Examkin

Question

Difficulty: EasyInclined Planes

A civil engineer is designing a road to reach the summit of a steep mountain. Instead of building a road that goes straight up the slope, the engineer designs a series of gradual switchbacks (zigzags). Ignoring friction and air resistance, how does the switchback design affect the physical task for a vehicle climbing the mountain compared to a direct, steep route?

  1. A
    The design reduces the total amount of work the vehicle must perform because the slope is not as steep.
  2. B
    The design reduces the actual weight of the vehicle against gravity, which reduces the required engine force.
  3. The design requires less force from the vehicle's engine, but the total amount of work done to reach the summit is unchanged.Answer
  4. D
    The design requires less force from the vehicle's engine, which directly decreases the total amount of work performed.

Answer

The design requires less force from the vehicle's engine, but the total amount of work done to reach the summit is unchanged.
A switchback acts as an inclined plane. By making the path longer and more gradual, the mechanical advantage increases. This means the vehicle's engine does not have to provide as much force at any given moment to push the vehicle upward. However, because this smaller force must be applied over a much longer distance, the total amount of work done against gravity (Force × Distance) remains exactly the same as taking a shorter, steeper route.

Step-by-Step Solution

1
Identify the simple machine principle at work.
A switchback road acts as an inclined plane, stretching the vertical climb over a much longer physical distance.
To determine which mechanical principles govern the vehicle's climb.
2
Analyze how the inclined plane affects the required force.
Because the slope is more gradual, the mechanical advantage increases, meaning the engine has to provide less effort force to push the vehicle upward at any given moment.
To understand the immediate benefit of using a ramp or switchback.
3
Apply the principle of conservation of work.
Work is equal to Force multiplied by Distance. The switchback decreases the force but increases the distance by the exact same proportion, meaning the total work done to lift the vehicle to the summit remains exactly the same.
To complete the comparison between the switchback and the direct route.

Key Concept

Ideal Mechanical Advantage and Work on an Inclined Plane
Rate this question

Topics

Inclined Planes

More questions from this topic