Mechanical Advantage Formula, Definition, Solved Examples

Mechanical Advantage Formula: Mechanical advantage is a computational concept used to quantify the increased force within a mechanical system. It represents the relationship between the force applied to a load and the force required to counteract that applied force. This ratio is dimensionless, as both quantities involved are forces. Another definition of mechanical advantage describes it as the force generated by a machine relative to the force applied to it. The formula for mechanical advantage is expressed as:

MA= F _B ​/ F _A

where MA is the mechanical advantage, F _B is the force exerted by the object, and F _A is the effort required to overcome the force exerted by the object.

Mechanical Advantage Formula Solved Examples

Example 1: Calculate the mechanical advantage when a force of 1200 N is applied to lift an object, and the load to be overcome is 600 N.

Solution: Given: F _A =1200N F _B =600N

Using the Mechanical Advantage Formula: MA= F _B ​/F _A

Substituting the values: MA= 1200 600 ​

MA=0.5

Therefore, the mechanical advantage in this example is 0.5.

Note: A mechanical advantage less than 1 indicates that the machine requires more input force than the output force, suggesting a trade-off in favor of distance or speed.

Example 2: A lever system requires a force of 150 N to lift a load of 300 N. Determine the mechanical advantage.

Solution: Given: F _A =150N F _B =300N

Using the Mechanical Advantage Formula:

MA= F _B ​/F _A

Substituting the values: MA= 300 ​ / 150

MA=2

The mechanical advantage in this example is 2.

Example 3: In a pulley system, a force of 80 N is applied to lift an object, and the load to be overcome is 160 N. Calculate the mechanical advantage.

Solution: Given: F _A =80N F _B =160N

Using the Mechanical Advantage Formula: MA= F _B ​/F _A

Substituting the values: MA= 160 ​/80

MA=2

So, the mechanical advantage in this pulley system is also 2.

Example 4: A ramp is used to raise a crate, requiring an input force of 200 N to overcome the weight of the crate, which is 400 N. Calculate the mechanical advantage of the ramp.

Solution: Given: F _A =200N F _B =400N

Using the Mechanical Advantage Formula: MA= F _B ​/F _A

Substituting the values: MA= 400 ​/ 200

MA=2 The mechanical advantage in this example is 2.

Example 5: In a simple pulley system, a force of 120 N is applied to lift a load of 120 N. Determine the mechanical advantage.

Solution: Given: F _A =120N F _B =120N

Using the Mechanical Advantage Formula: MA= F _B ​/F _A

Substituting the values: MA= 120 ​/120

MA=1

So, the mechanical advantage in this pulley system is 1.

Example 5: In a simple pulley system, a force of 130 N is applied to lift a load of 130 N. Determine the mechanical advantage.

Solution: Given: F _A =130N F _B =130N

Using the Mechanical Advantage Formula: MA= F _B ​/F _A

Substituting the values: MA= 130 ​/130

MA=1

So, the mechanical advantage in this pulley system is 1.

These examples illustrate the calculation of mechanical advantage in different scenarios involving the application of force to overcome loads in mechanical systems.

Mechanical advantage is a crucial concept in the analysis of mechanical systems, providing a quantitative measure of the amplification of force within these systems. It is calculated as the ratio of the force applied to overcome a load ( F _A ) to the force exerted by the object being lifted ( F _B ). A mechanical advantage greater than 1 indicates that the machine amplifies force, while a value less than 1 suggests a trade-off in favor of distance or speed.

Understanding mechanical advantage is essential for designing and optimizing machines to perform tasks with the desired balance of force and motion.

Explore Now Online Course of Class 9 Neev Fastrack 2024 and Class 10 Udaan Fastrack 2024 to enhance your Physics knowledge. and build a strong foundation.