65 620
Assignments Done
99,2%
Successfully Done
In October 2018

Answer to Question #7254 in Calculus for LeighAnne Manwiller

Question #7254
Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 45 cm to a length of 66 cm. How much work is needed to stretch it from 60 cm to 74 cm? Your answer must include the correct units.
Expert's answer
Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 45 cm to a length of 66 cm. How much work is needed to stretch it from 60 cm to 74 cm? Your answer must include the correct units.

Let's make the following denominations:
L1 = 45 cm (natural length)
L2 = 66 cm
A1 = 2 J
L3 = 60 cm
L4 = 74 cm

We need to find the stiffness of the spring:
x1 = L2-L1 = 66 - 45 = 21 cm;
A1 = k*x1²/2 ==> k = 2*A1/x1² = 2*2/21² = 4/121.

Let's find the work needed to stretch a spring from 45 cm to 60 cm:
x2 = L3-L1 = 60 - 45 = 15 cm
A2 = k*x2²/2 = 4/121 * 15² / 2 = 450/121 J.

Let's find the work needed to stretch a spring from 45 cm to 74 cm:
x3 = L4-L1 = 74 - 45 = 29 cm
A3 = k*x3²/2 = 4/121 * 29² / 2 = 1682/121 J.

So, the work needed to stretch a spring from 60 cm to 74 cm is
A = A3 - A2 = 1682/121 - 450/121 = 112/11 J.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

Assignment Expert
29.01.13, 16:09

You're welcome! We are glad to be helpful.
If you really liked our service please press like-button beside answer field. Thank you!

Spencer
25.01.13, 04:50

Thank you!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions