The inclined plane of Fig. forms an angle α = 30° with the horizontal. The mass ratio m 2 /m 1 = η = 2/3. The coefficient of friction between the body m 1 and the inclined plane is equal to k = 0.10. The masses of the pulley and the threads are negligible. Find the magnitude and the direction of acceleration of the body m 2 when the system of masses starts moving.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
a 2 = g ( η – sin α – k cos α ) / ( η + 1) = 0.05 g.
Sol. For checking the direction of friction, let us assume there is no friction. Then net force acting on the
system along the string in vertically downward direction is given by
m 2 g – m 1 g sin α = (m 1 + m 2 ) a
η m 1 g – m 1 g/2 = (m 1 + η m 1 ) a
a = 
⇒ a > 0.
So, the friction will act down the incline FBD of m 1 gives: –
T – f – m 1 g sin α = m 1 a. ⇒ T – k m 1 g cos α – m 1 g sing α = m 1 a ——(i)
∴ FBD of m 2 , m 2 FBD
m 2 g – T = m 2 a ——(ii)
from (i) and (ii)
a = 
Putting η = 
, α = 30º and k = 0.1
a = 0.05 g (downward for m 2 )
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