Find the work done in lifting a book as described: a) The book weighs 4 lbs and is lifted through 5 ft.

1. Find the work done in lifting a book as described:

a) The book weighs 4 lbs and is lifted through 5 ft.

b) The book has mass 4 kg and is lifted through 5 m.

2. An object located x units from a fixed starting position is moved along a straight path by a force of 10/(1 + x)2 pounds. How much work is done in moving the object through 9 feet?

3. The graph of a force function (in newtons) is shown. How much work is done by the force in moving an object through a distance of 8 meters?

1 2 3 4 5 6 7 8

4. A force of 10 lbs is required to hold a spring stretched 4 in beyond its natural length. How much work is done in stretching the spring from its natural length to 8 in beyond its natural length?

5. A spring has a natural length of 30 cm. If a 25 N force is required to keep it stretched to a length of 40 cm, how much work is required to stretch it from 30 cm to 40 cm?

? 69 For the given cable problem, do the following:

a) Draw a picture, and set up the Riemann Sum ?

Wi that approximates the work.

b) Express the work as an integral and evaluate it.

6. A heavy rope, 50 ft long and weighing 30 lbs hangs over the edge of a building. How much work is required to pull the rope to the top of the building?

7. For the rope in Problem (6), how much work is required to pull half the rope to the top of the building?

Hint: Consider the top and bottom halves separately.

8. A cable weighing 2 lbs/ft is used to lift 800 lbs of coal up a mineshaft 500 ft deep. Find the work done.

Hint: Consider the cable and coal independently.

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9. A 10 m long cable with a mass of 25 kg hangs from a hook. Find the work done in lifting the lower end of the chain (straight up) to hang from the same hook, as shown.

Hint: Be careful with the distance di.

y = 10

y = 0

Solutions to Selected Problems

1. a) 20 ft-lbs

b) 196 J

2. 9 ft-sbs

3. 180 J

4. 20

3 ft-lbs

5. 1.25 J

6. a) Wi = 3 5y

? i ?y

b) 750 ft-lbs

7. a) Top half: Wi = 3 5y

? i ?y

Bottom half: 15(25)

b) 562.5 ft-lbs

8. a) Cable: Wi = 2y ? i ?y

Coal: 800(500)

b) 650,000 ft-lbs

9. a) Wi = 24.5(10 ? 2y?i )?y

b) 612.5 J

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