Finding the kinetic friction between the block and surface

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SUMMARY

The discussion focuses on calculating the coefficient of kinetic friction (Uk) between a block and a horizontal surface when subjected to a pulling force. Given parameters include a mass (M) of 5.0 kg, a force (F) of 14 N, and an angle (Theta) of 35°. The initial calculation yielded Uk as 0.234, but the correct value is 0.28. The error was identified as neglecting the vertical component of the force (Fsin(theta)) in the normal force calculation.

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  • Basic algebra for solving equations
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Homework Statement


[/B]
The block shown is pulled across the horizontal surface at a constant speed by the force shown. If M = 5.0 kg, F = 14 N and Theta= 35°, what is the coefficient of kinetic friction between the block and the horizontal surface?

Homework Equations



Fx = Fcos(theta)
Ff = Fn * Uk (Friction equation)
F=ma
Fn = mg

The Attempt at a Solution



I did it by myself and got 0.234, but the answer says it's 0.28. Can you explain this to me?

My work:
a = F / m
a =( Fcos(35) - Fn * Uk ) / m= 0
Fcos(35) / Fn = Uk
14*cos(35) / (5 * 9.8) = 0.234 = Uk

I don't know where I did wrong
 

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Nevermind! I got it! I forgot the Fsin(theta)
It is
Fcos(theta) - Uk(mg - Fsin(theta)) = 0
14 * cos(35) / (5*9.8 - 14 sin(35)) = 0.28 = Uk
 

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