Conservation of (Angular) Momentum

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SUMMARY

The discussion focuses on the application of the conservation of energy principle to determine the maximum height a wooden block of mass m reaches when sliding up an incline with an initial speed vi. The equation derived is h = [mvi^2 - ukmgcos(theta)d]/mg, where d represents the distance traveled up the ramp. The user seeks clarification on how to express the final answer in terms of h, as defined in a previous part of the problem, specifically H = vi^2/2g. Additionally, the user inquires about adapting the solution for a hoop with radius R.

PREREQUISITES
  • Understanding of conservation of energy principles in physics
  • Familiarity with kinetic and potential energy equations
  • Knowledge of friction and its effects on motion
  • Basic trigonometry related to angles and inclines
NEXT STEPS
  • Explore the concept of work done against friction in inclined planes
  • Study the derivation of energy conservation equations in physics
  • Learn how to express variables in terms of known quantities in physics problems
  • Investigate the dynamics of rolling objects, such as hoops, on inclines
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Students studying physics, particularly those focusing on mechanics, as well as educators seeking to clarify concepts related to energy conservation and motion on inclines.

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Hi.
The problem is "A wooden block of mass m slides with an initial speed of vi up a straight incline that makes an angle of theta with the horizontal. If the incline is rough with a coefficient of kinetic friction uk, determine the maximum height it rises in terms of h found in part a (which was H = vi^2/2g)"

So what I did was conservation of energy. KE at the bottom = PE at the top + Work.
mgh + Fd = 1/2mv^2
h = [mvi^2 - ukmgcos(theta)d]/mg
pPoblem is, I don't know what d is and it can't be part of my final answer. I know it's the distance that the block travels up the ramp, but how do I figure that out.
Also, since it says in terms of h found in part a, does that mean I set everything equal to vi^2/2g?

How would I do this with a hoop with radius R?
 
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Sorry. Realize this is in the wrong spot.
 

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