Two boxes start sliding down the ramp shown in the figure. Package A has a mass

Question

Two boxes start sliding down the ramp shown in the figure. Package A has a mass of 5kg and a coefficient of kinetic friction of 0.20. Package B has a mass of 10.0 and a coefficient of kinetic friction of 0.15. How long does it take package A to reach the bottom?

Please provide a pictorial diagram and free-body diagram. Also, start with variable questions and state any reasonable assumptions. Confirm your analysis with limiting cases. Thank you!

Btw, here is my work thus far- please make corrections:

Force A= (massA*gravity*sintheta) - (coefficient*massA*gravity*costheta)

Force B= (massB*gravity*sintheta) - (coefficient*massB*gravity*costheta)

Total Force= (Force A + Force B)

Acceleration = Total Force / (massA + massB)

Explanation / Answer

let's start with calculating net force applicable on mass A,

5(a) = 5 (9.8) sin 20 + 10 (9.8 ) sin 20 - (0.2) 5 (9.8) cos 20 - ( 0.15) (10) (9.8 ) cos 20

a = 3.3517 + 6.7036 - 1.8418 - 2.7627

a= 5.45 m/s^2

2 m = 1/2 ( 5.45)t^2

t = 0.8567 sec apprx

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