2.0 An understanding of mechanical advantage and work helps in determining the efficiency of machines In this section you will learn how a machine can increase a force and how it affects the speed of an object

2.1 Machines Make Work Easier A machine can make work easier by increasing the amount of force that you exert on an object You could not exert enough force to lift a car by yourself but by using a lever you could

MA= Output Input Mechanical Advantage The amount by which a machine can multiply a force Mechanical Advantage (MA)= Output Force Input Force MA= Output Input

input force =The force applied to the machine (measured in Newtons) Person pushing the lever to lift the car output force =The force the machine applies to the object – much larger than input (measured in Newtons) The lever lifting the car

Example Take a look on pg 280 Fig 2.2 MA= F output F input =180N 45N F=Force in newtons (N) MA= F output F input =180N 45N = 4

Try this It take 350 N of force on the handle of a jack in order to lift a car. It take 15 000 N of force to lift the car off the ground. Calculate the mechanical advantage of a jack MA= F output F input

Speed Ratio Calculating the speed ratio is another way of analyzing how machines work. Speed measures the distance an object travels in a given amount of time.

Speed ratio= a measure of how the speed of the object is affected by a machine Speed Ratio(SR)= Input distance Output distance

Example Take a look at Pg 281 fig 2.3 SR = d input d output SR = 4m 1m d = distance SR = d input d output SR = 4m 1m SR = 4 This means that it is 4 times faster than the load that you are lifting

Let’s try together A pulley system lifts a load 5m when two people pull the rope 10m. What is the speed ratio of the pulley system? SR=d input d output

SR= d input d output SR= 10m 5m SR= 2

Effect of Friction The difference between the theoretical and the real value of the mechanical advantage is the result of friction *is the force that opposes motion Rub your hand together

Friction can be an important factor in a mechanical system because it opposes motion. This means that extra force is needed to overcome friction whenever you move an object. The speed ratio represents the ideal mechanical advantage (as if friction did not exist)

Efficiency Friction also affects it efficiency. Efficiency is a measurement of how well a machine or device uses energy You can calculate the efficiency of a machine by Efficiency=Mechanical Advantage X 100 Speed Ration

For example A pulley has a speed ratio of 3 and a mechanical advantage of 2 Efficiency (%)=MA X 100 SR = 2 X 100 = 66.67% 3

So in complex machines, the many subsystems are each affected by friction and other factors. Because of this, complex machines are often very inefficient. A typical car engine has an efficiency of only about 15% That means the 85% of the energy from the gas is NOT used to move the car.

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