1 Work, Power, and Machines

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1 CHAPTER 13 1 Work, Power, and Machines SECTION Work and Energy KEY IDEAS As you read this section, keep these questions in mind: What is work, and how is it measured? How are work and power related? How do machines make work easier? What Is Work? Imagine trying to lift the front end of a car without a jack. You might exert a lot of force and not move the car at all. Exerting all that force may seem like hard work, but in scientific terms, you did no work at all. In science, there are many different kinds of work. Here, we will deal only with work against gravity. This kind of work occurs when a force causes an object to move away from Earth s surface. You can use the equation below to calculate the work done on an object: work force distance W Fd In this equation, distance is the distance the object moves above Earth s surface. Work only occurs when the object is moving. If the object is not moving, no work is occurring. READING TOOLBOX Compare As you read this section, create a table comparing work, power, and mechanical advantage. Include the equations used to calculate each, the units used to measure each, and the definition of each. 1. Apply Concepts Is the weightlifter doing any work when she holds the barbell motionless above her head? Explain your answer. This weightlifter did work on the barbell to lift it over her head. Work is measured in newton-meters (N m). You can also use joules (J) to measure work. One newton-meter equals one joule. Remember that one newton is equal to one kilogram-meter per second squared (kg m/s 2 ). Therefore, one joule is also equal to one kilogram-meter squared per second squared (kg m 2 /s 2 ): 1 N m 1 J 1 kg m 2 /s 2 You can use different units for work to make solving problems easier. Interactive Reader 269 Work and Energy

2 Math Skills 2. Calculate A student lifts an apple to a height of 1 m. The apple weighs 1 N. How much work does the student do on the apple? Show your work. CALCULATING WORK FROM FORCE AND DISTANCE To calculate the amount of work done on an object, you must know the force applied and the distance the object moved. Let s look at an example of how to calculate the work done on an object. A crane uses an average force of 5,200 N to lift a metal beam 25 m into the air. How much work does the crane do on the beam? Step 1: List the given and Step 2: Write the equation. Step 3: Insert the known values and solve for the unknown value. force, F = 5,200 N distance, d = 25 m W = Fd W = (5,200 N) (25 m) W = 130,000 N m W = 130 kj work, W So, the crane does about 130 kj of work on the beam. 3. Explain If the car were being moved sideways, could you determine the force on the car by using the weight equation? Explain your answer. CALCULATING WORK FROM MASS AND DISTANCE If you know the mass of an object, you can calculate how much work it takes to lift the object. For example, suppose a car has a mass of 1,200 kg. A mechanic uses an electric lift to raise the car 0.50 m off the ground. How much work does the lift do on the car? In order to use the work equation, you must know the force exerted on the car. Because the car is being lifted straight up, the force on the car is equal to the car s weight. Therefore, you can use the equation for weight, w mg, to find the force on the car. In this equation, g is free-fall acceleration (9.8 m/s 2 ). Here s how to solve this problem: Step 1: List the given and Step 2: Write the equations. Step 3: Insert the known values and solve for the mass, m = 1,200 kg distance, d = 25 m w = mg W = Fd force, F (equal to weight, w) work, W w = (1,200 kg) (9.8 m/s 2 ) w = 12,000 kg m/s 2 = 12,000 N W = (12,000 N) (0.50 m) W = 6,000 N m = 6.0 kj So, the lift does about 6.0 kj of work on the car. Interactive Reader 270 Work and Energy

3 How Are Work and Power Related? Like work, power has a very specific meaning in science. Power is the rate at which work is done or energy is used. In other words, power is how much work is done in a given amount of time. The equation for power is: power work time P W t The SI unit for power is the watt (W). One watt is the amount of power needed to do one joule of work in one second (1 J/s). Be careful not to confuse the symbol for work, W, which is in italics, with the symbol for watt, W, which is not in italics. Power increases when more work is done in a given amount of time. Power also increases when you do work in less time. For example, imagine climbing a flight of stairs slowly. Now, imagine running up the stairs. In both cases, you do the same amount of work, because you move your weight through the same distance. However, it takes less time to climb the stairs running. Therefore, your power output is higher if you run up the stairs. Let s look at an example of how to calculate power. Lifting an elevator 18 m takes 100 kj of work. If the elevator moves 18 m in 20 s, what is the power output of the elevator? 4. Define What is power? 5. Identify Name two things that can cause power output to decrease. Step 1: List the given and Step 2: Write the equation. work, W = 100 kj time, t = 20 s P = W t power, P Step 3: Insert the known values and solve for the unknown value. P = 100 kj 20 s P = 5 kj/s = 5,000 J/s P = 5,000 W = 5 kw So, it takes about 5 kw of power to lift the elevator. Interactive Reader 271 Work and Energy

