Mass on an inclined plane w/ FRICTION (use work energy theorem)

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SUMMARY

The discussion focuses on solving a physics problem involving a mass on an inclined plane with friction, specifically using the work-energy theorem. The parameters include a mass of 5 kg, an initial velocity of 40 m/s, an incline angle of 30°, and a coefficient of friction of 0.15. Participants attempted to calculate the distance the mass travels up the ramp before stopping and its speed upon returning, while also addressing the energy lost during the process. Key equations discussed include the work-energy theorem and expressions for work done against gravitational and frictional forces.

PREREQUISITES
  • Understanding of the work-energy theorem in physics
  • Knowledge of inclined plane dynamics and forces
  • Familiarity with friction coefficients and their impact on motion
  • Ability to manipulate equations involving gravitational potential energy and kinetic energy
NEXT STEPS
  • Explore detailed examples of the work-energy theorem in inclined plane problems
  • Learn how to calculate normal force on an inclined plane
  • Study the effects of different coefficients of friction on motion
  • Investigate energy loss calculations in mechanical systems
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Students studying physics, educators teaching mechanics, and anyone interested in understanding the dynamics of motion on inclined planes with friction.

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Mass on an inclined plane with friction!
There is a mass at the bottom of an inclined plane. It travels with an initial velocity up the inclined plane at an angle θ. There is a coefficient of friction on the ramp. How far up the ramp will the mass go before stopping? What is the speed of the block when it returns to the bottom of the ramp? What percent of the initial total mechanical energy was lost during the mass's trip (going up and then back down?
m=5 kg
vo=40 m/s
θ=30°
S=the distance you are looking for
Coefficient of friction (μ) = 0.15

Work energy theorem=mg(hf-ho) + 1/2 m (vf^2-vo^2) +fs

Attempt:
i set up the work energy theorem and simplified it down to "work=mghf-1/2mvo^s+μ
mgs" and solved for s
and then i used "work= -mgho + 1/2mvf^s +μ
mgs to solve for vf
i honestly had no clue what to do for the third part of this problem

I don't think my answers are right bc i got 0.598 m fr the first part and 2.23 m/s fr the second part...and i couldn't figure out the third part

Help would be appreciated. Thank u very much to all!
 
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work= -mgho + 1/2mvf^s +μ
I think this should be 0 = mg*h - ½m⋅Vo² + μ*Fn*s
since no work is done except the included friction work; it has initial velocity but the final velocity is zero, h is the height it goes up. Express h in terms of s and the angle of the ramp. You will solve for s to find the answer. The normal force, Fn needs to be figured out from the force of gravity and the angle.
 

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