Final answer:
The work done by friction on the polar bear as it slides down a 40 m hill is calculated using the work-energy principle, resulting in -17,493.75 J, which indicates that the work done by friction is not one of the provided options.
Step-by-step explanation:
The question asks about the work done by friction as a polar bear slides down a hill. To solve this, we need to apply the concept of mechanical energy conservation and the work-energy principle. The mechanical energy conservation states that the sum of kinetic and potential energy in a system remains constant if only conservative forces are doing work. However, since there is friction, we'll use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.
In this case, we first calculate the change in kinetic energy (KE) of the polar bear. The KE at the top of the hill is 0 since the bear starts from rest, and the KE at the bottom is (1/2)m*v^2, where 'm' is the mass of the polar bear and 'v' is its velocity at the bottom. Calculating this gives us (1/2)*450kg*(26.5m/s)^2, which yields 158,906.25 J. Next, we consider potential energy (PE). The PE lost by the bear as it slides down the hill is m*g*h, where 'g' is the acceleration due to gravity (9.8m/s^2) and 'h' is the height of the hill (40m). This results in 450kg*9.8m/s^2*40m = 176,400 J.
Since the total mechanical energy is conserved, the work done by non-conservative forces (friction in this case) is the difference between the PE lost and the KE gained:
Work by friction = change in KE - PE lost = 158,906.25 J - 176,400 J = -17,493.75 J. Thus, the correct answer is not given in the options provided. The work done by friction is negative because it acts in the opposite direction of the bear's motion.