Section 10.2 Machines  Objectives Demonstrate a knowledge of the usefulness of simple machines. Differentiate between ideal and real machines in terms of efficiency. Analyze compound machines in terms of combinations of simple machines. Calculate efficiencies for simple and compound machines

BENEFITS OF MACHINES Machine – device that changes force needed to do work. It eases the load either by changing the magnitude or direction of a force, but does not change the amount of work done. Input Work – the work you do. Wi   Output Work – the work the machine does. Wo Work - is the transfer of energy by mechanical means. The Output Work can never be larger than the Input Work. Effort Force – force exerted on a machine. Denoted by Fe. Resistance Force – force exerted by a machine. Denoted by Fr.

BENEFITS OF MACHINES Mechanical Advantage – is the ratio of Resistance Force to Effort force. Denoted by MA. It is the Resistance Force divided by Effort force. MA = Fr / Fe When the mechanical advantage is greater than one, the machine increases the force you apply. We can calculate the mechanical advantage of a machine using the definition of work. The input work is the product of the effort force you exert and the displacement of your hand.

BENEFITS OF MACHINES The output work is the product of the resistance force and the displacement caused by the machine.   A machine can increase force, but it cannot increase energy. An ideal machine transfers all the energy, so the output work equals the input work. Wo = Wi This leads to Frdr = Fede

BENEFITS OF MACHINES This can be rewritten as Fr / Fe = de / dr And MA = Fr / Fe So for an ideal machine we can say MA = de / dr Ideal Mechanical Advantage – the ratio of effort distance to resistance distance in a simple machine.  IMA = de / dr

BENEFITS OF MACHINES Note: you measure distances moved to calculate the Ideal Mechanical Advantage (IMA) and you measure the forces exerted to find the Actual Mechanical Advantage (MA).   Efficiency – ratio of output work (or output energy) to input work (or input energy) multiplied by 100. It equals the Mechanical Advantage divided by the Ideal Mechanical Advantage times 100. Efficiency = (Wo / Wi) x 100% Efficiency = Fr / Fe x 100% de / dr Efficiency = (MA / IMA) x 100%

BENEFITS OF MACHINES All real machines have efficiencies less than 100% thus we can express efficiency in terms of Mechanical Advantage and Ideal Mechanical Advantage.   Lower efficiency means that a greater effort force is needed to exert the same resistance force.

COMPOUND MACHINES All machines, no matter how complex, are combinations of up to 6 simple machines.   The 6 Simple Machines (shown in figure 10-10 p. 206) Lever Pulley Wheel and Axle Inclined Plane Wedge Screw

COMPOUND MACHINES Compound Machine – machine consisting of 2 or more simple machines. It consists of 2 or more simple machines linked so that the resistance force of one machine becomes the effort force of the second machine. Read p. 270 The Mechanical Advantage of a complex machine is the product of the mechanical advantages of the simple machines it is made up of.

COMPOUND MACHINES Do Example Problem 4 p. 271 A) IMA = de / dr = gear radius / wheel radius IMA = 4 / 35.6 = .112   B) Efficiency = (MA / IMA) x 100% 95% = (MA / .112) x 100% 95%(.112) / 100% = MA .1064 = MA C) MA = Fr / Fe .1064 = Fr / 155 16.492 N = Fr D) IMA = de / dr can change to meters and get the following .112 = de / 14 .112 = de / .14 1.568 cm = de .01568 m = de Do Practice Problems p. 272 # 24-28 Read p. 272 (Multi-Gear Bicycle)

THE HUMAN WALKING MACHINE Lever Systems of the body are complex, but each system has 4 parts 1. A rigid bar (bone) 2. A source of force (muscle contraction) 3. A fulcrum or pivot (movable joints between bones) 4. A resistance (weight of the body or an object being moved)  Do 10.2 Section Review p. 273 # 29-33