Calculating Velocity of Snowboarder Down Slope

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SUMMARY

The discussion focuses on calculating the velocity of a snowboarder descending a slope before a jump, utilizing the principles of potential energy and friction. The potential energy is defined as mgh, where m is the mass (100 kg), g is the gravitational acceleration (9.8 m/s²), and h is the height related to the slope angle theta. The frictional force is determined by the normal force, mgcos(theta), and the coefficient of kinetic friction (μk = 0.05). The goal is to derive an equation that accounts for energy lost to friction and ultimately calculates the snowboarder's velocity at the bottom of the slope for various angles theta.

PREREQUISITES
  • Understanding of potential energy and its formula (mgh)
  • Knowledge of friction and normal force calculations (mgcos(theta))
  • Familiarity with the work-energy theorem
  • Basic trigonometry for slope calculations
NEXT STEPS
  • Research the conservation of energy principles in physics
  • Learn how to apply the work-energy theorem in practical scenarios
  • Explore the effects of varying the angle theta on friction and velocity
  • Investigate advanced friction models for different surface conditions
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Physics students, mechanical engineers, and sports scientists interested in the dynamics of motion and energy transfer in snowboarding scenarios.

GoSS190
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Need to find the equation for the velocity of a snowboarder going down a slope about to hit a jump. I know that the potential energy for going down the hill is mgh and that friction depends on the normal force which is mgcos(theta) and the distance going down the slope. I need to figure out what the equation for finding the opposing energy that is being produced by friction. I am looking to find the velocity at the bottom for all values of theta.

The known variables are..
m=100 kg
g=9.8 m/s^2
d=100 meters or the hypotenuse of the hill
mu (k)=.05
 
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Hi GoSS190! :smile:

Combine conservation of energy with the work-energy theorem …

energy "lost" to friction = work done by friction. :wink:
 

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