4 6. Describe How do machines make work easier? How Do Machines Make Work Easier? Many people think that machines reduce the amount of work we have to do to move an object. However, machines do not change the amount of work done on an object. Instead, they make work easier by changing the way the force is applied. For example, in the picture below, the ramp increases the distance over which the force is applied. F = 225 N W = F d W = 225 N 1.00 m W = 225 N m = 225 J 7. Compare How does the amount of work done in the top picture compare with the work done in the bottom picture? W = F d W = 75.0 N 3.00 m W = 225 N m = 225 J d = 1.00 m F = 75.0 N d = 3.00 m To lift a box straight up, the mover applies a large force over a small distance. To move the box up the ramp, the mover applies a smaller force over a longer distance. 8. Explain Why doesn t a machine that increases force break the law of conservation of energy? Many machines make work easier by changing the size or direction of the force we apply. The force we apply is called the input force. For example, people use jacks to lift cars off the ground. A person applies a light, downward input force to the handle of the jack. The jack changes the input force into a stronger, upward force, the output force. The output force lifts the car. In this way, a person can lift a very heavy car. It may seem that changing a small force into a large force breaks the law of conservation of energy. However, the jack doesn t only increase the force applied. It also decreases the distance over which the force is applied. Therefore, the total amount of work stays the same. Many machines increase force by decreasing the distance over which the force is applied. This process is called multiplying the force. The car jack is an example of a machine that multiplies force. Other machines, such as ramps, multiply distance. They make work easier by allowing you to exert a smaller force over a longer distance. Interactive Reader 272 Work and Energy

5 What Is Mechanical Advantage? Scientists and engineers use a quantity called mechanical advantage to describe how much a machine multiplies force or distance. Mechanical advantage is the ratio between output force and input force. It is also the ratio between input distance and output distance. The mechanical advantage equation is: output force mechanical advantage input distance input force output distance A machine with a mechanical advantage greater than one multiplies force. Such machines can help you move or lift large objects, such as cars and heavy boxes, more easily. Jacks and many pulleys multiply force. A machine with a mechanical advantage of one does not multiply force. Such machines only change the direction of the force. Some pulleys work this way. A machine with a mechanical advantage less than one multiplies distance. It also produces an output force that is smaller than the input force. Ramps work this way. Some of the joints in your body, such as your elbow, also work this way. CALCULATING MECHANICAL ADVANTAGE You can calculate mechanical advantage if you know input and output forces or distances. For example, imagine a jack that lifts a 9,900 N car with an input force of 150 N. What is the mechanical advantage of the jack? Follow these steps to solve this problem: Step 1: List the given and Step 2: Write the equation. Step 3: Insert the known values and solve for the unknown value. input force = 150 N output force = 9,900 N mechanical advantage = mechanical advantage output force input force mechanical advantage = 9,900 N 150 N mechanical advantage = Identify What does mechanical advantage measure? Apply Concepts How can you tell without doing any calculations whether a machine has a mechanical advantage greater or less than one? In a small group, brainstorm some ideas about how you could figure this out. Math Skills 10. Calculate A ramp is 5.0 m long and 1.5 m high. What is the mechanical advantage of the ramp? Show your work. (Hint: The height of the ramp is the output distance.) The jack has a mechanical advantage of 66. Therefore, the output force from the jack is 66 times greater than the input force. Interactive Reader 273 Work and Energy

6 Section 1 Review SECTION VOCABULARY mechanical advantage a number that tells how many times a machine multiplies force; it can be calculated by dividing the output force by the input force power a quantity that measures the rate at which work is done or energy is transformed work the transfer of energy to a body by the application of a force that causes the body to move in the direction of the force; it is equal to the product of the magnitude of the component of a force along the direction of displacement and the magnitude of the displacement 1. Apply Concepts A short ramp and a long ramp each reach a height of 1 m. Which ramp has a greater mechanical advantage? Explain your answer. 2. Calculate A student weighs 565 N. She climbs 3.25 m vertically up a flight of stairs. It takes her 12.6 s. What is her power output? Show your work. 3. Describe The student from the question above carries a stack of books up the same flight of stairs. If she still takes 12.6 s, how will her power output change? Explain your answer. 4. Compare What is the difference between work and power? 5. Apply Concepts A certain machine changes a large input force into a smaller output force. How does the machine affect the distance over which the force is applied? Explain your answer. Interactive Reader 274 Work and Energy