# Spring Force Problem

1. Jan 6, 2006

### PrudensOptimus

(a). Since K = W = Integral ( F dx )

and F = Fx = -6x

K = -3 (x ^2) evaluate from 0 to 4
= 48
m/2 v^2 = 48
v = 6.9m/s

correct?

(b). since m/2 v^2 = -3x^2
and v = 5

x = sqrt ( -25/3 )

is not right because it would give me a complex number...

2. Jan 6, 2006

### daniel_i_l

In this case the body had an initial speed at x=0 (otherwise how could it have a positive velocity at x=3)
Find the initial velocity using the velocity at x=3, then you should get the correct answers for a and b.

3. Jan 6, 2006

### andrevdh

Have you done SHM, because this is such type of problem? You can therefore use the SHM equations (or try to derive them yourself!). Note that since
$$F=-6x$$
we have that
$$a=-\frac{6}{m}x$$
which gives
$$a=-\omega^2x$$
Not to confuse you, but as the problem is stated one might think that the force also has an y-component (which I think is not the case, since then it is not possible to answer the questions).

4. Jan 6, 2006

### Tide

HINT: (a) The work done represents the change in kinetic energy.

HINT: (b) The change in potential plus kinetic energy is 0.

5. Jan 6, 2006

### PrudensOptimus

so the sum of all external forces = 0?

6. Jan 6, 2006

### Tide

Energy is conserved so