Final answer:
The increase in thermal energy is found by calculating the work done by the frictional force, which involves the distance the crate is moved, the coefficient of kinetic friction, and the normal force component.
Step-by-step explanation:
The question is focused on calculating the increase in thermal energy as a result of pulling a crate up an incline with a certain force and subject to friction. To find this increase in thermal energy, we need to understand that the work done against friction contributes to heating up both the crate and the incline surface. This work can be calculated using the formula for work done by friction, which is:
Wfriction = frictional force × distance × cos(θ)
With a coefficient of kinetic friction of 0.25, the tension in the rope of 100 N and the distance of 5.1 m, we must calculate the force of friction. The frictional force is equal to the normal force (which is the weight component perpendicular to the surface) multiplied by the coefficient of friction. We also need to account for the angle of the rope in relation to the incline, but since the rope is pulling the crate up, it reduces the normal force by a small amount due to the vertical component of the tension. However, this aspect can often be ignored for simplicity unless the problem specifically asks for that level of precision.
The thermal energy increase is then just the work done by friction, which assumes all the work done against friction is converted to heat. So, the increase in thermal energy would be calculated only with the frictional work done assuming all other forces are balanced and that there's no net work done on the crate.