. A rescue helicopter lifts a stretcher case off a hillside. The injured climber and stretcher have a mass of 180 kg and the rope supporting them has a breaking force of 2000 N. Calculate:

(a) the tension in the rope when the stretcher and climber are suspended from the rope at rest
(b) the maximum vertical acceleration possible before the rope breaks

(a) To calculate the tension in the rope when the stretcher and climber are suspended at rest, we can use the equation F = mg, where F is the force (tension), m is the mass, and g is the acceleration due to gravity.

Given:
Mass of the climber and stretcher (m) = 180 kg
Acceleration due to gravity (g) = 9.8 m/s^2

Using the equation F = mg:
Tension (F) = mass (m) × acceleration due to gravity (g)
Tension (F) = 180 kg × 9.8 m/s^2
Tension (F) = 1764 N

Therefore, the tension in the rope when the stretcher and climber are suspended at rest is 1764 N.

(b) To calculate the maximum vertical acceleration possible before the rope breaks, we need to consider the breaking force of the rope.

Given:
Breaking force of the rope = 2000 N

Using the equation F = ma, where F is the force (breaking force), m is the mass, and a is the acceleration:
2000 N = 180 kg × a

Rearranging the equation:
a = 2000 N / 180 kg
a ≈ 11.11 m/s^2

Therefore, the maximum vertical acceleration possible before the rope breaks is approximately 11.11 m/s^2.

To solve these problems, we'll need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

(a) To find the tension in the rope when the stretcher and climber are suspended from the rope at rest, we can assume there is no acceleration, so the net force must be zero. Since the only forces acting on the system are the weight of the stretcher and climber and the tension in the rope, we can write:

Tension - Weight = 0

The weight of the stretcher and climber can be calculated using the equation:

Weight = mass x gravity

where the mass is 180 kg and gravity is approximately 9.8 m/s^2. Plugging these values in, we get:

Weight = 180 kg x 9.8 m/s^2 = 1764 N

Now, substituting this into the previous equation, we have:

Tension - 1764 N = 0
Tension = 1764 N

Therefore, the tension in the rope when the stretcher and climber are suspended at rest is 1764 N.

(b) To find the maximum vertical acceleration possible before the rope breaks, we need to find the maximum net force that the rope can withstand.

The maximum net force is equal to the breaking force of the rope, which is given as 2000 N.

Using Newton's second law, we can write the equation:

Net force = mass x acceleration

Rearranging the equation to solve for acceleration, we get:

Acceleration = Net force / mass

Given that the mass is 180 kg and the net force is 2000 N, we can plug these values in to find the acceleration:

Acceleration = 2000 N / 180 kg ≈ 11.11 m/s^2

Therefore, the maximum vertical acceleration possible before the rope breaks is approximately 11.11 m/s^2.