Newtonian mechanics of a metal slab

In summary, a 90 kg metal slab is 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 0.65. The normal force and friction force are both present, and the equations Fnet = ma and Fk = µ * Fn can be used to solve for the acceleration of the slab. However, since there is no y component to the friction force and no angle involved in the x direction, the equations must be rearranged in order to isolate either Fk or Fn and solve for the acceleration.
  • #1
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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  • #2
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?
 

FAQ: Newtonian mechanics of a metal slab

What is Newtonian mechanics?

Newtonian mechanics is a branch of classical mechanics that describes the motion of objects under the influence of forces. It was developed by Sir Isaac Newton in the 17th century and is based on his three laws of motion.

What is a metal slab?

A metal slab is a rectangular piece of metal, typically with a uniform thickness, that is used in various industrial and engineering applications. It can be made of different types of metal such as steel, aluminum, or copper.

How does Newtonian mechanics apply to a metal slab?

Newtonian mechanics can be used to analyze the motion of a metal slab under different forces, such as gravity, friction, and applied forces. It can also be used to calculate the stress and strain on the slab when it is subjected to external forces.

What are some examples of Newtonian mechanics in a metal slab?

Some examples of Newtonian mechanics in a metal slab include calculating the acceleration of a slab sliding down an inclined plane, determining the force required to bend a slab, and analyzing the impact of a falling object on a slab.

What are the limitations of Newtonian mechanics in a metal slab?

There are some limitations of Newtonian mechanics in a metal slab, such as not taking into account the microscopic behavior of atoms and molecules within the metal, and not being able to accurately predict the behavior of the slab under extreme conditions such as high temperatures or velocities.

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