2 0 An understanding of mechanical advantage and

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

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 �F=Force in newtons (N) �MA= F output F input �=180 N 45 N =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 �d = distance �SR = d input d output = 4 m 1 m 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 5 m when two people pull the rope 10 m. What is the speed ratio of the pulley system? �SR=d input d output

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

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

�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 Speed Ration X 100

�For example • A pulley has a speed ratio of 3 and a mechanical advantage of 2 • Efficiency (%)=MA X 100 SR = 2 X 100 3 = 66. 67%

�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.

�Do 2. 1 handout