Calculus
posted by Kaitlyn .
Suppose that 5 J of work is needed to stretch a spring from its natural length of 28 cm to a length of 36 cm.
(a) How much work is needed to stretch the spring from 32 cm to 34 cm? (Round your answer to two decimal places.)
(b) How far beyond its natural length will a force of 15 N keep the spring stretched? (Round your answer one decimal place.)

W = (1/2) k x^2
where x is the stretch or compress length
here x = .36  .28 = .08 meter
so
5 = .5 k (.0064)
k = 1563 N/m so (1/2) k = 781
a)
work to .34  work to .32
subtract the .28 from both
.06 and .04
= 781 (.06^2.04^2)
=1.562 J
b) F = k x
15 = 1563 * x
x = .00960 m
= .96 cm
Respond to this Question
Similar Questions

Calculus
If 6 J of work is needed to stretch a spring from 10cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14cm, what is the natural length of the spring? 
Calculus
If 9 J of work are needed to stretch a spring from 9 cm to 10 cm and 15 J are needed to stretch it from 10 cm to 11 cm, what is the natural length L of the spring? 
CALCULUS
If 6 J of work are needed to stretch a spring from 12 cm to 13 cm and 10 J are needed to stretch it from 13 cm to 14 cm, what is the natural length L of the spring? 
college physics
To stretch a spring 7.00 cm from its unstretched length, 16.0 J of work must be done. What is the force constant of this spring? 
Calculus
If the work required to stretch a spring 1 ft beyond its natural length is 6 ftlb, how much work is needed to stretch it 6 in. beyond its natural length? 
Calculus
If 27 J of work are needed to stretch a spring from 18 cm to 24 cm and 45 J are needed to stretch it from 24 cm to 30 cm, what is the natural length of the spring? 
Calculus
if the work required to stretch a spring 1 ft beyond its natural length is 12 ftb, how much work is needed to stretch 9 inches beyond its natural length? 
AP calculus
If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring? 
Calculus
If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring? 
Calculus 2
Suppose that a spring has a natural length of 25 cm, and that 8 J of work is needed to stretch from a length of 50 cm to 80 cm. How far beyond its natural length will a force of 32 N keep the spring stretched?