Finding the kinetic friction between the block and surface

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The discussion focuses on calculating the coefficient of kinetic friction between a block and a horizontal surface, given a mass of 5.0 kg and a pulling force of 14 N at an angle of 35°. The initial calculation yielded a coefficient of 0.234, but the correct answer is 0.28. The error was identified as neglecting the vertical component of the force, specifically Fsin(theta), which affects the normal force. The correct formula incorporates this component, leading to the accurate calculation of 0.28 for the coefficient of kinetic friction. The resolution highlights the importance of considering all forces acting on the block.
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Homework Statement


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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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