10.8.2 Calculating Work

Question 1

Calculating Work

Answer 1

• 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

Question 2

note

Answer 2

• 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).

Question 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 ?

Answer 3

20 ft

Question 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?

Answer 4

500 ft-lb

Question 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?

Answer 5

18,000 N-m

Question 6

Which results in the greatest amount of work?

Answer 6

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

Question 7

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

Answer 7

200 lb-ft

Question 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?

Answer 8

22,220 N-m

Question 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.

Answer 9

true

Question 10

Which results in the least amount of work?

Answer 10

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

Question 11

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

Answer 11

kg-cm

Question 12

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

Answer 12

8 ln 9 ft-lb