Find the max compression of the spring

[isukatphysics69]

Homework Statement

Homework Equations

ke = .5mv^2

The Attempt at a Solution

E_i= .5m₁v²₁ + .5m₂v²₂ + PE_s(PE_s initially 0)

E_f= .5m₁v²₁ + .5m₂v²₂ + PE_s(PE_s is now .5(16.2)(.267²)set them equal and then solve for velocity right? is this the right approach?

 

[haruspex]

Homework Statement

View attachment 225073

Homework Equations

ke = .5mv^2

The Attempt at a Solution

E_i= .5m₁v²₁ + .5m₂v²₂ + PE_s(PE_s initially 0)

E_f= .5m₁v²₁ + .5m₂v²₂ + PE_s(PE_s is now .5(16.2)(.267²)set them equal and then solve for velocity right? is this the right approach?

What about GPE?

 

[Sergio Rodriguez]

Why do you use two different velocities for two tied bodies?
And the system is set in motion by the gravity, and there is no GPE in the equations.

 

[isukatphysics69]

omg thank you guys completely forgot gpe also yes i know the velocities are the same but just labeled like that thank you
@haruspex @Sergio Rodriguez

 

[isukatphysics69]

ok what is going on here i took into account gpe and got 1.59m/s and incorrect
GPE = mgdcosθ
initially 0 because distance was 0 at initial state
The energy of the whole system is initially 0

 

[isukatphysics69]

wait a second i will try something here i see something wrong. spe is negative, the spring wants to snap back i was using positive

 

[isukatphysics69]

ok i need help
initial energy is 0 for this system, final energy is
E_FINAL = .5m₁v²_FINAL + .5m₂v²_FINAL +.5(16.2)(.267²)+((.481)(9.8)(-.267))
So

0 = .5m₁v²_FINAL - .5m₂v²_FINAL +.5(16.2)(.267²)+((.481)(9.8)(-.267))
solve for v_FINAL
why is this not correct?

 

[haruspex]

ok i need help
initial energy is 0 for this system, final energy is
E_FINAL = .5m₁v²_FINAL + .5m₂v²_FINAL +.5(16.2)(.267²)+((.481)(9.8)(-.267))
So

0 = .5m₁v²_FINAL - .5m₂v²_FINAL +.5(16.2)(.267²)+((.481)(9.8)(-.267))
solve for v_FINAL
why is this not correct?

Why the sign change on the second term?

 

[isukatphysics69]

Why the sign change on the second term?

sorry that is not what i meant i meant

0 = .5m₁v²_FINAL + .5m₂v²_FINAL -.5(16.2)(.267²)+((.481)(9.8)(-.267))

i meant to put negative spring potential energy sorry for confusion

 

[isukatphysics69]

ok i just got the answer by doing something i was telling myself not to do
so it says speed. I was getting a negative value and i was going to square root it but knew i didn't want to square root a negative. since it says speed i decided to omit the negative and got the correct answer of 1.37m/s

 

[isukatphysics69]

0 = .5m₁v²_FINAL - .5m₂v²_FINAL - .5(16.2)(.267²)+((.481)(9.8)(.267))

and solving for v gave the correct answer

couple of things here, i thought that the ((.481)(9.8)(.267)) at the end of the equation should have been ((.481)(9.8)(-.267)) because it was moving downward
and when i was doing the algebra i got a negative value under the square root. i had to multiply it by negative 1 to get a positive and then took the square root and got the correct answer. My gut was telling me not to do that for hours and i have tried this way earlier and saw a negative under the square root and instantly gave up and tried a different approach.

 

[haruspex]

i meant to put negative spring potential energy

Why? The KE and spring PE are both gains in energy. The only energy lost is the GPE.

ok i just got the answer by doing something i was telling myself not to do
so it says speed. I was getting a negative value and i was going to square root it but knew i didn't want to square root a negative. since it says speed i decided to omit the negative and got the correct answer of 1.37m/s

Your reasoning was correct. v² should not have turned out negative.
I am mystified as to how you got the right answer from that equation.
Go back to your post #7, correct the sign on the m₂v² term and try again.

 

[Sergio Rodriguez]

0 = .5m₁v²_FINAL - .5m₂v²_FINAL - .5(16.2)(.267²)+((.481)(9.8)(.267))

and solving for v gave the correct answer

Yes, the KE is always positive.
The GPE could be zero at the lowest level and positive at the initial position or begin with zero and negative later. But the SPE is positive because the spring is stretching and gaining energy.