Mechanical Advantage & Effeciency

Objectives Explain how a machine makes work easier Describe and give examples of the force- distance trade-off that occurs when a machine is used Describe & Calculate mechanical advantage Describe & Calculate effeciency Explain why machines are not 100% efficient

What is a machine? Machines make work easier by 1)Changing the amount of force you exert 2)Changing the distance over which you exert the force 3)Changing the direction the force is exerted

Which is easier? Opening a paint can with your fingers? OR Opening a paint can with a screwdriver? The force is multiplied and redirected.

Which is easier? Lifting a heavy box into a truck? Pushing a heavy box up a ramp into a truck? OR The force is both multiplied and redirected.

When using a machine to do work, two forces are involved. Input Force (F in ) –The force you apply to the machine in doing work (W in ) Output Force (F out ) –The force that the machine applies in doing work (W out )

Two types of work are involved. Ideally, without friction W in = W out (F in ) (d in ) = (F out ) (d out ) Work input is the amount of work done on a machine. –Input force x input distance Work output is the amount of work done by a machine. –Output force x output distance How are the two related?

Force-distance trade-off To decrease the force needed, increase the distance To increase the force needed, decrease the distance Examples: wheelbarrow and hammer

Force-Distance Trade-off (increases force) Wheel barrow –Small force in a greater distance (lift handle of wheelbarrow) –Large force applied a shorter distance (load in wheelbarrow lifted)

Force-Distance Trade-off (decreases force) Hammer –Large force applied over a short distance –Small force applied over a long distance

Measuring the benefits: Mechanical Advantage Mechanical Advantage tells you how many times the machine multiples the force. –a machine with a large mechanical advantage can make lifting a heavy load easier Actual Mechanical Advantage (Reality) AMA = (F out )/(F in ) Ideal Mechanical Advantage (No Friction) IMA = (d in )/(d out )

Calculating Mechanical Advantage 1.What is the mechanical advantage of a machine that applies 200N to an object when you apply 50N to the machine? Equation MA = (Fout)/(Fin) MA = (200N)/(50N) MA = 4

Calculating Mechanical Advantage 2.You apply 2000 N to a machine and the machine applies 200 N to an object. What is the mechanical advantage? Equation MA = (Fout)/(Fin) MA = (200N)/(2000N) MA = 0.1

Calculating Mechanical Advantage 3.You apply 10 N to a machine and the machine applies 10 N to another object. What is the mechanical advantage. Equation MA = (Fout)/(Fin) MA = (10N)/(10N) MA = 1 Can such a machine be useful?

Mechanical Advantage:What does it mean? Mechanical Advantage = 1 –There is no advantage to using the machine Mechanical Advantage > 1 –The machine makes work easier Mechanical Advantage < 1 –The machine makes work harder

Efficiency We said that the input work equals the output work, or: W in = W out However, some output work is lost due to friction. The comparison of work input to work output is called efficiency. No machine has 100 percent efficiency due to friction. What would improve the efficiency of a machine? (Hint: What reduces friction?)

Calculating Efficiency How efficient is a machine that takes 40 J of work and produces 30 J of work? Equation Eff = (Wout)/(Win) X 100% Eff = (30J)/(40J) X 100% Eff = 75%

Calculating Efficiency You do 250,000 J of work to cut a lawn with a hand mower. If the work done by the mower is 200,000 J, what is the efficiency of the lawn mower? Equation Eff = (Wout)/(Win) X 100% Eff = (200,000J)/(250,000J) X 100% Eff = 80%