Final answer:
Climbing a mountain on a curved path is easier than going straight up because it requires less force to overcome gravity, distributing the effort over a longer distance. The increase in gravitational potential energy is the same for both paths, but energy consumption is less on a curved path. Additionally, curved paths are integral to everyday motion, providing easier negotiation of angles through angular motion and centripetal force.
Step-by-step explanation:
The reason someone would choose a curved path over a straight steep path has to do with the concepts of work, energy, and power in physics. When climbing a mountain on a zigzag or curved path, the incline is less steep compared to going straight up. This reduces the force required to overcome gravity, making it physically less demanding. Although the increase in gravitational potential energy is the same in both scenarios, assuming you reach the same elevation, the energy consumption is not the same. Using a curved path typically requires less energy because the effort is distributed over a longer distance, thus requiring less force at any given moment.
Banked curves are an application of curved paths, where the slope of the road helps you negotiate a curve without relying on friction. This principle is used in race tracks, where a greater banking angle allows vehicles to maintain higher speeds on curves. Similarly, zigzag paths reduce the effort required for each step, albeit at a slower overall speed compared to going straight up.
Furthermore, it is interesting to note that most motion we experience in daily life is along curved paths, not straight lines. The movement around curves requires not only advancing forward but also changing direction, which involves angular motion and centripetal force, further separating it from the simple linear motion of going straight up.