Calculating Velocity Using Spring Force and Energy Conservation

[driven4rhythm]

Homework Statement

http://img682.imageshack.us/img682/8177/f141.jpg http://g.imageshack.us/img682/f141.jpg/1/
If the block is subjected to a force of = 500 , determine its velocity when = 0.6 . When = 0, the block is at rest and the spring is uncompressed. The contact surface is smooth. The spring is placed between the wall and the 6-block.

Homework Equations

Unsure

The Attempt at a Solution

I converted F to F along x-axis and it's equal to 400N. I took the integral of F=k*ds from 0 to .6 and got 300N in the negative x direction. I know that as s changes the force does and thus the acceleration is different all the time. I just can't figure out what to do with the spring force.

 

[AEM]

Recall that Newton's law actually says,

ma = The sum of the forces. Therefore you need to start with

$$m\frac{d^2x}{dt^2} = 400 - kx$$

 

[PhanthomJay]

Homework Statement

http://img682.imageshack.us/img682/8177/f141.jpg http://g.imageshack.us/img682/f141.jpg/1/
If the block is subjected to a force of = 500 N[/color], determine its velocity when s[/color] = 0.6 m[/color] . When s[/color] = 0, the block is at rest and the spring is uncompressed. The contact surface is smooth. The spring is placed between the wall and the 6 kg[/color] block.

Homework Equations

Unsure

The Attempt at a Solution

I converted F to F along x-axis and it's equal to 400N. I took the integral of F=k*ds from 0 to .6 and got 300N in the negative x direction. I know that as s changes the force does and thus the acceleration is different all the time. I just can't figure out what to do with the spring force.

See my notes above in red. They are my assumtions, since you left out the units. You are going to get into some difficulty by using your method, because the spring force is a variable force. You can still determine it as an average force ( ks/2), and use Newton's laws and the kinemaric equations to solve for v, but it's easier to use conservation of total energy, if you are familiar with it . Are you?

 

[driven4rhythm]

See my notes above in red. They are my assumtions, since you left out the units. You are going to get into some difficulty by using your method, because the spring force is a variable force. You can still determine it as an average force ( ks/2), and use Newton's laws and the kinemaric equations to solve for v, but it's easier to use conservation of total energy, if you are familiar with it . Are you?

Sorry I didn't realize when I copied the problem over that the numbers and such were pictures and not text. Yes, I am familiar with conservation of energy.

 

[PhanthomJay]

Sorry I didn't realize when I copied the problem over that the numbers and such were pictures and not text. Yes, I am familiar with conservation of energy.

Good, give it a try using the energy method, it'll save you a lot of heartache, I would think. Just don't confuse the conservation of mechanical energy equation (delta K + delta U = 0) with the conservation of total energy equation (delta K + delta U = work done by non conservative forces). Use the latter.