Ramps are Simple Machines
About 4 min read
A ramp is an inclined plane that allows you to move an object to a greater height with less force than is needed to simply lift the object. A ramp can also be used to ease an object from a higher to a lower height.
Although it has no moving parts, a ramp is still considered a simple machine. It is called an inclined plane since it is a flat surface at an angle. The ideal force mechanical advantage (MAF) of a ramp is the weight of the object divided by the force required to move it up the ramp.
Resistance from friction can affect the mechanical advantage of a ramp. Since the friction of sliding an object up a ramp can increase the force required, rollers or wheels are usually used to reduce the friction and increase the force mechanical advantage.
Questions you may have include:
- What are the relationships of the ramp components?
- What is the idea force mechanical advantage?
- What is the mechanical advantage including inertia and friction?
This lesson will answer those questions.
Relationships of ramp components
When you push an object of weight w up a ramp or inclined plane, the input force or effort required is a function of the incline angle. Thus:
FI = w*sin(α)
FO = w
where
- FI is the input or effort force in netwtons or pounds
- w is the weight of the object
- sin(α) is the sine of angle α (small Greek letter alpha)
- FO is the load or resulting output
Note: We use small w to denote weight, while large W is work done.
Also note: The angle α must be greater than zero (α > 0). Otherwise there is no inclination, and the mechanical advantage becomes meaningless.
Pushing a load up a ramp
Force mechanical advantage
The force mechanical advantage of the ramp is:
MAF = FO/FI
MAF = w/w*sin(α)
MAF = 1/sin(α), provided α > 0
For example, when the angle of the ramp is α = 45°, the mechanical advantage is MAF = 1/0.707 = 1.414.
Note that speed and distance mechanical advantages are not really relevant with ramps.
Other factors
There can be other factors that affect the force mechanical advantage of a ramp. Friction can reduce the mechanical advantage. Rollers can be used to reduce the effect of friction.
Effect of friction
In the real world, there is friction that resists the motion.
Components related to friction
When an object is on a ramp, its weight can be broken into components, parallel and perpendicular to the surface of the inclined plane.
Relationships of ramp weight components
If w is the weight of the object, then
- w*sin(α) is force pulling the object down the ramp
- w*cos(α) is the normal force pushing the object against the surface
The friction equation is:
fr = μw*cos(α)
where
- fr is the resistive force of friction
- μ (small Greek letter mu) is the coefficient of friction between the two surfaces
- cos(α) is the cosine of angle α
Mechanical advantage with friction
Friction between the ramp and the object will require a greater input or effort force to overcome the resistance. In order to obtain the desired output force for a machine with friction, the ideal input force or effort must be increased by the amount of friction. This will reduce the force mechanical advantage.
MA’F = FO/(FI + fr)
where
- MA’F is the force mechanical advantage including friction
- FO is the desired output force or load
- FI is the ideal input force or effort
- fr is the resistive force of friction on the machine
Insert values to MA’F
FO = w
FI = w*sin(α)
fr = μw*cos(α)
MA’F = w/[w*sin(α) + μw*cos(α)]
MA’F = w/w[sin(α) + μcos(α)]
Thus:
MA’F = 1/[sin(α) + μcos(α)]
This force mechanical advantage is independent of the weight of the object but dependent on the coefficient of friction.
Special case
When α = 0°, sin(α) = 0 and cos(α) = 1. Thus:
MA’F = 1/μ
Summary
A ramp is an inclined plane that allows you to move a heavy object to some height with less force than needed to lift the object. A ramp can also be used to ease an object to a lower height.
Although it has no moving parts, a ramp is still considered a simple machine. It is called an inclined plane since it is a flat surface at an angle. The force mechanical advantage (MAF) of a ramp is the weight of the object divided by the force required to move it up the ramp.
Resistance factors of inertia and friction can affect the mechanical advantage of a ramp. An accelerating object requires a force to overcome its inertia. Since the friction of sliding an object up a ramp can increase the force required, rollers or wheels are usually used to reduce the friction and increase the force mechanical advantage.
Climb the ramp to success
Resources and references
Websites
Inclined Plane – Wikipedia
Questions and comments
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