Question

Consider a 528 N cat burglar supported by a cable as in the figure.

a) find the tension in the inclined cable
b) find the tension in the horizontal cable

In the figure the angle between the "roof" and the inclined cable is 30.1.

Answer 1

First of all, the tension in the vertical cable MUST be equal to the weight of the burglar (Newton’s 3rd law). Call it T3, so:

T3 = w = 640N

Call the inclined cable T1 and the horizontal cable T2, the net horizontal forces sum to zero so from Newton’s 2nd law:

?F(x) = 0 = T1cos? - T2
T2 = T1cos?----------------->(1)

The net vertical forces are also zero:

?F(y) = 0 = T1sin? - mg
T1 = mg / sin?
= 640N / sin38.0°
T1 = 1040N (rounded)----------------------->(2)

Plugging (2) into (1):

T2 = T1cos?
= 1040Ncos38.0°
= 820N (rounded)