Answer to Question #176648 in Physics for Abdul Qadeer

Question

An electric lamp of mass 0,8 kg is attached by an

electric cable to the ceiling at point D. To position

it directly over her desk, Thembi has pulled the

lamp to one side by a string tied to the lamp

holder H and fixed to point E

on the ceiling. Thembi is curious as to whether the

tension in the electric cable is affected

when the lamp is pulled aside. To investigate this, she measures the angles which the cable and the string

make with the ceiling and finds them to be 60 and 40 respectively as shown in the diagram at the right.

Answer 1

$$W=T_1\sin{60}+T_2\sin{40}\\T_1\cos{60}=T_2\cos{40}\\ W=T_1\sin{60}+T_1\frac{\cos{60}\sin{40}}{\cos{40}}\\ 0.8(9.8)=T_1\sin{60}+T_1\frac{\cos{60}\sin{40}}{\cos{40}}\\T_1=6.1\ N\\6.1\cos{60}=T_2\cos{40}\\T_2=4.0\ N$$