Defining Simple Machine Efficiency
The efficiency of a simple machine quantifies how effectively it transfers input work into output work. It is fundamentally defined as the ratio of the work output to the work input. In practical terms, especially in introductory physics, this is often expressed using the concepts of Mechanical Advantage and Velocity Ratio.
Key Concepts
- Mechanical Advantage (MA): The ratio of the output force (load) to the input force (effort). It indicates how much the machine multiplies force. \(MA = \frac{\text{Load}}{\text{Effort}}\)
- Velocity Ratio (VR): The ratio of the distance moved by the effort to the distance moved by the load. It represents the inverse of the force multiplication. \(VR = \frac{\text{Distance moved by Effort}}{\text{Distance moved by Load}}\)
Efficiency Formula
The efficiency (\(\eta\)) of a simple machine is calculated as the ratio of the mechanical advantage (MA) to the velocity ratio (VR).
The formula is:
\(\eta = \frac{MA}{VR}\)
Efficiency is usually expressed as a percentage, calculated by multiplying the ratio by 100%. A perfect machine would have an efficiency of 100%, but real machines always have efficiencies less than 100% due to factors like friction.
Relating to Options
Comparing the derived formula \(\eta = \frac{MA}{VR}\) with the given options:
- Option 1: \(\text{VR} \times \text{MA}\) - Incorrect.
- Option 2: \(\text{VR} / \text{MA}\) - Incorrect.
- Option 3: \(\text{MA} / \text{VR}\) - Correct. This matches the definition.
- Option 4: \(1 / (\text{VR} \times \text{MA})\) - Incorrect.
Therefore, the efficiency of a simple machine is defined as the mechanical advantage divided by the velocity ratio.
Similar Questions
- The work done by a 10 Newton force acting on a body, which results in the displacement of 2 m in the direction of the force, is __________.
- An object of mass 1 kg is moving with a velocity 10 m/s. Find the kinetic energy of the object.
- The efficiency of a machine can never be ______.
- In practice, the work output of a machine is ______ the work input due to the effect of friction.
- How much energy is used by an 80% efficient, 2kW motor running at a peak load for 5 hours?
- A pump is required to lift 600 kg of water per minute from a well 25m deep and to eject it with a speed of 50 m/s. If \(g = 10 \text{ m/s}^2\), the power required to perform the above task is
- A lorry and a car moving with the same kinetic energy are brought to rest by applying the same retarding force. Then:
- In practice, the work output of a machine is always less than the work input due to the effect of ______.
- Ideal machines are those imaginary machines which are ______.
- An object of mass m follows a circular path of radius r with a constant speed v in uniform circular motion. Then, the work done by the centripetal force for the object to move once in a full circle is
Important Questions from Work Power and Energy
Which of the following is an example of potential energy?
_______ is one of the chemical used to produce Ocean Thermal Energy.
A body of mass 2kg is thrown up vertically with a kinetic energy of 500J. If the acceleration due to gravity is 10 m/s2, the height at which the kinetic energy of the body becomes half of the original values is _____
Arjun has a mass of 50 kg, he eats banana of 1000 calories. If this energy is used up to lift him from the ground, the height to which he can climb is _______. Take g = 10 m/s2 and 1 calories = 4.2 Joule.
When a body of mass 'm' attains a velocity 'v' from rest in time 't', then kinetic energy of translation is:
