How much work is required to stretch a spring by an additional 4.0 cm?

[Calpalned]

Homework Statement

If it requires 5.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additioanl 4.0 cm?

Homework Equations

Force done on spring: $F_P = kx$
Work: $\frac {1}{2}kx^2$

The Attempt at a Solution

I solved for K and got 25000.
Plugging it into the equation for the work on a spring, I get $\frac {1}{2}(25000)(0.06)^2$ where 0.06 is the total length stretched. Doing it that way, I get the right answer.

However, why can't I use the original information (5 J) and simply add it to the remaining 4 cm? $5 + \frac {1}{2}(25000)(0.04)^2$ Work is area under the force/displacement graph. Therefore, both ways should work, but that's the case.

 

[SammyS]

Homework Statement

If it requires 5.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additioanl 4.0 cm?

Homework Equations

Force done on spring: $F_P = kx$
Work: $\frac {1}{2}kx^2$

The Attempt at a Solution

I solved for K and got 25000.
Plugging it into the equation for the work on a spring, I get $\frac {1}{2}(25000)(0.06)^2$ where 0.06 is the total length stretched. Doing it that way, I get the right answer.

However, why can't I use the original information (5 J) and simply add it to the remaining 4 cm? $5 + \frac {1}{2}(25000)(0.04)^2$ Work is area under the force/displacement graph. Therefore, both ways should work, but that's the case.

That's because $(0.06)^2\ne(0.02)^2+(0.04)^2\$ .

 

[haruspex]

Your force-displacement graph should be a triangle. Mark O, A, B, C at 0, 2, 4, 6 cm on the x axis, with D, E, F on the slope above A, B, C respectively. You want area ACFD. You won't get that by adding OAD to OBE.