Finding spring constant K and compression distance

[mpittma1]

Homework Statement

https://scontent-a-sjc.xx.fbcdn.net/hphotos-frc3/t1.0-9/10294335_1407511836191702_8633020308624670643_n.jpg

Homework Equations

PE=.5kx^2
F=-kx

The Attempt at a Solution

I honestly just don't know how to approach a problem where you have to find both the spring constant and the compression distance...

Ive tried employing conservation of momentum, I've tried working backwards with M1...

Im pretty sure I need to find an equation that would solve for either K or x and then use that to find the other value.

Am I on the right track?

 

[SammyS]

Homework Statement

https://scontent-a-sjc.xx.fbcdn.net/hphotos-frc3/t1.0-9/10294335_1407511836191702_8633020308624670643_n.jpg

Homework Equations

PE=.5kx^2
F=-kx

The Attempt at a Solution

I honestly just don't know how to approach a problem where you have to find both the spring constant and the compression distance...

I've tried employing conservation of momentum, I've tried working backwards with M1...

I'm pretty sure I need to find an equation that would solve for either K or x and then use that to find the other value.

Am I on the right track?

Conservation of momentum and conservation of energy will each be usefully to solve relevant aspects of this problem.


Can you see how you may find the the velocity that m₁ attains after the spring fully expands and before m₁ gets to the friction surface?

 

[mpittma1]

Conservation of momentum and conservation of energy will each be usefully to solve relevant aspects of this problem.


Can you see how you may find the the velocity that m₁ attains after the spring fully expands and before m₁ gets to the friction surface?

Ya i see that;

100N = .5M₁V₁²

so V₁ = 10m/s

right?

 

[paisiello2]

Start with conservation of momentum to get v2 in terms of v1.

You can get v1 from conservation of energy.

 

[SammyS]

Ya i see that;

100N = .5M₁V₁²

so V₁ = 10m/s

right?

Not what I had in mind.

100 N is the maximum force exerted by the spring. (1/2) mv² is Kinetic Energy. Those are not equal. They're totally different physical quantities.


Calculate the amount of work done by friction in bringing m₁ to rest.

 

[mpittma1]

Not what I had in mind.

100 N is the maximum force exerted by the spring. (1/2) mv² is Kinetic Energy. Those are not equal. They're totally different physical quantities.


Calculate the amount of work done by friction in bringing m₁ to rest.

Ya i noticed that after i posted.

i will try that though

 

[mpittma1]

Not what I had in mind.

100 N is the maximum force exerted by the spring. (1/2) mv² is Kinetic Energy. Those are not equal. They're totally different physical quantities.


Calculate the amount of work done by friction in bringing m₁ to rest.

wf = ukmgd = (.75)(2)(9.8)(2) = 29.4 J

 

[mpittma1]

would impulse momentum help here?

 

[SammyS]

would impulse momentum help here?

Not really.

Are you familiar with the Work - Energy Theorem ? It tells you the relationship between work done and change in Kinetic Energy.

 

[mpittma1]

Not really.

Are you familiar with the Work - Energy Theorem ? It tells you the relationship between work done and change in Kinetic Energy.

Ya W_net=ΔKE

So, set 100N = ΔKE of mass 1 and find the initial velocity produced by the spring?

 

[mpittma1]

disregard that last post its the same mistake as the first time...

 

[mpittma1]

K I am getting close;

.5m₁v₁²=wf

v₁ = sqrt(29.4) = 5.422

and to find v2

v2=(m₁v₁/m₂) = 1.36m/s

 

[mpittma1]

ugh finally got it!

thanks for all the help!

 

[NascentOxygen]

Where did that 29.4 value materialize from?

 

[mpittma1]

Where did that 29.4 value materialize from?

Its the value of the work done by friction

W_f=μk*m*g*d

 

[NascentOxygen]

Its the value of the work done by friction

W_f=μk*m*g*d

Ah. I can now see that you worked that out earlier.