Skills Worksheet Math Skills Work After you study each sample problem and solution, work out the practice problems on a separate sheet of paper. Write your answers in the spaces provided. PROBLEM A car has run out of gas. Fortunately, there is a gas station nearby. You must exert a force of 715 N on the car in order to move it. By the time you reach the station, you have done 2.72 10 4 J of work. How far have you pushed the car? SOLUTION Step 1: List the given and unknown values. Given: force, F = 715 N work, W = 2.72 10 4 J Unknown: distance, d =? m Step 2: Rearrange the work equation to solve for distance. work = force distance W = Fd Step 3: Insert the known values into the equation, and solve. d = 38.0 m PRACTICE 1. You must exert a force of 4.5 N on a book to slide it across a table. If you do 2.7 J of work in the process, how far have you moved the book? Holt Science Spectrum 83 Work and Energy
2. A catcher picks up a baseball from the ground. If the unbalanced force on the ball is 7.25 10 2 N and 4.35 10 2 J of work is done to lift the ball, how far does the catcher lift the ball? 3. The smallest bird is the Cuban bee hummingbird, which has a mass of only 1.7 g. If this bird did 8.8 10 4 J of work by exerting an upward force of 3.4 10 4 N, how far did it fly? 4. The world s most powerful tugboats are built in Finland. One of these boats can do 9.8 10 7 J of work through a distance of 35 m. What is the force exerted by the tugboat? 5. A child pulls a sled up a snow-covered hill. In the process, the child does 405 J of work on the sled. If she walks a distance of 15 m up the hill, how large a force does she exert on the sled? Holt Science Spectrum 84 Work and Energy
Math Skills continued PROBLEM Suppose a weightlifter s power output is 178 W during the time he does 3,310 J of work on the weights. How long does it take the weightlifter to raise the weights? SOLUTION Step 1: List the given and unknown values. Given: power, P = 178 W work, W = 3,310 J Unknown: time, t =? s Step 2: Rearrange the power equation to solve for time. Step 3: Insert the known values into the equation, and solve. t = 18.6 s PRACTICE 6. In order to sail through the frozen Arctic Ocean, the most powerful icebreaker ever built was constructed in the former Soviet Union. At the heart of the ship s power plant is a nuclear reactor with a power output of 5.60 10 7 W. How long will it take for this power plant to do 5.35 10 10 J of work? Holt Science Spectrum 85 Work and Energy
7. The heaviest loads ever raised were part of the offshore Ekofisk complex in the North Sea. The 4.0 10 7 kg complex was raised 6.5 m by over a hundred hydraulic jacks. The work done on the complex during the raising was approximately 2.6 10 11 J. Suppose the power output of all the jacks was 5.7 10 8 W. How long did it take the jacks to raise the complex? 8. Borax was mined in Death Valley, California, during the nineteenth century. It was transported from the valley by massive86wagons, each pulled by a team of 21 mules. Suppose each mule s power output was 746 W (about 1 hp). If in a certain time interval the total work done by the team on the wagon was 2.35 10 7 J, how long was that interval of time? 9. A certain steam turbine is designed to be used as both a power generator and as a pump. When used as a generator, the turbine provides enough power to do 3 10 10 J of work in 1 min. What is the power output of the turbine? 10. The space shuttle, which was first launched on April 12, 1981, is the world s first reusable space vehicle. The shuttle is placed in orbit by three engines that do 1.4 10 13 J of work in 8.5 min. What is the power output of these engines? Holt Science Spectrum 86 Work and Energy
Skills Worksheet Math Skills Mechanical Advantage After you study each sample problem and solution, work out the practice problems on a separate sheet of paper. Write your answers in the spaces provided. PROBLEM A wheelbarrow has a mechanical advantage of 2.2. The output distance extends from the load s center of mass to the wheel, and the input distance is from the handles to the wheel. For an output distance of 0.45 m, what is the input distance? SOLUTION Step 1: List the given and unknown values. Given: mechanical advantage = 2.2 output distance = 0.45 m Unknown: input distance =? m Step 2: Write the mechanical advantage equation, and rearrange it to solve for input distance. Because the given information involves only distance, only the second form of the equation is needed. Step 3: Insert the known values into the equation, and solve. input distance = 2.2 0.45 m input distance = 0.99 m PRACTICE 11. If an input force of 202 N is applied to the handles of the wheelbarrow in the sample problem, how large is the output force that just lifts the load? Holt Science Spectrum 87 Work and Energy
12. Suppose you need to remove a nail from a board by using a claw hammer. What is the input distance for a claw hammer if the output distance is 2.0 cm and the mechanical advantage is 5.5? 13. An axe is driven into a piece of wood a distance of 3.0 cm. If the mechanical advantage of the axe is 0.85, how far is the wood split? 14. The mechanical advantage of a wheel and axle is 8.93 10 2. If the wheel s output force is 2.22 10 3 N, what is the input force that turns the axle? 15. An Archimedean screw is a screw within a closely fitting cover, so that water can be raised when the screw is turned. The screw has a mechanical advantage of 12.5. If the screw is turned several times, so that the input distance is 1.57 m, how much water has been lifted upward by the screw? Holt Science Spectrum 88 Work and Energy