Newtonian mechanics of a metal slab

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SUMMARY

The discussion focuses on calculating the acceleration of a 90 kg metal slab being pulled by a tractor with a force of 600 N at an angle of 35° from the horizontal. The coefficient of friction between the slab and the ground is µ = 0.65. The relevant equations include Fnet = ma and Fk = µ * Fn, where Fk is the friction force and Fn is the normal force. The user struggles to isolate the normal force and friction force to solve for acceleration, indicating a need for clarity in resolving forces acting on the slab.

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  • Understanding of Newton's laws of motion
  • Familiarity with friction concepts, specifically static and kinetic friction
  • Knowledge of vector decomposition in physics
  • Ability to apply trigonometric functions in physics problems
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This discussion is beneficial for physics students, educators, and anyone interested in mastering Newtonian mechanics, particularly in the context of force analysis and friction in real-world applications.

uchicago2012
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Homework Statement


A 90 kg metal slab is pulled across the ground by a tractor. The coefficient of friction between the slab and the ground is µ = 0.65. If the force of the tractor on the slab is 600 N and is directed at 35° from the horizontal, what is the acceleration of the slab?

Homework Equations


Fnet = ma
Fk = u * Fn
where Fk = friction force and Fn = normal force and u = coefficient of friction

The Attempt at a Solution


So I thought there were four forces acting on the metal slab: Fn, the normal force, Fg, gravity, F, the 600 N force from the tractor, and Fk, the friction force.

Fnet,y = FN + F sin theta - mg - Fk sin thetaFk = ma
Fnet,x = F cos theta - Fk cos thetaFk = ma

theta = 35 degrees, measured from positive direction of the x axis
thetaFk = 215 degrees, measured from positive direction of the x axis

Only now that I've arranged everything I can't figure out how to isolate either Fk or Fn so I can solve the thing. I tried:

rearrange equations so:
Fky = Fk sin thetaFk = -ma + Fn + F sin theta - Fg
Fkx = Fk cos thetaFk = -ma + F cos theta

Then, by trig, tan thetaFk = Fky/Fkx, so
tan thetaFk = (-ma + Fn + F sin theta - Fg) / (-ma + F cos theta)

but acceleration doesn't cancel out completely to give Fn so I'm stumped. Am I heading in the completely wrong direction?
 
Physics news on Phys.org
There is no y component to the friction force (assuming level ground)...and in the x direction, ther is no angle involved with the friction force (theta = 0) ...and what's the acceleration in the y direction?
 

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