Spring constant and conservation of energy

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SUMMARY

The discussion centers on calculating the launching speed of a ball from a pinball machine using a spring with a force constant of 36 N/cm. The spring is compressed by 4.25 cm, and the incline angle is 10.1 degrees. The relevant equations include potential energy (PE = 0.5k(xf - xi)^2) and kinetic energy (KE = 0.5mv^2). The solution involves applying the conservation of energy principle, equating the spring's potential energy to the kinetic energy of the ball at the release point, while also considering gravitational potential energy due to the incline.

PREREQUISITES
  • Understanding of spring potential energy and kinetic energy equations
  • Knowledge of conservation of energy principles
  • Familiarity with basic physics concepts such as force constants and mass
  • Ability to perform calculations involving angles and energy transformations
NEXT STEPS
  • Calculate the launching speed using the conservation of energy approach
  • Explore the effects of incline angles on potential and kinetic energy
  • Investigate the role of friction in energy conservation problems
  • Review the implications of unit analysis in physics problems
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Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators looking for practical examples of applying theoretical concepts in real-world scenarios.

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Homework Statement


The ball launcher in a pinbgall machine has a spring that has a force constant of 36 N/cm. THe surface on which the ball moves is inclined theta=10.1 degrees with respect to the horizontal. If the spring is initially conressed 4.25 cm, find the launching speed of a .120 kg bawhen the plunger is released. Friction and the mass of the plunger e negligible.

Homework Equations



PE=.5k(xf-xi)^2
KE=.5mv^2

The Attempt at a Solution


I'not sure what launching speed is supposed to be, it supposed to be an answer that doesn't require units. Does that mean I need to be finding the spring constant? If so, do I just set the KE=PE?
 
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They give you the spring constant. 36 N/cm.

So think conservation of energy.

Spring potential depressed = kinetic energy at release point plus additional increase in gravitational potential energy at release point .
 
The force constant is the spring constant. You're looking for a velocity.

Think about it if we compress a spring at some angle we are storing potential energy in the spring, but we also have to take into account gravity, does this help?
 
It can't be simply velocity that I'm looking for because an answer not requiring units is needed. Any other ideas?
 
I'm pretty sure it's got units -- it asks for the launching speed. Speed's have units of distance per time.
 
I know... it should but, I'm doing homework through lon-capa and it's telling me that it doens't require units, so it can't be asking for velocity.
 
They ask for speed.

Calculate it as m/s.

Ignore their not asking for units.
 

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