Efficiency and MA

Applied Physics and Chemistry Work Lecture 4

Mechanical Advantage Mechanical advantage tells how much the

machine is helping us Two ways to calculate MA: IMA: Ideal Mechanical Advantage

Neglects the effect of friction IMA = de/dr

AMA: Actual Mechanical Advantage Includes the effect of friction MA = Fr/Fe

MA Problems You got roped into helping your parents’ friends

move. They have a ramp leading up into the back of a truck. The ramp is 6 m long, and the back of the truck is 1.5 m off the ground. What is the MA of this simple machine?

When watching a circus act, you notice the tumblers using a first class lever and wonder how if one of them jumps, it can propel two of them into the air.  When the tumbling lever is measured, it shows the effort arm (which they jump on) is 8 meters long, the resistance arm (where their tumbler is being propelled from) is 2 meters long.  What is the mechanical advantage of this lever?

More MA Problems A toy car has the following measurements for

its wheels:  the radius axle (the small wheel) measures 1 cm.  The radius of the larger wheel (the one that touches the pavement) measures a whopping 10cm.  What is the mechanical advantage of these large wheels? 

A 10 m ramp is used to lift a 600 N box to a height of 2 m. The effort force as a person pushes the box up the ramp is 160 N. What is the AMA of this simple machine?

What is the IMA of the ramp?

Efficiency In a real machine, not all input work is

available as output workEfficiency is the ratio of output work to input work

Eff = (Wo/Wi) x 100 Eff = (MA/IMA) x 100

Efficiency Problems A 10 m ramp is used to lift a 600 N box to a

height of 2 m. The effort force as a person pushes the box up the ramp is 160 N. What is the efficiency of this simple machine?

A worker uses a pulley system to raise a 24 kg carton 16.5 m. A force of 129 N is exerted and the rope is pulled 33 m. What is the efficiency of the system?