10.8.1 An Introduction to Work

Question 1

An Introduction to Work

Answer 1

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

Question 2

note

Answer 2

• Most people have a good idea of what work means to them, but in physics and mathematics work has a very specific meaning.
• Work is the energy used when moving an object. For work to be done, a force must be applied to an object and that object must move in the direction of the force. Thus, pushing against a wall might take a lot of effort, but doesn’t do any work.
• When a force is constant, work can be found by multiplying the magnitude of the force by the change in distance.
• But forces do not have to be constant. To find the work done using a variable, or changing, force you have to use calculus. F(x) means the force at a particular x-value. It’s a notational way of saying “changing force.”
• Notice that the integral looks a lot like the formula for a constant force. The force is multiplied by a change in distance, this time dx. The integral sums up all the infinite little pieces.

Question 3

Which of the following is the work done by a non-constant force F (x) = −x applied to an object moving along the x‑axis from 0 to 2?

Answer 3

−2

Question 4

Which of the following statements about work is not correct?

Answer 4

For a changing force, work is the product of the force and the change in distance.

Question 5

Which of the following is the work done by a constant force F moving an object along a straight line from a to b ?

Answer 5

W=F⋅(b−a)

Question 6

Which of the following is the work done by a non-constant force F = F (x) = x moving an object along the x‑axis from 0 to 2?

Answer 6

2

Question 7

Suppose you lift a weight of 20 lb a vertical distance of 35 ft. Which of the following shows the work that has been done?

Answer 7

700 foot-pounds

Question 8

Which of the following is the work done by a non-constant force F(x)=sinx moving an object along the x-axis from 0 to π?

Answer 8

2

Question 9

Which of the following is the work done by a changing force F = F (x) moving an object along a straight line from a to b ?

Answer 9

W=∫baF(x)dx

Question 10

If a horizontal force of 60 newtons is applied to a heavy box in order to push it a distance of 20 meters along a rough floor, which of the following is the work done by the force?

Answer 10

1200 newton-meters

Question 11

Which of the following is the work done by a non-constant force F (x) = x moving an object along the x‑axis from 2 to 0?

Answer 11

−2

Question 12

Let W1 be the work done by a constant force F moving an object along a straight line for a distance D. Let W2 be the work done by a constant force 3 F moving an object along a straight line for a distance D/3. Compare W1 and W2.

Answer 12

W1 = W2