Final answer:
The work done by the climber in lifting herself and the backpack, assuming a vertical climb of 2.50 meters, would be 1612.5 Joules.
Step-by-step explanation:
The question at hand deals with a particular aspect of physics known as mechanical work. Mechanical work is defined as the force applied to an object times the distance moved by that object in the direction of the force.
To calculate the work done by the climber in lifting herself and the backpack, we use the formula Work = Force x Distance, where the force is the weight of the climber and the distance is how high she climbs.
Assuming she climbs a vertical distance of 2.50 meters, the work done W would be W = 645N * 2.50m = 1612.5 Joules.
When considering the rope stretch, it is a slightly different physics problem involving Young's modulus and the properties of the material from which the rope is made.
However, assessing the stretch of the rope is not necessary for calculating the work done in lifting herself and the backpack.