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Old Mar 9th 2018, 10:28 AM   #1
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Work and Energy - spring

Referring to Figure 2, the collar A (mass = 20 kg),is released from rest and slides down the rough rod (μ = 0.4), impacting the spring (k = 1.6 kN/m) after travelling a distance L of 0.5m.
The rod is inclined at an angle θ = 60˚. Calculate, (i), the velocity of the collar at the moment
of impact with the spring, and, (ii), the maximum compression of the spring.

https://imgur.com/TorENhp - Link to figure 2

I did the first part and got the right velocity - 2.56 m/s but I am having troubles with the second part. I know that at the beginning there is only Epe (potential energy). Considering gravity acts vertically down then Epe = mgLsin60 , right? And that energy is going to be equal to the energy in the second compressed state = -mgxsin60 + 1/2 k(-x)^2
Are my assumptions correct? I am a bit confused whether the heights should be L and x respectively or Lsin60 and xsin60. What about Es? Would it be equal to 1/2 kx^2 or 1/2 k(xsin60)^2?
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Old Mar 9th 2018, 11:12 AM   #2
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Work and Energy - spring

You should also add the work done by friction. This will be
Mg*(Mu)*Cos(60)*(0.4)*(X)
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Old Mar 9th 2018, 12:02 PM   #3
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Hello Veirian...

In problems with springs, I always liked to include the spring in the system.
I might be late in replying (to help) but here are a couple of similar examples
of possible interest.

1) This is a cohort of your problem.
Box Bounces Between Springs | THERMO Spoken Here!

2) Here I model the linear spring internal energy as U = U[T, (Lo - L)].
Rock Falls onto a Spring | THERMO Spoken Here!

Good luck with your studies... TSH
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