Solve Spring Problem: Help for Homework Statement

[bulldog23]

Homework Statement

A moving 1.3 kg block collides with a horizontal spring whose spring constant is 491 N/m.

A) The block compresses the spring a maximum distance of 5.0 cm from its rest postion. The coefficient of kinetic friction between the block and the horizontal surface is 0.49. What is the work done by the spring in bringing the block to rest? REMEMBER: Work has a sign.

B) How much mechanical energy is being dissipated by the force of friction while the block is being brought to rest by the spring?

C) What is the speed of the block when it hits the spring?

Homework Equations

W=F_0*d

The Attempt at a Solution

I am unsure how to approach this problem. If someone could please walk me through it, that would help a lot! My teacher gave us this problem, but we haven't even learned this stuff yet. So please help me out!

 

[Hootenanny]

Let's take question (A) first. So, when the block collides with the srping it has some kinetic energy, when the block stops it has no kinetic energy. Some of this kinetic energy will be used to do work against friction, what do you think the rest of this kinetic energy will be used for?

 

[bulldog23]

Is the rest of the kinetic energy used to hold the spring in place?

 

[Hootenanny]

Is the rest of the kinetic energy used to hold the spring in place?

Not hold in place, but to compress the spring yes. So, do you know the expression for the potential energy stored in a compressed spring?

 

[bulldog23]

Is it F=kx?

 

[Hootenanny]

Is it F=kx?

Close, that's the force required to compress a spring by xm; how about the energy stored?

 

[bulldog23]

PE=1/2kx^2?

 

[Hootenanny]

PE=1/2kx^2?

Sounds good to me. So, how much potential energy is stored after the block collides with the spring?

 

[bulldog23]

So then do I plug in the 491 N/m for k and 5 m for x? If I do that I get 6137.5 J.

 

[Hootenanny]

So then do I plug in the 491 N/m for k and 5 m for x? If I do that I get 6137.5 J.

The value is correct, but what about the sign?

 

[bulldog23]

It should be negative because it is opposing the force of the block, right?

 

[bulldog23]

So is that all you have to do for part A?

 

[Hootenanny]

It should be negative because it is opposing the force of the block, right?

Yes, since the force extered by the spring is in the opposite direction to the direction in which the block is moving, the work is negative.

So is that all you have to do for part A?

Yup. Now for part (B) you do exactly the same, but this time for friction.

 

[bulldog23]

It says that the answer for part A is wrong though. Doesn't the coefficient of the kinetic friction play into the problem somewhere?

 

[Hootenanny]

It says that the answer for part A is wrong though. Doesn't the coefficient of the kinetic friction play into the problem somewhere?

Is this a Webassign problem? Try rounding your answer to 3sf. And no, the spring is still compressed the same amount regardless of friction, therefore, the work done by the spring will be the same.

 

[bulldog23]

I tried it again and it said that it was wrong. We must have gone wrong somewhere...

 

[Hootenanny]

I tried it again and it said that it was wrong. We must have gone wrong somewhere...

Wait, I see what's happened, we've used x = 5m, when actually x = 5cm = 0.05m

I can't believe I missed that.

 

[bulldog23]

So then the answer should be -.61375 J ? So then how do I do the same thing with friction for part B?

 

[Hootenanny]

So then the answer should be -.61375 J ?

Yes, but be careful, web assign is notoriously pedantic about accuracy and rounding, I would say use 3sf or the accuracy it tells you to use in the question.

 

[bulldog23]

Alright, it accepted the answer. I am lost when it comes to Part B

 

[Hootenanny]

Alright, it accepted the answer. I am lost when it comes to Part B

Do you know an expression for the friction force exerted by a surface on an object?

 

[bulldog23]

Is it -U_k*mgd?

 

[Hootenanny]

Is it -U_k*mgd?

I'm afraid not, do any of these look familiar?

 

[bulldog23]

Is it F_k=U_k *N?

 

[bulldog23]

Oh never mind I got part B. Can you help me with part C though?

 

[Hootenanny]

So you know that before the block collides with the spring it has some kinetic energy, after it's done work against the friction and the spring, it has no kinetic energy. So the total kinetic energy before the block collides with the spring would be...?