WorkSpring of Unknown LengthLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Problem 4-23</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
A spring obeying Hooke's Law is extended to a total length of 5 cm. To extend it beyond that to a total length of 10 cm requires 25 joules. To extend it further to a total length of 14 cm requires an additional 40 joules. Find the natural length of the spring.
Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, the unknown length of the spring, be given in centimeters.Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, the unknown spring constant, be given in Newtons per meter.The relevant equations can be written 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 and 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where the Units palette was used to include units.Control-drag the first equation.
Press the Enter key.Context Menu: Simplify\342\211\273SimplifyLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=simplify( );LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Control-drag the second equation.
Press the Enter key.Context Menu: Simplify\342\211\273SimplifyLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Using equation labels, form a sequence of the two simplified equations in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.
Press the Enter key.Context Menu: Solve\342\211\273SolveLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=solve( { } );LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=