Newtonian mechanics of a metal slab

AI Thread Summary
To determine the acceleration of a 90 kg metal slab being pulled by a tractor with a force of 600 N at a 35° angle, the net forces acting on the slab must be analyzed. The forces include the normal force (Fn), gravitational force (Fg), the applied force (F), and the frictional force (Fk). The equations of motion, Fnet = ma, are set up for both the x and y directions, but the user struggles to isolate Fn and Fk to solve for acceleration. The discussion highlights confusion regarding the components of the friction force and the lack of acceleration in the y-direction, indicating a need for clarification on the forces involved. Understanding these dynamics is crucial for accurately calculating the slab's acceleration.
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?
 
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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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