# Work and Simple Machines

## Work and Power

In science, force and distance determine the amount of work done. Machines and technology help reduce the amount of work people have to do. For example, luggage movers deliver luggage to and from airplanes. They reduce the amount of work employees and passengers have to do.

### Defining Work

In science, work is when a force moves an object in the same direction the force is being exerted. Work is done when a teacher lifts a chair, a horse pulls a wagon, and a dancer leaps into the air. However, not all forces result in work. In order for work to be done, two conditions must be met. First, a force must be exerted on an object that causes that object to move. Second, the force must be exerted in the same direction the object moves.

One student lifts a book from the floor to a shelf 1 meter above the ground. A second student lifts the same book to the same height and then carries it to a shelf across the room. Which student does more work on the book? The answer might surprise you because the answer is neither student. Both students do the same amount of work on the book.

Work is done only when a force causes an object to move in the same direction the force is being applied. Therefore work is done when an upward force is exerted to lift the book. If the force is exerted in a direction different from the direction in which the object moves, no work is done. This means no additional work is done when the book is carried across the room, because the force on the book is upward, and the direction of motion is horizontal.

### Calculating Work

The amount of work done is shown by the equation:

When force is measured in newtons and distance is measured in meters, the unit of work is the newton,meter (N•m), which is also known as a joule (J), the SI unit for work.

The work done can be determined if the force and the distance are known. Suppose a weight lifter lifts a dumbbell weighing 70 N a distance of 1 m. How much work does he do? The force required to lift an object near Earth’s surface is equal and opposite to the weight of the object, so the weight lifter must exert an upward force of 70 N to lift the dumbbell. The force moves the dumbbell a distance of 1 m.

Because the second weight lifter raised the dumbbell twice as high, twice as much work was done. Finally the third weight lifter raised twice as much weight twice as high. This represents the greatest amount of work.

### Defining and Calculating Power

Power measures the rate at which work is done. It can be calculated using the following equation:

When work is measured in joules, and time in seconds, the unit of power is the joule per second, which is the same as the SI unit watts (W). Power can be calculated if the work and time are known. For example, what is the power when a person does 140 J of work in 20 s?

If the time decreased to 10 s, the power would double.

1. If 1250 J of work is done on an object that weighs 50 N, how far can that object be raised? A. 5m B. 25m C. 125m D. 1200m
2. A crane lifts a car that weighs 16,000 N 12 min 5 s. What is the power of the crane?
A. 267 W B. 6,667 W C. 38,400 W D. 960,000 W

## Machines

A machine is any device that makes doing work easier. For any type of machine, work is done on the machine and by the machine. The work that is done on the machine is the input work and the work that the machine does is the output work.

Work is a force exerted over some distance; therefore two forces are involved when a machine is used. The force exerted on a machine is called the input force, so the input work done on a machine is equal to the input force times the distance over which the input force is exerted. The force exerted by the machine is called the output force. So, the output work, or the work done by the machine, is equal to the output force times the distance over which the output force is exerted.

### Simple Machines

The most basic machines are called simple machines, which are machines that do work with only one movement of the machine. There are six basic types of simple machines: inclined plane, screw, wedge, lever, wheel, and axle.

#### Inclined Plane

Walking or driving straight up a steep incline is much more difficult than traveling along the winding, sloped path. A gentler slope reduces the amount of force needed to move an object. The simple machine that takes advantage of this principle is the inclined plane. An inclined plane is a flat surface set at an angle to a horizontal surface. A ramp is an example of an inclined plane.

The same amount of work is done to lift a box as is done to push that box up an inclined plane. To lift the box, the amount of work done is equal to the force of 1,500 N times the distance of 1 m, or $W = 1,500 N \times 1 m = 1,500 J$. To push the box along the ramp, the amount of work done is equal to the force of 300 N times the distance of 5 m, or $W = 300 N \times 5 m = 1,500 J$. The same amount of work is done to lift the box as is done to push that box up the ramp. The advantage of the inclined plane is that the plane enables the mover to use a smaller force. The trade-off is that the force must be exerted over a longer distance.

#### Screw

Some simple machines are modified versions of other simple machines. A screw is an inclined plane wrapped in a spiral around a central cylinder. The spirals, or threads, of the screws form small ramps that run upward from the tip. Unlike a ramp over which a person might push a box, the inclined plane of a screw moves through an object or material. Screws are found in many common devices, such as jar lids, light bulbs, and bolts.

