10.8.2 Calculating Work Flashcards Preview

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Flashcards in 10.8.2 Calculating Work Deck (12):
1

Calculating Work

• Work is the energy used when applying a force over a distance.
• For a changing or variable force F(x) on [a, b], work is given by the integral

2

note

- Work is the energy used to move an object. If the object doesn’t move in the direction of the force, then no work is done.
- Finding the work done by a constant force is pretty simple. You just multiply the magnitude of the force by the change in distance.
- Work is measured in force units times distance units. Be careful when talking about work. You have to make sure you are using the right units.
- For a variable force, work is computed using a definite
integral.
- Consider this example. Remember that if Prof. Burger didn’t move the refrigerator, he would have done no work no matter how hard he pushed.
- The force Prof. Burger is using to move the refrigerator is a variable force defined in terms of x.
- To calculate the work, plug the force and the positions into the work formula.
- Remember, the natural log of one is zero.
- The force unit is the pound (lb). The distance unit is the foot (ft). Thus, the work unit is the foot-pound (ft-lb).

3

A force described by F (x) = x − 2 lb (where x > 0) acts between x = 2 ft and x = k ft. A total of 162 lb-ft of work is done. What is k ?

20 ft

4

A refrigerator is pushed 10 feet across a kitchen with a constant force of 50 lb. How much work is done moving the refrigerator?

500 ft-lb

5

A crane raises a 12,000 N marble sculpture at a constant velocity onto a pedestal 1.5 m above the ground outside an art museum. How much work is done by the crane?

18,000 N-m

6

Which results in the greatest amount of work?

Applying a force of F (x) = x N over a distance of 8 m.

7

What is the work done by a force described by F=100sinθlb over the distance betweenθ=0 and θ=π ft?

200 lb-ft

8

What is the work done by a force described by F = 8x^ 3 + 6x^ 2 + 4x + 2 N over the distance between x = 0 and x = 10 m?

22,220 N-m

9

Evaluate the following as true or false:
The work done by a varying force F over a distance D is equal to the work done by the average value of the force F held constant over the entire distance D.

true

10

Which results in the least amount of work?

Applying the force F = 4x lb over the distance from x = 0 to x = 3.

11

Which of the following is not an acceptable unit for work?

kg-cm

12

What is the work done by a force F = 8/x lb over the distance between x = 1 and x = 9 ft?

8 ln 9 ft-lb

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