Conservative Forces and Friction

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SUMMARY

The discussion focuses on calculating the height (h) of a ramp for a toy rollercoaster that slides down without friction and then crosses a rough patch. The rollercoaster has a mass of 1.50 kg and must achieve a speed of 3.50 m/s after traversing a rough surface with a coefficient of kinetic friction (µk) of 0.770. The kinetic energy (Kf) after crossing the rough patch is calculated to be 9.188 J, while the work done against friction is determined to be 1.132 J. The relationship between initial kinetic energy (Ki) and gravitational potential energy (mgh) is established to solve for h.

PREREQUISITES
  • Understanding of kinetic energy (K = 1/2mv^2)
  • Knowledge of gravitational potential energy (U = mgh)
  • Familiarity with the concept of friction and its coefficient (µk)
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the initial speed of the rollercoaster just before hitting the rough patch using energy conservation principles.
  • Explore the effects of different coefficients of friction on the speed of objects in motion.
  • Learn about energy loss due to friction in mechanical systems.
  • Investigate the relationship between height and speed in gravitational potential energy scenarios.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of energy conservation, friction, and motion in mechanical systems.

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Homework Statement



A 1.50 kg toy rollercoaster rests on a ramp of height h. When the toy rollercoaster is released, it slides without friction to the bottom of the ramp, and then continues on a flat surface with a rough patch of width 10.0 cm that has a coefficient of kinetic friction µk = 0.770. Find h such that the toy rollercoaster's speed after crossing the rough patch is 3.50 m/s.


Homework Equations



K = 1/2mv^2
U = mgh

The Attempt at a Solution



Kf = 1/2mv^2 = 1/2(1.5kg)(3.5 m/s)^2
Kf = 9.188

fk = ukN = .77(mg) = 11.319 (multiplied by the distance of .1m = 1.132)

I can't do mgh because I don't know h. I know I probably need to figure out how fast the toy roller coaster was going right before it hit the rough patch, but I can't seem to figure that out without knowing "h" so I am stuck here with no idea where to go.
 
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Change in KE is equal to work down against rough surface. So Ki = Kf + fk*d
And Ki = mgh.
Find h
 
Ahh, brilliant. Thank you so much!
 

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