A 90 kg rock climber is stationary off the side of an overhanging cliff hanging onto her climbing rope. Another rope is tied to her foot and is attached at the other end to her 30 kg rock-climbing dog, also hanging out 2 m below her. Tied to the dog’s foot is yet another rope that is attached to the dog’s favorite 2 kg stick, 1.5 m below. What is the tension in the rope that is holding up the climber?

Thanks!

When the bodies are at rest, the tension in the ropess just equal the weight that is suspended beneath them.

The lower body (the stick) has gravity down of m3•g=2•9.8=19.6 N and the tension (T3) in the lower string is
T3 = 19.6 N.
The rope between the climber and the dog:
T2= (m3+m2)g=32•9.8=313.6 N.
The upper rope:
T1=(m1+m2+m3)g=122•9.8=1195.6N

To find the tension in the rope holding up the climber, we can analyze the forces acting on each object in the system.

Let's start from the top and work our way down:

1. The rope holding up the climber: Let's call the tension in this rope T1. Since the climber is stationary and not accelerating, the net force acting on the climber must be zero.

The forces acting on the climber are its weight (mg) and the tension in the rope (T1). The weight is given by mg = (90 kg)(9.8 m/s^2) = 882 N. Since the net force is zero, T1 - mg = 0, so T1 = mg = 882 N.

Therefore, the tension in the rope holding up the climber is 882 N.

2. The rope holding the dog: Let's call the tension in this rope T2. The forces acting on the dog are its weight (mg) and the tension in the rope (T2).

The weight of the dog is given by mg = (30 kg)(9.8 m/s^2) = 294 N.

Since the dog is hanging at a constant height, the net force acting on the dog must be zero. Therefore, T2 - mg = 0, so T2 = mg = 294 N.

3. The rope holding the stick: Let's call the tension in this rope T3. The forces acting on the stick are its weight (mg) and the tension in the rope (T3).

The weight of the stick is given by mg = (2 kg)(9.8 m/s^2) = 19.6 N.

Since the stick is hanging at a constant height, the net force acting on the stick must be zero. Therefore, T3 - mg = 0, so T3 = mg = 19.6 N.

In summary:

- The tension in the rope holding up the climber (T1) is 882 N.
- The tension in the rope holding the dog (T2) is 294 N.
- The tension in the rope holding the stick (T3) is 19.6 N.

Please note that these values assume idealized conditions and do not take into account any other forces or factors that may affect the system.