A sphere weighs 200N resting on a wall. It is supported by a rope 20 degrees from the wall. What will be the tension force on the rope?

Answer 1

Resolve T in two components
T(x)= T•sinα,
T(y)= T•cosα.
T(x)/ T(y)= tanα =>
T(x)=T(y) • tanα.
The sphere is at rest:
N =T(x),
mg=T(y)
N/mg= T(x)/T(y) = tanα,
N =mg•tanα =200•0.364=72.8N,
T(x) =72.8.
T=T(x) /sinα =72.8•0.342 = 212.9 N