Two packages at UPS start sliding down the 20 ? ramp shown in the figure. Packag

Question

Two packages at UPS start sliding down the 20? ramp shown in the figure. Package A has a mass of 3.50kg  and a coefficient of kinetic friction of 0.210. Package B has a mass of 8.50kg  and a coefficient of kinetic friction of 0.140.
(Figure 1)

Two packages at UPS start sliding down the 20? ramp shown in the figure. Package A has a mass of 3.50kg and a coefficient of kinetic friction of 0.210. Package B has a mass of 8.50kg and a coefficient of kinetic friction of 0.140. How long does it take package A to reach the bottom?

Explanation / Answer

a1=gsin???1gcos?

a2=gsin???2gcos?

Because

?1>?2

we have

a1<a2

Therefore both the bodies have the same acceleration "a"

Then once again drawing the corresponding free body diagrams which also involve the force of contact between the blocks, we arrive at (Correct me if am wrong)

a=(m1+m2)gsin??gcos?(m1?1+m2?2)(m1+m2)

After this it is easy to calculate the time

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