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1 Mechanical Advantage Here is a summary of what you will learn in this section: A m achine is a mechanical system that reduces the force required to accomplish work. Machines m ake work easier by increasing the force, increasing the distance, or changing the direction of the force. The force applied to the machine is called the input force, and the force applied by the m achine is called the output force. The am ount by which a m achine can multiply an input force is called mechanical advantage. Mechanical advantage can be calculated by using the equation MA = Fout/F jn. When you think of a machine, chances are that you imagine something complex like a car or a bicycle. However, machines can be as simple as a wrench or a screwdriver. A machine is any mechanical system that reduces the force required to accomplish work. Removing a tight nut from a holt using only your fingers is almost impossible since you cannot apply enough force. A wrench multiplies the amount of force that you can apply with your fingers in order to remove the nut (Figure 4.19). Similarly, a ramp makes it easier to raise a mass a vertical distance. In this section, you will learn how machines make work easier. Figure 4.19 A wrench makes it easier to remove a nut from a bolt. B 1 5 Starting Point Skills 0 Everyday Machines A machine is any mechanical system that reduces the force needed to do work. For example, a car jack allows you to lift a car that you would not be able to lift without the jack. Work with a partner and make a list of as many machines as you can think of. Compare your list with those of two other groups and add any machines that are different from the ones on your original list. Keep this list for the next activity. Mechanical systems use forces to transfer energy. 113

2 Functions of Machines To move from the ground floor of a building to the second floor requires work. Usually this work is done by climbing stairs between the levels. Suppose that all the stairs were removed and replaced by a vertical rope (Figure 4.20). Most people would not be able to provide enough force to climb the rope to the next level. Stairs, therefore, are a machine that allows people to do the work more easily. Machines make work easier in three ways: by increasing the force that can be applied to an object Figure 4.20 Stairs are an example of a machine that makes work easier. by increasing the distance over which the force is applied by changing the direction of a force Figure 4.21 The force that the jaws apply to the nut is greater than the force that the person applies to the handles. Figure 4.22 The length of the ramp is greater than the height of the truck. By using a ramp to do the work over a longer distance, the person uses less force. Increasing the Force It is almost impossible to crack a hard nut with your bare hands. A nutcracker is a machine that increases the applied force (Figure 4.21). When you apply a force to the handles, the jaws of the nutcracker apply a greater force on the nut. However, the distance that you move each handle is greater than the distance that each jaw moves. Remember from the last section that work is the product of force and distance. When you work on the handles, you apply a small force over a large distance. The jaws of the nutcracker apply a large force over a small distance. However, the work done by the jaws of the nutcracker is no greater than the work done by you when you squeeze the handles. This is true for all mechanical systems. Increasing Distance The ramp in Figure 4.22 allows the cart to be loaded into the truck with less force than if it were lifted straight up. Regardless of how the cart is loaded, the cart in the truck has gained gravitational potential energy since it is now above the road. This means that work was done to move the cart into the truck. 114 UNIT B Systems in Action

3 I Lifting the cart straight up, without a ramp, requires a large force over a small distance (the height). When you use a ramp, the distance that the cart is moved increases and thus the force 1 applied decreases. Changing Direction Some machines change the direction of the force you apply. The pulley used at the top of a flagpole is one example, as shown in Figure When the soldier applies a downward force on the rope, an upward force is exerted on the flag. Input and Output Forces Whenever a machine is used to do work, two forces are always involved. When you exert a force on the machine, the machine exerts a force on the object. For example, suppose you need to lift a car using a jack, as shown in Figure When you apply a force to the handle of the jack, the jack applies a force to the car. The force that is applied to the machine is called the input force, symbolized by Fin. The force that the machine applies to the object is called the output force, symbolized by F t. In the case of our car jack, the input force is the person pushing on the handle, and the output force is the jack pushing up the car. The input force (Fin) is defined as the force exerted on the machine. The output force (Fout) is defined as either the force that the machine applies to the object or the force required to move the object without using a machine. The input force is sometimes called the effort force, and the output force is sometimes called the load force. Figure 4.23 A flag can be lifted upwards by applying a downward force on the rope. Figure 4.24 The input force, Fin, and output force, Fout, using a car jack Mechanical systems use forces to transfer energy. 115

5 M A = ^Fin = 12 (3000 N) (250 N) The jack has a mechanical advantage of 12. This means that the jack will output 12 times the amount of force that Wei inputs. Suppose that Jason and his wheelchair have a total weight of 910 N (Figure 4.25). A force of 130 N is required to push Jason up the ramp. In this example, we think of the output force as the force required to move the object without the ramp. Lifting Jason and the wheelchair up without the ramp would require a force of 910 N. Now we use our equation to calculate mechanical advantage. Figure 4.25 The ramp has a mechanical advantage greater than 1 since the force needed to push the wheelchair up the ramp is less than the force needed to lift the wheelchair straight up. = 7 F in (910 N) (130 N) The ramp has a mechanical advantage of 7. Mechanical Advantage of I Not only can a machine multiply the input force and increase the distance over which the force is applied, but a machine can also change the direction of the force. Figure 4.26 shows an object attached to a rope that passes over a fixed pulley. If you pull down on the rope with a force, the same amount of force is applied to the object. A fixed pulley is a machine that does only one thing: it changes the direction of the force. The mechanical advantage of this machine is 1 since the input and output force are the same size. Machines that have a mechanical advantage of 1 only change the direction between the input and the output forces. These machines do not make the work easier hut are instead used for tasks in which the direction of the force must change. Suggested Activity B19 Quick Lab on page 120 Figure 4.26 Machines that have a mechanical advantage of 1 only change the direction between the input and the output forces. Mechanical systems use forces to transfer energy. 117

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EXPERIMENT MANUAL Franckh-Kosmos Verlags-GmbH & Co. KG, Pfizerstr. 5-7, 70184 Stuttgart, Germany +49 (0) 711 2191-0 www.kosmos.de Thames & Kosmos, 301 Friendship St., Providence, RI, 02903, USA 1-800-587-2872