Question

- A variable force of 6x^−2 pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 17 ft. (Round your answer to two decimal places.)

____ ft-lb

- The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use the Midpoint Rule with n = 4 to estimate the work W done by the force in moving an object from x = 3 to x = 35.

x	3	7	11	15	19	23	27	31	35
f(x)	5	5.5	7.3	8.8	9.5	8.1	6.5	5.4	4.3

W = _____ J

- Suppose that 5 J of work is needed to stretch a spring from its natural length of 26 cm to a length of 37 cm.

(a) How much work is needed to stretch the spring from 31 cm to 35 cm? (Round your answer to two decimal places.)
____ J

(b) How far beyond its natural length will a force of 50 N keep the spring stretched? (Round your answer one decimal place.)
____ cm

- A spring has natural length 20 cm. Compare the work W₁ done in stretching the spring from 20 cm to 30 cm with the work W₂ done in stretching it from 30 to 40 cm. (Use k for the spring constant)

W₁ = ____ J

W₂ = ____J

- If 12 J of work are needed to stretch a spring from 14 cm to 18 cm and 20 J are needed to stretch it from 18 cm to 22 cm, what is the natural length of the spring?
____ cm