There are three ropes that are tied to a small, very light ring. Two of these ro

Question

There are three ropes that are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles. Rope1 is a attached to a wall to the left and pulls along the negative x-axis. It is 0.76 m long, and the tension on it is 55 N. Rope 2 is attached to a wall directly above the ring and pulls along the positive y-axis. It is 0.52 m long, and the tension on it is 75 N. What are the magnitude and direction of the tension T 3 in the third rope?

What is the magnitude of the tension?

What is the angle rope 3 makes with respect to the positive x-axis?

Explanation / Answer

here by using

T3 = sqrt( T1^2 + T2^2 )

T3 = sqrt( 55*55 + 75*75 )

T3 = 93 N

so the magnitude of the T3 is 93 N

so then

theta = tan^-1( T2 / T1 )

theta = tan^-1( 75 / 55)

theta = 53.74 degree

then theta + 9 0 = 143.74 deg clockwise from rope 2

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