Mechanical Advantage Relationships

There are three types of mechanical advantages in machines: force, distance, and speed. For a given machine, there are relationships between these mechanical advantages.

Note: Most science books only consider force mechanical advantage, but we will discuss all three, since they are equally important.

This lesson will answer those questions. Useful tool: Units Conversion

---

Mechanical advantages

The mechanical advantage of a machine is defined as its output divided by its input.

Distance mechanical advantage

The distance mechanical advantage is:

MA_D = D_O/D_I

where

• MA_D is the distance mechanical advantage
• D_O is the distance the load moves or the output distance
• D_I is the distance the effort moves or the input distance

Note: In this notation, MA is NOT M times A. It simply stands for Mechanical Advantage.

(See Distance Mechanical Advantage for more information.)

Speed mechanical advantage

The equation for the speed mechanical advantage is:

MA_S = S_O/S_I

where

• MA_S is the speed mechanical advantage
• S_O is the output speed of the load
• S_I is the input speed of the effort

(See Speed Mechanical Advantage for more information.)

Force mechanical advantage

The force mechanical advantage equation is:

MA_F = F_O/F_I

where

• MA_F is the force mechanical advantage
• F_O is the output force or load
• F_I is the input force or effort required to move the object

(See Force Mechanical Advantage for more information.)

Distance-speed relationship

Since distance equals speed times time, there is a distinct relationship between distance mechanical advantage and speed mechanical advantage. For a given amount of time, t:

D_O = S_Ot

D_I = S_It

Divide output distance by input distance:

D_O/D_I = S_Ot/S_It = S_O/S_I

Thus:

MA_D = MA_S

Distance MA = Speed MA

Distance-force relationship

According to the Law of Conservation of Energy, the output energy or work equals the input energy or work. Work is defined as a force times the distance moved. Thus:

W_O = W_I

W_O = F_OD_O

W_I = F_ID_I

where

• W_O is the output work
• W_I is the input work

Thus:

F_OD_O = F_ID_I

Divide to get:

F_O/F_I = D_I/D_O

Therefore:

MA_F = D_I/D_O = 1/MA_D

Thus, Force MA = 1/Distance MA = 1/Speed MA.

Example

In jacking up a car, you must move the jack-handle a greater distance than the car is lifted.

Distance MA = Speed MA

and

Force MA = 1/Distance MA = 1/Speed MA

---

Take advantage of the situation

---

Resources and references

Websites

The Mechanical Advantage of Machines – Carolina Curriculum (PDF)

Introduction to mechanical advantage – Khan Academy (video)

Mechanical advantage – Wikipedia

Machines Resources

---

Questions and comments

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

---

Share

Click on a button to bookmark or share this page through Twitter, Facebook, email, or other services: