Proportionality of frictional force

[Dennydont]

Homework Statement

A mass-spring system consisting of a mass of 2.9 kg attached to a spring is subject to a frictional force which is both proportional and opposite to the velocity. The mass is displaced from rest and oscillates back and forth with an ever decreasing amplitude. It is found that after 8.8 seconds the amplitude is half what it was originally. What is the value of the constant of proportionality for the frictional force?

I don't even know where to begin with this! What equations are relevant?! All I know is that the final answer should have units of kg/s or g/s.

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

I don't even know where to begin with this!

... yes you do!
How would you normally begin a problem with a mass and more than one force?
Note: you can start a problem without knowing how to finish it.

 

[Dennydont]

... yes you do!
How would you normally begin a problem with a mass and more than one force?
Note: you can start a problem without knowing how to finish it.

Well there is the equation for frictional force: F_f=μF_n

 

[Simon Bridge]

Thats the usual relation, it says the amount of friction is proportional to the amount of normal force, but the problem statement gives you a different one for this situation. Use that instead. What does the description say the friction is proportional to?

 

[Dennydont]

Thats the usual relation, it says the amount of friction is proportional to the amount of normal force, but the problem statement gives you a different one for this situation. Use that instead. What does the description say the friction is proportional to?

To the velocity, but it is also opposite to the velocity?

 

[Simon Bridge]

Well done, so how do you write that down as maths?

 

[Dennydont]

Well done, so how do you write that down as maths?

Good question... I don't know. The drag force equation?

 

[Simon Bridge]

Dont try to think of specific equations just yet. You are constructing a new equation... it may be one you have not seen before or it may be that, once you write it down, you'll recognize it. Just think of the maths as a language.

You can write out the maths for "the friction is proportional to the normal force" ok.
There is nothing here you have not done before.

 

[Sam Fielder]

Well done, so how do you write that down as maths?

So would we say that Ff=-vμ ?? To say that the frictional force is proportional and opposite to the velocity multiplied by a constant?

 

[haruspex]

So would we say that Ff=-vμ ?? To say that the frictional force is proportional and opposite to the velocity multiplied by a constant?

Please don't answer questions that were directed to the original poster of the thread. You could have asked that via a private conversation with Simon.

 

[Chestermiller]

Dennydont,

A more fundamental question: Have you drawn a free body diagram yet, or do you feel like you have advanced beyond the point where you need to use free body diagrams?

Chet