Classical Mechanics - Static Equilibrium

A 2-kilogram box hangs by a massless rope from a ceiling. A force slowly pulls the box horizontally to the side until the horizontal force is 10 Newtons. The box is then in equilibrium as shown above. The angle that the rope makes with the vertical is closest to

A. arctan 0.5
B. arcsin 0.5
C. arctan 2.0
D. arcsin 2.0
E. 45^o

(GR8677 #07)

Solution:

F_x = F − T sin θ = 0
T sin θ = F 

F_y = T cos θ − mg = 0
T cos θ = mg

T sin θ / T cos θ = tan θ = F/mg =  10/(2 × 10) = 0.5
θ = arctan 0.5

Answer: A