In the figure, a block of mass M hangs at rest. The rope that is fastened to the wall is horizontal and has a tension off 38 N. The rope that is fastened to the ceiling has a tension of 70 N, and makes an angle θ with the ceiling. What is the angle θ?
-
For the rope from the ceiling, break the force into components in the vertical and horizontal directions, Tx and Ty respectively:
Tx = T*cos(q) Ty = T*sin(q) q = angle of rope with respct to celiing, T = 70 N
Sum of foirce in x and y must repsectively be zero since block foes not move:
Fx = 0 = T*cos(q) - 38 N ---> cos(q) = 38/T = 38/70 --> q = arccos(38/70) = 57.12 deg
Fy = 0 = T*sin(q) - mg
Tx = T*cos(q) Ty = T*sin(q) q = angle of rope with respct to celiing, T = 70 N
Sum of foirce in x and y must repsectively be zero since block foes not move:
Fx = 0 = T*cos(q) - 38 N ---> cos(q) = 38/T = 38/70 --> q = arccos(38/70) = 57.12 deg
Fy = 0 = T*sin(q) - mg
-
It'd be nice, if you had the picture to go with it..