Conservation of energy problem on an igloo

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SUMMARY

The conservation of energy problem involves calculating the initial speed of Jin, who slides down a hemispherical igloo with a radius of 2.40 meters. After traveling 1.60 meters along the surface, he loses contact with the igloo. The relevant equations include the conservation of mechanical energy (KEi + PEi = KEf + PEf) and the potential energy formula (PE = mgh). The final velocity upon leaving the igloo is determined to be 3.16 m/s, which is derived from the height difference calculated using trigonometry.

PREREQUISITES
  • Understanding of conservation of mechanical energy principles
  • Familiarity with potential energy (PE = mgh) and kinetic energy (KE = 0.5mv²) equations
  • Basic trigonometry for calculating heights on a semicircle
  • Knowledge of motion dynamics at the point of losing contact with a surface
NEXT STEPS
  • Study the application of conservation of energy in different physical scenarios
  • Learn about the dynamics of motion at the point of losing contact with a curved surface
  • Explore advanced trigonometric applications in physics problems
  • Investigate the effects of friction on energy conservation in similar problems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation principles, as well as educators seeking to enhance their teaching methods for related topics.

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Homework Statement


Jin is sitting on top of a hemispherical, frictionless igloo of radius 2.40 meters. His friend pushes him, giving him an initial speed. Jin slides along the igloo and loses contact with it after he has traveled 1.60 meters along the surface. What was his initial speed?


Homework Equations


KEi+PEi=KEf+PEf

Ei=Ef

F=macos(angle)

Work=KE+PE

Work=Fx(delta x)

S=(angle)(radius)

PE=mgh

KE=.5(m)(v^2)


The Attempt at a Solution



I drew a picture of a semicircle and used the S=theta(r) equationand trignometry to find that the hieghts (2.40m initial and 1.89m when leaves igloo). I used the conservation of energy to find that the velocity when Jin leaves the igloo is 3.16m/s. How would I find the initial velocity?
 
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How did you find 3.16? Kinetic in the initial condition is not zero.. You are trying to find the velocity.. How could it be zero?

Also think about what happens at the exact moment it leaves the semicircle and what kind of motion it executes.. You didnt write one equation you need.

Hope it helps
 

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