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 52 N. The rope that is fastened to the ceiling has a tension of 91 N, and makes an angle θ with the ceiling. What is the angle θ?
A) 55°
B) 35°
C) 30°
D) 63°
E) 45°

Question

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 52 N. The rope that is fastened to the ceiling has a tension of 91 N, and makes an angle θ with the ceiling. What is the angle θ? 
A) 55° 
B) 35° 
C) 30° 
D) 63° 
E) 45°

Quizplus · Accepted Answer

We can start by drawing a free body diagram of the block:

```
    T1
     ↑
     │
     M
     ↓
T2 ←–––––––┘
```

where `T1` is the tension in the horizontal rope and `T2` is the tension in the diagonal rope. We know that the block is at rest, so the net force on it must be zero. In other words, the magnitudes of the two tensions must be equal:

```
T1 = T2
```

We also know that `T1 = 52 N` and `T2 = 91 N`. So we can substitute and solve for the angle `θ`:

```
T2 sin(θ) = T1
91 sin(θ) = 52
sin(θ) = 52/91
θ ≈ 55°
```

Therefore, the answer is A) 55°.

In the Figure, a Block of Mass M Hangs at Rest