Question
Asked Oct 9, 2019
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The system shown in the figure below has an acceleration of magnitude 1.15 m/s2, where m1 = 4.30 kg and m2 = 9.40 kg. Assume that the coefficient of kinetic friction between block and incline is the same for both inclines.

a) Find the coefficient of kinetic friction.

b) Find the tension in the string.

т,
т,
35.0°
35.0
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т, т, 35.0° 35.0

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Expert Answer

Step 1

Given:

Mass of block, m1 = 4.30 kg

Mass of block, m2 = 9.40 kg

Acceleration of the system, a = 1.15 m/s2

 

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T т, m mg sin 3 5 mg cos350 m2g cos350 m2g sin 35 mg m2g free body diagram for block m free body diagram for block m

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Step 2

Since there is no motion in vertical direction

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for block m Nmgcos 35 where, N normal force m = mass g acceleration due to gravity for block m N m,g cos35 where N2 normal force m2mass acceleration due to gravity g

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Step 3

Equation of motion for the ...

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for block m Т-f- mgsin35° — т,а .(1) where, T tension fi=frictional force on m т, = mass a acceleration for block m т,gsin35° - T - S, — т,а .... (2) where, T tension ffrictional force on m2 1 m2 mass a acceleration add equation (1) and (2) T--mgsin35° +m2gsin 35° - T- f =a(m +m2) --mg sin 35° +m2g sin 35° - f a(m, + m2) .....3)

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