First Off, I\'ve tried this problem for over 2 hours. So please whoever does the

Question

First Off, I've tried this problem for over 2 hours. So please whoever does the problem, can you do it on paper and upload a photo of it? With the free body diagrams and equation sets? I've uploaded one of my attempts to the problem but my answer is not correct.

Don't forget: acceleration is ft/s2, mass is slugs, force is lbs.

"A 4.00 lb block and a 13.0 lb block, connected together by a string, slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the first block mentioned and the plane is 0.10; between the second block and the plane it is 0.20. Find the tension (in pounds) in the string if the first block leads."

Thank You in advance for you guidance on this problem.

Explanation / Answer

Lets call (lbxg) as a unit of force, where lb is pound and g is acceleration due to gravity(9.8m/s2)

force on the 4lb block due to friction = 4lb x ?g cos? =0.4 cos30 (lbxg) ..........?=0.1

force on 4lb block due to gravity alon ghe plane = 4lb x g sin30 = 2(lb xg) ......sin30=0.5

force on the 13lb block due to friction =13lb x ?g cos? = 2.6cos30 (lbxg) ......? =0.2

force on 13lb block due to gravity alon ghe plane = 13lb x g sin30 =6.5 (lb x g)

4lb is leading. so net force on 4lb = 2 (lbxg) - 0.4cos30 (lbxg) -T

acceleration of 4lb block = force/mass = 0.5g - 0.1cos30g - (T/4)

net force on 13 lb block = T+ 6.5 (lbxg) - 2.6cos30 (lbxg)

acceleration of 13 lb block = (T/13) +0.5g - 0.2cos30g

both accelerations are equal as the string is connected,

0.5g - 0.1cos30g - (T/4) = (T/13) +0.5g - 0.2cos30g

T/13 + T/4 = 0.2cos30g-0.1cos30g = 0.0866g

T = 13x4 /(13+4) x 0.0866 lbg = 0.2649 lbg ? 2.596 lb-wt ....(g=9.8m/s2)

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