Conservation of Energy pinball problem

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SUMMARY

The discussion centers on calculating the launching speed of a ball in a pinball machine using the conservation of energy principle. The spring has a force constant of 1.10 N/cm, and the ball is launched from a 10.0° incline after being compressed 5.00 cm. The correct calculation yields a speed of 1.61 m/s, while an initial miscalculation resulted in 0.377 m/s due to incorrect unit conversions. Participants identified that the error stemmed from inconsistent unit usage, specifically failing to convert all measurements to meters.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with spring mechanics and Hooke's Law
  • Basic knowledge of trigonometry, particularly sine functions
  • Proficiency in unit conversion between centimeters and meters
NEXT STEPS
  • Review Hooke's Law and its application in spring mechanics
  • Learn about energy conservation in inclined planes
  • Practice unit conversion techniques in physics problems
  • Explore the effects of friction on energy conservation in mechanical systems
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of energy conservation in practical applications such as pinball machines.

SamTsui86
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The ball launcher in a pinball machine has a spring with a force constant of 1.10 N/cm (Fig. P5.71). The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 5.00 cm, find the launching speed of a 0.100 kg ball when the plunger is released. Friction and the mass of the plunger are negligible.

p5-71.gif


so here's what i did

Ei = Ef, so

1/2kx^2 = mgsin@x + 1/2 mv^2

I got .377 m/s for the answer, but the real answer is 1.61 m/s

Plz tell me what i did wrong.

Thank You
 
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Apparently you did the arithmetic wrong. I used your formula and got 1.61 m/s (actually, I got 161 but then realized I was still in cm/s !)
 
ohhh, i made the same mistake too, except convert on of them to m but not all. Thank You
 

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