A 3.40 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of 55.0° with the horizontal, as in the figure below. The block accelerates to the right at 6.00 m/s(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}. Determine the coefficient of kinetic friction between block and ceiling.

Ugghhh so... this is what I did...

F = 85.0 N

m = 3.40 kg

a = 6.00 m/s^{2}

f_{k}= μ_{k}n

1) Forces in the x-direction:

F cos θ

f_{k}(kinetic friction)

Forces in the y-direction:

F sin θ

n (normal force)

2) Sum of forces

ƩF_{x}= F cos θ + f_{k}= 0

ƩF_{y}= F sin θ + n = 0

ƩF_{y}= F sin θ + n = 0

ƩF_{y}= n = -F sin θ

3) ƩF_{x}= F cos θ + μ_{k}n = 0

3) ƩF_{x}= F cos θ + μ_{k}(-F sin θ) = 0

3) ƩF_{x}= F cos θ + μ_{k}(-F sin θ) = 0

3) ƩF_{x}= 85 cos 55 - μ_{k}(85 sin 55) = 0

3) ƩF_{x}= 85 cos 55 = μ_{k}(85 sin 55)

3) ƩF_{x}= (85 cos 55)/(85 sin 55) = μ_{k}

3) ƩF_{x}= 0.700 = μ_{k}

So I got this wrong, the answer is actually 0.781 (???)

I don't know what to do!

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# Homework Help: How do I determine the wretched coefficient of kinetic friction? It's impossible

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