Speed of mass on spring at 0.05 m displacement

[Dark Visitor]

A mass of .4 kg, hanging from a spring with a constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through a point at .05 m displacement? The starting displacement of the mass is .10 m from its equilibrium position.

* zero
* 1.4 m/s
* 1.7 m/s
* 1.2 m/s



I am confused with this one. I don't know where to begin. Any help would be appreciated. I need to have this done by Monday. Thanks.

 

[ideasrule]

Have you tried the conservation of energy?

 

[Dark Visitor]

How do I do that? I mean I know what it is, but what numbers go where?

 

[denverdoc]

This is a bit like the pendulum problem we just did. The relevant eqns are F=-ky where k is the force constant of the spring (given) Also, if we are to take ideasrule tip, we know that the energy (potential) stored in the spring is 1/2ky^2.

When the spring-mass is set into motion some of the potential energy in the spring will be converted to kinetic energy but the sum is always the same, ie

1/2mv^2+1/2ky(t)^2=1/2k(y')^2 where y(t) is the location as a function of time and relative to the equilibrium position and y' is the equilibrium position with the mass. I believe this approach allows us to ignore the potential energy from gravity. Try it and let me know. In this case, y'=0.1 and y(t)=0.05

 

[Dark Visitor]

I see what you're saying, but how do I find k for all of the equations? I know I probably have to use F = -ky, but how do I use it?

 

[denverdoc]

I see what you're saying, but how do I find k for all of the equations? I know I probably have to use F = -ky, but how do I use it?

The K is given. This is the 80N/m. Using energy conservation, you should not have to use F=-ky. Sorry if I misled you, I didn't realize that K was given and thought we had to solve for it using that.

 

[Dark Visitor]

Just to make sure I am doing this right, I am using the equation you gave me before to find v?

 

[denverdoc]

Just to make sure I am doing this right, I am using the equation you gave me before to find v?

yes, the one that has elements of potential and kinetic energy.

 

[Dark Visitor]

Okay, I finally got .38729 as my velocity.

 

[denverdoc]

show some work, I'll check in the meantime.

 

[Dark Visitor]

Okay, try your best to follow along. It's hard to type something like this:

v = $$\sqrt{}(1/2(80 N/m)(.1 m)² - 1/2(80 N/m)(.05 m)²)/ 1/2(4 kg)$$

Which I got:

v = $$\sqrt{}(.4 - .1)/2)$$

which led me to that answer. (SUP means exponent, so (SUP 2 SUP) means squared. It messed that up for some reason.

 

[denverdoc]

Hmmm, I get a different answer than given as well, but it is 3.87m/s. Let me think about this for a minute, I'm wondering if he is giving the equilibrium of the spring w/o the mass.

 

[denverdoc]

Well i did the math again, and got 1/2mv^2=1/2 k(0.01-0.0025)/m

v^2=80(0.0075)/.4=1.5 so I'm sticking with 1.2 for the answer. But no guarantees.

 

[Dark Visitor]

But 1.5 wasn't an answer. Are we going to stick with 1.2? And why 1.2?

 

[Dark Visitor]

So should I just say 1.2? And how do I show how I arrived at that answer?

 

[denverdoc]

So should I just say 1.2? And how do I show how I arrived at that answer?

1.5 was v^2 so v=1.22 Your work was fine, just recheck the math.

 

[Dark Visitor]

Yes! I found my mistake. And you were right. Thanks a lot.

 

[Dark Visitor]

Yes! You were right, and I checked it and found my error. Thank you!