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Difficulty: EasySimple Machines

An inclined plane of length 5 m5\text{ m} is used to lift a load of 400 N400\text{ N} through a vertical height of 1 m1\text{ m}. If an effort of 100 N100\text{ N} is applied parallel to the incline, what is the efficiency of the machine?

  1. 80%80\%Answer
  2. B
    125%125\%
  3. C
    25%25\%
  4. D
    20%20\%

Answer

The efficiency of the machine is 80%80\%.
The correct answer of 80%80\% is obtained by finding the velocity ratio (distance moved by effort divided by distance moved by load, 5/1=55 / 1 = 5) and the mechanical advantage (load divided by effort, 400/100=4400 / 100 = 4), then calculating efficiency as (MA/VR)×100%=(4/5)×100%=80%(\text{MA} / \text{VR}) \times 100\% = (4 / 5) \times 100\% = 80\%.

Step-by-Step Solution

1
Calculate the Velocity Ratio (VR) of the inclined plane
VR=Length of inclineHeight=5 m1 m=5\text{VR} = \frac{\text{Length of incline}}{\text{Height}} = \frac{5\text{ m}}{1\text{ m}} = 5
Velocity Ratio is the distance moved by the effort divided by the distance moved by the load.
2
Calculate the Mechanical Advantage (MA)
MA=LoadEffort=400 N100 N=4\text{MA} = \frac{\text{Load}}{\text{Effort}} = \frac{400\text{ N}}{100\text{ N}} = 4
Mechanical Advantage measures how many times a machine multiplies the applied force.
3
Calculate the Efficiency
Efficiency=(MAVR)×100%=(45)×100%=80%\text{Efficiency} = \left(\frac{\text{MA}}{\text{VR}}\right) \times 100\% = \left(\frac{4}{5}\right) \times 100\% = 80\%
Efficiency is defined as the ratio of Mechanical Advantage to Velocity Ratio expressed as a percentage.

Key Concept

Efficiency of Simple Machines (Inclined Plane)
Estimated Time:45s
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Topics

Simple Machines

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