Final answer:
The work done by the person climbing the ladder, which is also the increase in gravitational potential energy, is 2934.75 J. This energy comes from the person's muscles converting chemical energy into mechanical energy.
Step-by-step explanation:
The work done by a person while climbing up a ladder to a height of 4.55 m is equal to the increase in gravitational potential energy (PEg) of the person-Earth system. The work done, W, can be calculated using the formula W = Fd = mgh, where F is the force applied (equal to the weight of the person), d is the distance covered (the height of the ladder), m is the mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height. For a person weighing 645 N, the work done is:
W = Fd = (645 N)(4.55 m) = 2934.75 J
Thus, the increase in gravitational potential energy is 2934.75 J. The energy needed to climb comes from the person's muscles converting chemical energy from food into mechanical energy, which then increases the person's PEg.