Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
An inclined plane is a simple machine consisting of a sloping surface that connects a lower level to a higher level, used to lift heavy loads with less effort.
It acts as a force multiplier. The effort () is applied along the slope, while the load () is lifted vertically to a height ().
The Mechanical Advantage () of an inclined plane is always greater than because the length of the slope () is always greater than the vertical height ().
As the angle of inclination decreases (making the slope gentler), the length of the plane increases, which increases the and reduces the effort required.
Real-world applications include ramps in hospitals, sloping roads on hills, staircases, and gangways of ships.
A winding road on a mountain is an example of an inclined plane that increases the distance of travel to reduce the effort needed by vehicles to climb steep heights.
📐Formulae
💡Examples
Problem 1:
A wooden plank long is used to push a drum onto a truck platform which is high. Calculate the Mechanical Advantage () of this inclined plane.
Solution:
Given: Length of plane () = , Height () = . Using the formula , we get .
Explanation:
The is , which means the machine multiplies the applied effort by times.
Problem 2:
A load of is pushed up a ramp of length and height . Calculate the effort required, assuming no friction.
Solution:
Step 1: Calculate . Step 2: Use to find Effort. .
Explanation:
By using the inclined plane, an effort of only is needed to lift a load of .
Problem 3:
Why is it easier to walk up a longer, gentler slope than a shorter, steeper one to reach the same height?
Solution:
A longer slope has a greater length () for the same height (). Since , the increases as increases.
Explanation:
According to the principle of simple machines, a higher requires less effort. Even though the distance walked is more, the force required from our legs is significantly reduced.