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Simple Machines - Inclined Plane

Grade 6ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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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.

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It acts as a force multiplier. The effort (EE) is applied along the slope, while the load (LL) is lifted vertically to a height (hh).

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The Mechanical Advantage (MAMA) of an inclined plane is always greater than 11 because the length of the slope (LL) is always greater than the vertical height (hh).

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As the angle of inclination decreases (making the slope gentler), the length of the plane increases, which increases the MAMA and reduces the effort required.

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Real-world applications include ramps in hospitals, sloping roads on hills, staircases, and gangways of ships.

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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

Mechanical Advantage (MA)=Length of the Plane (l)Vertical Height of the Plane (h)\text{Mechanical Advantage (MA)} = \frac{\text{Length of the Plane (l)}}{\text{Vertical Height of the Plane (h)}}

Mechanical Advantage (MA)=Load (L)Effort (E)\text{Mechanical Advantage (MA)} = \frac{\text{Load (L)}}{\text{Effort (E)}}

Work Done=Force×Distance\text{Work Done} = \text{Force} \times \text{Distance}

Effort (E)=Load (L)MA\text{Effort (E)} = \frac{\text{Load (L)}}{\text{MA}}

💡Examples

Problem 1:

A wooden plank 4 m4\text{ m} long is used to push a drum onto a truck platform which is 1 m1\text{ m} high. Calculate the Mechanical Advantage (MAMA) of this inclined plane.

Solution:

Given: Length of plane (ll) = 4 m4\text{ m}, Height (hh) = 1 m1\text{ m}. Using the formula MA=lhMA = \frac{l}{h}, we get MA=4 m1 m=4MA = \frac{4\text{ m}}{1\text{ m}} = 4.

Explanation:

The MAMA is 44, which means the machine multiplies the applied effort by 44 times.

Problem 2:

A load of 600 N600\text{ N} is pushed up a ramp of length 5 m5\text{ m} and height 2 m2\text{ m}. Calculate the effort required, assuming no friction.

Solution:

Step 1: Calculate MA=lh=52=2.5MA = \frac{l}{h} = \frac{5}{2} = 2.5. Step 2: Use MA=LEMA = \frac{L}{E} to find Effort. 2.5=600E⇒E=6002.5=240 N2.5 = \frac{600}{E} \Rightarrow E = \frac{600}{2.5} = 240\text{ N}.

Explanation:

By using the inclined plane, an effort of only 240 N240\text{ N} is needed to lift a load of 600 N600\text{ N}.

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 (ll) for the same height (hh). Since MA=lhMA = \frac{l}{h}, the MAMA increases as ll increases.

Explanation:

According to the principle of simple machines, a higher MAMA requires less effort. Even though the distance walked is more, the force required from our legs is significantly reduced.