Hill Climbing: Efficient Path?

📌 CONCEPT: The efficiency of the path taken by the cyclist depends on the work done, which is a product of the force applied and the distance traveled along the path of the displacement of the cyclist.

📐 RULE / FORMULA: Work done (W) is given by the formula W = F × d × cos(θ), where F is the force applied, d is the distance traveled, and θ is the angle between the force and displacement.

💡 WORKED EXAMPLE: Consider the two paths taken by the cyclist. For the steeper, shorter path, let F1 be the force applied and d1 be the distance traveled. For the gentler, longer path, let F2 be the force applied and d2 be the distance traveled. Comparing the two, if F1 × d1 × cos(45°) > F2 × d2 × cos(10°), then the steeper path is more efficient. Using the given slope of 1 in 5, we can calculate the angles and compare the work done in both cases.

⚠️ COMMON MISTAKE: Students often neglect to consider the angle between the force and displacement when calculating work done, leading to incorrect conclusions about the efficiency of the path taken by the cyclist.