In the fgure below, a spider is resting after starting to spin its web. The grav

Question

In the fgure below, a spider is resting after starting to spin its web. The gravitational force on the spider is 0163 N on the junction of the theee strands of silk. The junction is supported by different tension forces in the ho strands above n so that the resultant force on the unction is zero. The two stena strands are perpendicular, and we ha·cho the r and r aeto e to be at g hen the teise, r s T, (a) Find the temon Find the angle the is makes wth the oontal c) Find the angle the y axis makes with the horizontal

Explanation / Answer

As the spider creates a force down the vertical, the tension in the web creates a force countering the downward force in the vertical. The force of tension between the two strands sum to be 0.163 N (FTension) upward along the vertical. This is due to the fact that the spider and the web are at rest so:

Force of gravity on spider + force of tension from strands = 0 or

Force of gravity on spider = - force of tension from strands

Once you discover this, the Ty vector and the angle between the FTension and Tx  can be found. Ty and Tx are x and y components of Tension. Knowing this, use the formulas,

X = F cos theta and

Y = F sin theta

to find the Ty vector and the angle between the FTension and Tx.

First, find the angle between the FTension and Tx (?) by using the formulas previously mentioned, FTension, and Tx. The question states that Tx is 0.118 N and as previously mentioned FTension is 0.163 N. Use

Tx = FTension cos theta

cos theta = Tx / FTension

Theta = cos-1(0.118N / 0.163N) = 43.62 degrees

The Ty vector can then be calculated by:

Ty = FTension sin theta = (0.163N) sin (43.62 degrees) = 0.112 N

Then the answer is 0.112 N

To find the angle between the horizontal and Tx (x-axis), use the facts that the FTension is along the vertical axis, hence the angle between the horizontal and Tx is 90 degrees minus the angle between the y-axis and Tx, which is:

90 - theta = 90 - 43.62 = 46.38 degrees

So the angle between the horizontal and the x-axis is 46.38 degrees.

To find the angle between the horizontal and Ty (y-axis), subtract 180 degrees by the angle between Tx and the horizonal and the angle between the x and y axis, which is 90 degrees.

So

180 - (46.38 + 90) = 43.62 degree

The angle between the horizontal and the y-axis is 43.62 degrees.

Please rate my answer, good luck...

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