Chapter 5 Lesson 2

What is a machine? A machine is a device that makes doing work easier Machines can be simple. Some, like knives, scissors, and doorknobs, are used everyday to make doing work easier.

Making Work Easier Machines can make work easier by increasing the force that can be applied to an object. A second way that machines can make work easier is by increasing the distance over which a force can be applied. Machines can also make work easier by changing the direction of an applied force.

Increasing Force A car jack is an example of a machine that increases an applied force. The upward force exerted by the jack is greater than the downward force you exert on the handle.

Increasing Force However, the distance you push the handle downward is greater than the distance the car is pushed upward. The jack increases the applied force, but doesn't increase the work done.

Force and Distance The work done in lifting an object depends on the change in height of the object. The same amount of work is done whether the mover pushed the furniture up the long ramp or lifts it straight up. If work stays the same and the distance is increased, then less force will be needed to do the work.

Changing Direction Some machines change the direction of the force you apply. The wedge-shaped blade of an ax is one example.

The Work Done by Machines When you use an ax to split wood, you exert a downward force as you swing the ax toward the wood. The blade changes the downward force into a horizontal force that splits the wood apart.

The Work Done by Machines When you use a machine such as a crowbar, you are trying to move something that resists being moved. If you use a crowbar to pry the lid off a crate, you are working against the friction between the nails in the lid and the crate.

The Work Done by Machines You also could use a crowbar to move a large rock In this case, you would be working against gravity—the weight of the rock.

Input and Output Forces Two forces are involved when a machine is used to do work. The force that is applied to the machine is called the input force. Fin stands for the effort force. The force applied by the machine is called the output force, symbolized by Fout.

Input and Output Forces Two kinds of work need to be considered when you use a machine—the work done by you on the machine and the work done by the machine. The work done by you on a machine is called the input work and is symbolized by Win. The work done by the machine is called the output work and is abbreviated Wout.

Conserving Energy When you do work on the machine, you transfer energy to the machine. When the machine does work on an object, energy is transferred from the machine to the object. The amount of energy the machine transfers to the object cannot be greater than the amount of energy you transfer to the machine.

Work Fe × de = Fr × dr Win = Wout Conservation of Energy can never get more work out than you put in trade-off between force and distance Win = Wout Fe × de = Fr × dr

Ideal Machines Suppose a perfect machine could be built in which there was no friction. None of the input work or output work would be converted to heat. For such an ideal machine, the input work equals the output work.

Ideal Machines Suppose the ideal machine increases the force applied to it. This means that the output force, Fout, is greater than the input force, Fin. Recall that work is equal to force times distance.

Ideal Machines If Fout is greater than Fin, then Win and Wout can be equal only if the input force is applied over a greater distance than the output force is exerted over.

Mechanical Advantage The ratio of the output force to the input force is the mechanical advantage of a machine. The mechanical advantage of a machine can be calculated from the following equation.

Force Effort Force (Fe) force applied to the machine “what you do” Resistance Force (Fr) force applied by the machine “what the machine does”

Mechanical Advantage Mechanical Advantage (MA) number of times a machine increases the effort force MA > 1 : force is increased MA < 1 : distance is increased MA = 1 : only direction is changed

Mechanical Advantage Window blinds are a machine that changes the direction of an input force. A downward pull on the cord is changed to an upward force on the blinds.

Mechanical Advantage The input and output forces are equal, so the MA is 1.

Ideal Mechanical Advantage The mechanical advantage of a machine without friction is called the ideal mechanical advantage, or IMA. The IMA can be calculated by dividing the input distance by the output distance.

Efficiency Efficiency measure of how completely work input is converted to work output always less than 100% due to friction

Calculating Efficiency In an ideal machine there is no friction and the output work equals the input work. So the efficiency of an ideal machine is 100 percent. The efficiency of a real machine is always less than 100 percent.

Increasing Efficiency Machines can be made more efficient by reducing friction. This usually is done by adding a lubricant, such as oil or grease, to surfaces that rub together. A lubricant fills in the gaps between the surfaces, enabling the surfaces to slide past each other more easily.

Mechanical Advantage Fe Fr MA Fe = 20 N MA = Fr ÷ Fe Fr = 500 N A worker applies an effort force of 20 N to open a window with a resistance force of 500 N. What is the crowbar’s MA? GIVEN: Fe = 20 N Fr = 500 N MA = ? WORK: MA = Fr ÷ Fe MA = (500 N) ÷ (20 N) MA = 25 MA Fr Fe

Mechanical Advantage Fe Fr MA Fe = ? Fe = Fr ÷ MA Fr = 2000 N Find the effort force needed to lift a 2000 N rock using a jack with a mechanical advantage of 10. GIVEN: Fe = ? Fr = 2000 N MA = 10 WORK: Fe = Fr ÷ MA Fe = (2000 N) ÷ (10) Fe = 200 N MA Fr Fe