Mechanical Advantage Using Power
The mechanical advantage of an inclined plane is the ratio of the weight of the load on the ramp to the force required to pull it up the ramp. If energy is not dissipated or stored in the movement of the load, then this mechanical advantage can be computed from the dimensions of the ramp.
In order to show this, let the position r of a rail car on along the ramp with an angle, θ, above the horizontal be given by
where R is the distance along the ramp. The velocity of the car up the ramp is now
Because there are no losses, the power used by force F to move the load up the ramp equals the power out, which is the vertical lift of the weight W of the load.
The input power pulling the car up the ramp is given by
and the power out is
Equate the power in to the power out to obtain the mechanical advantage as
The mechanical advantage of an inclined can also be calculated from the ratio of length of the ramp L to its height H, because the sine of the angle of the ramp is given by
therefore,
Example: If the height of a ramp is H = 1 meter and its length is L = 5 meters, then the mechanical advantage is
which means that a 20 lb force will lift a 100 lb load.
The Liverpool Minard inclined plane has the dimensions 1804 meters by 37.50 meters, which provides a mechanical advantage of
so a 100 lb tension force on the cable will lift a 4810 lb load. The grade of this incline is 2%, which means the angle θ is small enough that sinθ=tanθ.
Read more about this topic: Inclined Plane
Famous quotes containing the words mechanical, advantage and/or power:
“The correct rate of speed in innovating changes in long-standing social customs has not yet been determined by even the most expert of the experts. Personally I am beginning to think there is more danger in lagging than in speeding up cultural change to keep pace with mechanical change.”
—Mary Barnett Gilson (1877–?)
“We took advantage of [the Indians’] ignorance and inexperience to incline them the more easily toward treachery, lewdness, avarice, and every sort of inhumanity and cruelty, after the example and pattern of our ways.”
—Michel de Montaigne (1533–1592)
“This was Pharaoh, direct descendent of our deity Amon, god of the sun, who rules the heavens as Pharaoh rules the earth. Again, he brought treasure, gold, and precious jewels taken from our enemies. For to Pharaoh riches were power and power was to be desired. And also again he brought many captives. For is it not by slaves that one becomes even richer and then has even more power?”
—William Faulkner (1897–1962)