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Two masses m 1 and m 2 are placed touching each other on an inclined plane forming an angle θ with the horizontal the coefficient of friction between the inclined plane and m 1 is µ 1 and that of between plane and m 2 is µ 2 where µ 1 > µ 2 . (a) Find the interaction force between the two masses. (b) What is the minimum angle q at which masses start sliding.

Two masses m1 and m2 are placed touching each other on an inclined plane forming an angle θ with the horizontal the coefficient of friction between the inclined plane and m1 is µ1 and that of between plane and m2 is µ2 where µ1 > µ2.


(a)    Find the interaction force between the two masses.


(b)    What is the minimum angle q at which masses start sliding.

Grade:upto college level

1 Answers

Shane Macguire
30 Points
7 years ago

(a)    Let R be the interaction force and F1 and F2 be the frictional force on m1 and m2, respectively.

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m1a = m1g sin θ + R – µ1N1           m2a = m2g sinθ – R – µ2N2

N1 – m1gcosθ = 0                        N2 – N2 – µ2 cosθ = 0

491_88597_Image~ 1.jpg

(b)    The two masses begin to slide just when the acceleration of m1 is not zero.

171_88597_Image~ 1.jpg

The limiting case is given by

m1g sinθmin + R – µ1m1g cosθmin = 0

Using R from part (a)

1507_88597_Image~ 1.jpg

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