Mechanical Advantage Formula

Mechanical advantage is a measurement that gives the ratio of the force provided to the load to the force needed to overcome the supplied force. It computes the amplified force obtained by the mechanical system. It can be interpreted as a computation that calculates the increased force exerted by the mechanical system. To put it another way, it is the ratio of the force created by a machine to the force applied to it for the purpose of evaluating the machine’s performance. It is denoted by the symbol M_A. It is a unitless quantity as it is a ratio of two forces and hence has no dimensional formula.

Formula

M_A = F_B/F_A

where,

M_A is the mechanical advantage,

F_B is the force exerted by the machine,

F_A is the force required to overcome the machine force.

Sample Problems

Problem 1. Calculate the mechanical advantage if a force of 500 N is required to overcome a machine force of 1000 N. 

Solution:

We have,

F_B = 1000

F_A = 500

Using the formula we get,

M_A = F_B/F_A

= 1000/500

= 2

Problem 2. Calculate the mechanical advantage if a force of 1200 N is required to overcome a machine force of 3600 N.

Solution:

We have,

F_B = 3600

F_A = 1200

Using the formula we get,

M_A = F_B/F_A

= 3600/1200

= 3

Problem 3. Calculate the mechanical advantage if a force of 300 N is required to overcome a machine force of 1500 N.

Solution:

We have,

F_B = 1500

F_A = 300

Using the formula we get,

M_A = F_B/F_A

= 1500/300

= 5

Problem 4. Calculate the force required to overcome a machine force of 1400 N if the mechanical advantage is 2.

Solution:

We have,

F_B = 1400

M_A = 2

Using the formula we get,

M_A = F_B/F_A

=> F_A = F_B/M_A

= 1400/2

= 700 N

Problem 5. Calculate the force required to overcome a machine force of 900 N if the mechanical advantage is 3.

Solution:

We have,

F_B = 900

M_A = 3

Using the formula we get,

M_A = F_B/F_A

=> F_A = F_B/M_A

= 900/3

= 300 N

Problem 6. Calculate the machine force if the value of force required to overcome it is 400 N and the mechanical advantage is 4.

Solution:

We have,

F_A = 400

M_A = 4

Using the formula we get,

M_A = F_B/F_A

=> F_B = M_AF_B

= 400 (4)

= 1600 N

Problem 7. Calculate the machine force if the value of force required to overcome it is 1300 N and the mechanical advantage is 2.

Solution:

We have,

F_A = 1300

M_A = 2

Using the formula we get,

M_A = F_B/F_A

=> F_B = M_AF_B

= 1300 (2)

= 2600 N