Finding the coefficient of static friction

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SUMMARY

The discussion centers on calculating the coefficient of static friction for a hot wheel on a linear track, where the track is inclined at a height of 6.45 cm with a hypotenuse distance of 189.5 cm. The mass of the hot wheel is 45.7 g. The primary equations referenced include potential energy (PE = mgh), work done by friction (Wf = Ffd), and the relationship between frictional force and mass (Ff = μmg). The conclusion emphasizes that the problem can be approached as a statics question, focusing on forces rather than energy, since the cart does not move initially.

PREREQUISITES
  • Understanding of potential energy (PE) and kinetic energy (KE) equations
  • Knowledge of work done by friction (Wf = Ffd)
  • Familiarity with the concept of static friction and its coefficient (μ)
  • Basic principles of statics and forces in equilibrium
NEXT STEPS
  • Research the calculation of static friction coefficients in wheeled systems
  • Explore the relationship between wheel radius and axle radius for friction analysis
  • Study rolling resistance properties of different wheel materials
  • Learn about statics problems and force equilibrium in inclined planes
USEFUL FOR

Students in physics or engineering courses, educators teaching mechanics, and anyone interested in understanding friction in wheeled systems.

rm_girl
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Homework Statement


So a hot wheel was put on a linear track, and one end of the track is slowly lifted until the cart starts to move. The height of the one end is measured as 6.45cm and distance (or hypotenuse) is 189.5cm
mass of hot wheel is 45.7 g


Homework Equations


PE = mgh
KE = 1/2mv2
Wf = Ffd
Ff = μmg

The Attempt at a Solution


So I was thinking of using PE = KE + Wf, but the car doesn't move, so I can't have KE in there. If that's the case, do I just set up the equation as PE = Wf ? and find the coefficient of static friction from there?
 
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This is a very strange question. Friction between the ramp and wheels has nothing to do with it - the wheels will roll, not slide. The initial resistance to motion comes from friction in the axles and, perhaps, rolling resistance in the wheels. To calculate the coefficient of friction in the axles the ratio of the wheel radius to axle radius is needed. Rolling resistance is a property of the wheel rubber, and I'm not sure of the details of that.
If we ignore all that and treat the cart as a wheelless block, this is a statics question, so energy is irrelevant. Just consider the forces at their limits prior to movement.
 

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