Energy/work on incline plane with springs

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SUMMARY

The discussion centers on calculating the velocities of two masses, 25 kg (m1) and 30 kg (m2), connected by a spring with a spring constant of 200 N/m, when m1 is pulled down an incline by 20 cm. The participants utilize energy conservation principles, noting that the spring stretches the same distance as m2 rises. Key equations include the conservation of energy equation: (0.5)kx² + m2gh1 = m2gh2 + (0.5)m2v². The conclusion emphasizes that both masses will have the same velocity when the spring returns to its unstretched state, despite the complexities introduced by the spring force and gravitational effects.

PREREQUISITES
  • Understanding of Newton's Second Law (NII) and forces acting on connected masses.
  • Knowledge of conservation of energy principles in mechanical systems.
  • Familiarity with spring mechanics, specifically Hooke's Law and spring constants.
  • Basic trigonometry to resolve forces and heights in inclined planes.
NEXT STEPS
  • Study the application of conservation of energy in systems with springs and pulleys.
  • Learn about the dynamics of connected masses and tension in strings.
  • Explore the effects of friction on inclined planes and how it alters energy calculations.
  • Investigate kinematic equations to relate acceleration and velocity in systems with multiple masses.
USEFUL FOR

Physics students, educators, and anyone interested in understanding mechanics involving springs and inclined planes, particularly in solving problems related to connected masses and energy conservation.

  • #31
Yep. You should solve using energy. My last post described how I would do it. You can answer haruspex's questions to get the same result.
 
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  • #32
Yea I know I messed up I thought 20 was the height for a second. Messed up but it is mg20 sin40
 
  • #33
Panphobia said:
Yea I know I messed up I thought 20 was the height for a second. Messed up but it is mg20 sin40

Well...If the initial height of m1 is 20+h ,then height of m1 at t=0 will be (20+h-20sin40°) .

Do you agree ?
 
  • #34
I do agree
 
  • #35
Good...

So the total mechanical energy of the system at t=0 =m1g(20+h-20sin40°) + m2g(40) + (1/2)k(20)2

Do you get the same expression ?
 
  • #36
ohhhhhhhhhhhh myyyyy, I didn't think of doing that, just adding the energies of m1 and m2. Now I get it so m1g(20+h-20sin40°) + m2g(40) + (1/2)k(20)2 = (1/2)m1v^2 + (1/2)m2v^2 + m2g20 + m1g(20 + h), then the m1g distributes and cancels with the mgh on the other side, and now it is solvable. Is that right?
 
  • #37
Panphobia said:
ohhhhhhhhhhhh myyyyy, I didn't think of doing that, just adding the energies of m1 and m2. Now I get it so m1g(20+h-20sin40°) + m2g(40) + (1/2)k(20)2 = (1/2)m1v^2 + (1/2)m2v^2 + m2g20 + m1g(20 + h), then the m1g distributes and cancels with the mgh on the other side, and now it is solvable. Is that right?

Excellent!

Well done :smile:
 
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  • #38
Man, you know what my problem is? I keep thinking back to high school physics where my teacher was awful, if I only used the knowledge I learned from the Uni lectures, I would be so much better off haha, but thanks :D
 
  • #39
m1g(20+h-20sin40°) + m2g(40) + (1/2)k(20)2 = (1/2)(m1+2)v2+ m2g(20) + m1g(20+h)

Rearranging a bit , -m1g(20sin40°) + m2g(20) + (1/2)k(20)2 = (1/2)(m1+2)v2

The above is what haruspex referrred in Post#27 .

I did not want to confuse you .First I wanted you to look at this approach and then thought of taking you to the better approach mentioned by haruspex .

Initially I had thought on the similar lines as haruspex ,but wasn't sure if that was simpler for you .
 
Last edited:
  • #40
If my dumb self had thought of treating the objects and spring as one whole system, then everything would have made so much more sense, but thanks though, your assistance really helped, now I actually know the concept and when the exam comes I will actually know what to do in this type of situation.
 
  • #41
Good luck :thumbs:
 

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