Question

A boy and a girl carry a 12.0 kg bucket of water by holding the ends of a rope with the bucket attached at the middle. FI tehre is an angle of 100.0 degrees between the two segments of the rope, what is the tension in each part?

I do not understand the work

Fw = mg = (12.0 kg)(9.80 s^-2 m0
= 118 N
2^-1 Fw = 2^-1 118 N = 59.0 N
cos 50.0 = T^-1 59.0 N (T = the tension in the rope)
T = (cos 50.0)^-1 59.0 N = (.643)^-1 59.0 N = 91.8 N

why did they cut the angle and half and the the 118 N

Thanks!

Answer 1

Fw represents the weight equal to mass times the acceleration due to gravity,
mg=12*9.8=117.6 N

In fact, the triangle of forces consists of an isosceles triangle with two equal side of T, and the base equals to 118 N.

The solution of the triangle is simplified by dividing it into two right triangles, the base thus equals half of 118=59 N.