1 = 116 lb F2 = 80 lb To find the force with which the person at C must pull, we can use the equation: F1 - F2 + F3 = 0 Now, let's solve for F3: F3 = F2 - F1 F3 = 80 lb - 116 lb F3 = -36 lb Since the force is negative, it means that the person at C must pull in the opposite direction of the other two forces. The magnitude of the force is 36 lb. Therefore, the person at C must pull with a force of 36 lb in the opposite direction of the other two forces.

Transcript

00:01 Hi, here in this given problem there is a ring and if we consider the cartesian axis passing through the center of this ring, the three ropes pulling this ring at three different points.

00:32 This is the rope b at which a force f2 whose magnitude is 80 pounds that is being applied at an angle of 30 degree from the positive x axis along counter clockwise direction another rope at which the force having a magnitude f1 is equal to 116 pounds it is being applied at an angle of 45 degree clockwise from negative x axis and the third rope c this was the first rope a this is the third rope c the magnitude of the force f3 that is missing we have to find it.

01:28 Its direction is also missing we have to find that one also.

01:32 So, to find it first of all we find the x component of force f1 which is given as 116 pounds multiplied by cosine of 45 degree which comes out to be equal to 82 .02 pounds as it is along negative x axis.

01:55 So, we can take it to be negative then we take x component of the force f2, f2x that is 80 pounds cos 30 degree which comes out to be equal to 69 .28 pounds.

02:18 Now it is clear that the force acting towards negative x axis is more than that acting towards positive x axis.

02:29 It means to balance the net force along x axis to make the net force along x axis to be equal to 0 x component of as f1x is more than f2x.

02:46 So, f3x should be along positive x axis should be along positive x axis.

03:11 So, f3 should lie in fourth quadrant means it should be lying somewhere here like this.

03:31 So, suppose the angle is theta like this...

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