#### Wedge

Like the screw, a wedge is a simple machine in which an inclined plane moves through or between objects. It is an inclined plane with one or two sloping sides. It is thick at one end and tapers to a thin edge. Wedges are generally used for separating objects or holding them in place. Knives, axes, and shovels are common examples. A wedge makes work easier by decreasing the required input force. In turn, the input force must be exerted over a longer distance. A wedge also changes the direction of the input force. As the carving tool is moved through the wood, the downward input force is changed into a horizontal force that pushes the wood apart.

#### Lever

A lever is a rigid bar that is free to rotate about a fixed point to lift something, known as the load. The fixed point the lever rotates about is the fulcrum. The part of the lever between the input force and the fulcrum is the input arm, and the part between the fulcrum and the output force is the output arm. Levers can be categorized into three classes. A crowbar, a seesaw, and a boat oar are examples of first-class levers. In a first-class lever, the fulcrum is located between the input and output forces, and the fulcrum’s position determines how easy it is to lift the load. The motion of the object being moved is in the direction opposite of the input force.

A wheelbarrow and a bottle opener are examples of second-class levers. In this type of lever, the output force is located between the input force and the fulcrum.

A fishing rod and a baseball bat are examples of third-class levers. A thirdclass lever’s fulcrum is at the end of the lever, and the input force is exerted between the fulcrum and the output force. In addition, a third-class lever does not change the direction of the input force. A third-class lever exerts a smaller output force over a longer distance.

#### Pulley

A pulley is a grooved wheel with a rope, chain, or cable running along the groove, and it can be fixed or movable. A fixed pulley is attached to something that does not move, such as a ceiling or a wall, with the distance the rope is pulled down equaling the distance the load moves upward. For the input work to equal the output work, the input force on the rope must equal the output force on the load; therefore a fixed pulley does not change either force or distance. It changes only the direction of the input force.

A pulley attached to the object being moved is called a movable pulley. Unlike a fixed pulley, a movable pulley multiplies force; therefore the input force must be exerted over a greater distance. When fixed and movable pulleys are combined, a system of pulleys is formed.

#### Wheel and Axle

A wheel and axle is a simple machine consisting of two circular objects of different sizes. The axle, which is the smaller of the two objects, is attached to the center of a larger wheel. The wheel and axle rotate together. The input force can be applied to either the wheel or the axle. Doorknobs, screwdrivers, and faucet handles are examples of wheel and axles.

### Compound Machines

Compound machines, like cars, are made up of more than one simple machine. Burning fuel in the cylinders of a car engine causes the pistons to move up and down. This makes the crankshaft rotate. The force exerted by the rotating crankshaft is transmitted to other parts of the car, such as the transmission and the differential. Both of these parts contain gears, which are wheel and axles. Cars also contain levers and pulleys.

1. A bicycle is a compound machine. Identify at least two simple machines that are used in a bicycle.

Work is the transfer of energy. Recall that energy is neither created nor destroyed-it is conserved. Therefore the output work cannot be greater than the input work for any machine. If a machine does not multiply work, how is it useful? A machine makes work easier by multiplying force or distance or changing the input force’s direction.

The number of times a machine increases the input force is the mechanical advantage (MA) of the machine. The MA of a machine is the ratio of the output force to the input force. It can be calculated using the following equation:

Both the input force and the output force are measured in newtons. As a result, the units cancel, and mechanical advantage does not have any units associated with it.

For a first-class lever, the closer the output force is to the fulcrum, the greater the mechanical advantage of the lever. Because a second-class lever multiplies force, its mechanical advantage is always greater than 1. For a third-class lever, however, $% $ so the mechanical advantage is always out in less than 1.

The mechanical advantage of a fixed pulley is 1. As shown below, a person needs to exert a force of 4 N to lift the 4-N weight. However, the person is able to pull downward instead of upward, which is easier.

The mechanical advantage of a movable pulley is greater than 1. It is equal to the number of rope segments holding up the load. Force is multiplied because the input force is exerted over twice the distance of the output force. A force of 2 N can be exerted to lift a load that weighs twice as much, which is 4 N.