Solve Mech. Energy Problem: Homework Statement & Equations

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SUMMARY

The discussion centers on a physics problem involving a child sliding down a playground slide with a straight section and a circular arc. The child starts at a height of 9 meters and the radius of the circular arc is 7.2 meters. The key equations referenced include the work-energy principle and the centripetal force equation, specifically F=mv²/r, to determine the height at which the child loses contact with the slide. The solution requires calculating the speed at the top of the circular arc and applying the appropriate forces to find the airborne height.

PREREQUISITES
  • Understanding of basic physics concepts, particularly energy conservation and forces.
  • Familiarity with the work-energy principle and its application in mechanics.
  • Knowledge of centripetal force and its role in circular motion.
  • Ability to manipulate equations involving gravitational potential energy and kinetic energy.
NEXT STEPS
  • Calculate the speed of the child at the top of the circular arc using energy conservation principles.
  • Apply the centripetal force equation F=mv²/r to determine the conditions for losing contact with the slide.
  • Explore the implications of negligible friction in mechanical energy problems.
  • Review examples of similar physics problems involving circular motion and energy conservation.
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Students studying physics, particularly those tackling mechanics and energy conservation problems, as well as educators looking for examples of practical applications of these concepts.

lgmavs41
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Just need some direction on the problem.

Homework Statement


A poorly designed playground slide begins with a straight section and ends with a circular arc. A child starts at point P and slides down both sections of the slide. At some point on the circular arc, the normal force goes to zero and the child loses contact with the ramp. Assuming the forces of friction are negligible, at what height from the ground will the child become airborne.

the height from point p to the ground is 9 m. The radius of the arc is 7.2 m.

Homework Equations


w=kf-ki+uf-ui; ki=0, ui=mg(9)

The Attempt at a Solution


well, i figure out the speed in which the particle will be when it hits the circular arc, where uf=mg(7.2). Now how do i figure out how high it will be from the ground when the child will become airborne? I think I need to use F=mv^2/r somewhere in the equation to figure out the force needed for the particle to stay in the circular path and not go flying off. But after that, I'm kind of lost.

Thanks for the help.
 
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BTW, the child touches the circular arc at the top of the circle which covers about a quarter of the circumference...well, picture the child sliding straight down then suddenly touches the top of the circle, which slides down in an arc. Sorry, i don't have the pic.
 

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