Ideal Mechanical Advantage

Expectation #28:  The student will calculate the Ideal Mechanical Advantage of a lever, an inclined plane, and a block and tackle system.

 Expectation #29:  The student will manipulate the following type of simple machines in order to understand the directional nature of forces and the multiplication of forces:  inclined plane, level, simple pulley, block and tackle, and wheel and axle.

Expectation#30:  The student will understand that no machine operates with perfect efficiency (Work_out is less than Work_in ) and identify friction as one reason for a decrease in efficiency.

1.     Have you used a machine today?  You probably know that a bicycle is  a machine.  Pencil sharpeners and can openers are also machines.  A machine is a device that makes work easier. 

2.     Some machines are powered by engines or electric motor; others are people-powered.  A simple machine is a device that does work with only one movement.  There are six types of simple machines.  Can you name some in the kitchen, in sports, in construction?

3.     Suppose you wanted to pry a lid off a wooden crate with a crowbar.  You would slip the end of the crowbar blade under the edge of the crate lid  and push down on the handle.  You would do work on the crowbar, and the crowbar would do work on the lid.  Two forces are involved when a machine is used to do work.  The force applied to the machine is called the effort force (F_e).  The force applied by the machine to overcome resistance is called the resistance force(F_r).  In the crate lid example, you apply the effort force to the crowbar handle.  The resistance force is the force the crowbar applies to the lid. 

4.     There are also two kinds pf work to be considered when a machine is used-the work done on the machine and the work done by the machine.  The work done on the machine is called work input(W_in); the work done by the machine is called work output(W_out). 

5.     Recall that work is the product of force and distance:  W = F x d. 

6.     Work input is the product of the effort force and the distance that force is exerted:  W_in =F_e  x d_e

7.     Work output is the product of the resistance force and the distance that force   moves:  W_out =F_r  x d_r.

8.     Remember that energy is always conserved.  So, you can never get more work out of a machine than you put into it.  In other words, W _out can never be greater than W_in.  In fact, whenever a machine is used, some energy is changed to heat due to friction.  So, W_out is always smaller than W_in.

9.     Although a perfect machine has never been built, it helps to imagine a frictionless machine in which no energy is converted to heat.  Such an ideal machine is one in which work input equals work output.  For an ideal machine,

W_in  =  W_out

F_e  x d_e  =F_r  x d_r

The number of times a machine multiplies the effort force is the mechanical advantage(MA) of the machine.  To calculate mechanical advantage, you divide the resistance force by the effort force.

          MA  = resistance force =          Fr

                    Effort force            F_e  

Calculating Mechanical Advantage

A worker applies an effort force of 20N to pry open a window that has a resistance force of 500N.  What is the mechanical advantage of the crowbar?

What is known?  Resistance force  =  500N

                             Effort force   =          20N

What is unknown?  Mechanical advantage

MA  = Fr

          Fe

MA  = 500N=  25

          20N

Practice Problem

Find the mechanical advantage needed to lift a 2000N rock, using a jack with a mechanical advantage of 10.

MA  =F_r/F_e

F_e=F_r/MA  = 2000N/10 =200N

MiniQuiz

1.  A simple machine does work with only one ________________________.

2. The force applied to a machine is called the ________________________.

3. The force applied by a machine is called the _______________________.

4. The number of times a machine multiplies is the ____________________ of the machine.

Section Wrap-Up

1.     Explain how simple machine can make work easier without violating the law of conservation of energy.

2.  A carpenter uses a claw hammer to pull a nail from a board.  The nail has a resistance of 2500N.  The carpenter applies an effort force of 125N.  What is the mechanical advantage of the hammer?

3.      Think Critically:  Give an example of a simple machine you’ve used recently.  How did you apply effort force?  How did the machine apply resistance force?

Vocabulary Terminology

1.     machine

2.     simple machine

3.     effort force

4.     resistance force

5.     ideal machine

6.     mechanical advantage

7.     lever

8.     fulcrum

9.     effort arm

10. resistance arm

11. pulley

12. wheel and axle

13. inclined plane

14. screw

15. wedge

16. bionics

17. compound machine

18. efficiency

19. power

Section 7.2  The Simple Machines

1.     A lever is a bar that is free to pivot, or turn, about a fixed point.  The fixed point of a lever is called the fulcrum.  The part of the lever on which the effort force is applied is called the effort arm.  The part of the lever that exerts the resistance force is called the resistance arm.

2.     The following equation, which assumes no friction, can be used to find the ideal mechanical advantage(IMA) of any lever.

IMA  = length of effort arm   = L_e

         length of resistance arm  L_r

A worker uses an iron bar to raise a manhole cover weighing 65N.  the effort arm of the lever is 60cm long.  The resistance arm is 10cm long.  What is the ideal mechanical advantage of the bar?

L_e = 60cm

resistance arm  L_r = 10cm

????ideal mechanical advantage  IMA

IMA = L_e/L_r

60cm/10cm  = 6.0

Complete the practice problems on page 187

Refer to page 199.  Create your own Rube Goldberg device