How do I calculate the height on a ramp for a rolling ball?

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SUMMARY

The discussion focuses on calculating the height a steel ball reaches when rolling up a 35-degree ramp. The ball, with a mass of 45 grams and a diameter of 2.2 cm, travels a distance of 0.132 meters up the ramp after completing 12 revolutions. The key to finding the height is applying trigonometric relationships in a right triangle, where the height can be derived from the distance traveled along the ramp, which serves as the hypotenuse. The user is encouraged to utilize sine or cosine functions to relate the height to the ramp distance.

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  • Understanding of basic trigonometry, specifically sine and cosine functions.
  • Familiarity with the concept of right triangles and their properties.
  • Knowledge of rotational motion and how it relates to linear distance.
  • Basic physics principles regarding energy conservation and motion.
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of rolling motion and inclined planes.

sportsnh
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I am confused as to how i solve for height in this problem. I can solve for the distance up the ramp the ball goes but not for the height above the ground.

The problem states: A steel ball has a mass of 45 grams and a diameter of 2.2 cm. The ball is moving and rolling at an initial velocity (not known) when it starts rolling up a 35 degree ramp and comes to a stop after turning 12 revolutions.

I solved for how far up the ramp the ball went by taking the 12 rev *2π rad * .011m /1 rev / 2π rad and got .132m.

I have looked at all the equations that i have but can't figure out how to solve for how high the ball goes up?
 
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right triangles

You have the angle of the ramp. Consider it as a right triangle--what trig relationships might relate height to distance up the ramp (which is the hypotenuse)?
 
thanks...i knew it was something very simple that i was missing
 

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