Why am I getting a negative? (Energy conservation)

[jegues]

Why am I getting a negative!? (Energy conservation)

Homework Statement

2kg block slides on a rough table with uk = 0.3, just before the block hits the spring V0 = 1.3 m/s. k = 120N/m. How far is the spring compressed?

Homework Equations

Ki + Us = Kf + Us - Eth

The Attempt at a Solution

Okay just before it touches the spring, what energy does it have?

Ki = 1/2(2)(1.3)^2 = 1.68 J

1.68J + 0 = 0 + 1/2kx^2 -fx
0 = 1/2kx^2-mgukx-1.68
0 = 60x^2 -5.88x - 1.68
x= 0.22 or x= -0.13

Why is my answer negative!?

The only thing i can think of that intially the spring is not compressed. (x=0) Once you compress the spring, the spring must get smaller, what's smaller than 0? -0.13

Can anyone clearly explain to me why this is negative!?

 

[jegues]

Bump, exams tomorrow hoping for an answer ASAP!

 

[hamster143]

Ki + Us = Kf + Us - Eth

Should be Ki + Us = Kf + Us + Eth.

Initial kinetic energy of the block, plus initial potential energy of the spring, equals: final kinetic energy of the block, plus final potential energy of the spring, plus energy expended to friction.

Then you solve the quadratic equation and you get two solutions, the negative solution is unphysical, the positive solution is your answer.

 

[jegues]

Oh I thought of it this way,

I start with a kinetic energy, and all of this energy is going to be converted into to spring energy, BUT there's friction, so just take away the energy friction consumes.

Is this wrong?

 

[hamster143]

Oh I thought of it this way,

I start with a kinetic energy, and all of this energy is going to be converted into to spring energy, BUT there's friction, so just take away the energy friction consumes.

Is this wrong?

Then you have to put the friction term on the left, with the '-' in front of it.

 

[jegues]

Thats correct, hopefully I can fix this understanding in my head before tomorrow :S.

Any tips how to think/understand this better?

 

[jegues]

Could it be as simple as saying, regardless of the circumstances of the problem my thermal energy is always going to be on the INITIAL side of my equation(for energy conservation) and it will always be NEGATIVE?

 

[jegues]

Could it be as simple as saying, regardless of the circumstances of the problem my thermal energy is always going to be on the INITIAL side of my equation(for energy conservation) and it will always be NEGATIVE?

Bump anyone know if what I stated above is correct?

 

[blaze33]

lol i was stuck in the same question as well but its kinda easy
and don't break ur head with this stuff.. just remember the equation u won't have time to think about it on the exam