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solidsnake11 · Mar 20, 2011, 02:34 PM

A toy of weight 2.8N is suspended from a horizontal beam by means of two cords that are attached to the same point on the toy.
One cord makes an angle of 60 degrees to the beam and the other cord makes an angle of 50 degrees to the beam.

Calculate the tension in each cord.

I really am not sure how to do this.

Any input would be greatly appreciated.

Thank you.

jcaron2 · Mar 20, 2011, 04:26 PM

The tension is directed along the length of each string. Essentially each string is applying a force (equal in magnitude to the tension) to the toy which is directed along the length of the string. However, since they're both angled away from vertical, you can break the forces into their horizontal and vertical components. I'll let you do that yourself, but if you're unsure how, let me know and I'll give you some more guidance.

Now, since the toy is stationary, we know that the total sum of all horizontal forces must be zero, along with the total sum of all vertical forces. Therefore, we can write two equations:

$A_x+B_x = 0$

$A_y+B_y -2.8N = 0$

In the first equation, the only two horizontal forces acting on the toy are the horizontal components of the two tensions, A and B. One is directed in the +x direction so it will have a positive sign, and the other is directed in the -x direction, so its sign will end up being negative.

Meanwhile, in the second equation there are a total of three vertical forces acting on the toy. The first two terms represent the vertical components of the string tensions (both are directed upward and will therefore have positive signs). The third term represents the force of gravity pulling down on the toy. That was given as 2.8N, and has a negative sign since it's directed downward.

So once you substitute in the appropriate expressions for Ax, Ay, Bx, and By (in terms of the unknown tensions A and B, along with some sines and cosines), you simply have to solve two equations for two unknowns (A and B).

Let me know what you get for an answer (or if you get stuck somewhere along the way).

Oh yeah, FYI, in the future you should post such questions in the homework forum.