2 masses are sliding to the left on 2 separate inclines. The pulley connecting t

Question

2 masses are sliding to the left on 2 separate inclines. The pulley connecting the left and right sides is massless and frictionless. The surfaces of the inclines have kinetic friction. On the left m_1 = 3 kg is sliding to the left initially at 0.5 m/s. The left shape is 20 degree, mu_k1 = 0.2. On the right m_2 = 3 kg is sliding to the left also at 0.5 m/s. The right shape is 30 degree mu_k2 = 0.3. Make free body diagrams for both m_1 & m_2. Extract equations of motion for m_1 & m_2. What acceleration do the two masses experience? Do they speed up or slow down? If they speed up, how fast are they going after sliding 1m? If they slow how far do they go before they come to rest?

Explanation / Answer

let the acceleration of botn masses = a, and tension =T

b Equations:

m1a= m1gsin20 - T - 0.2 m1 g cos 20

m2a= T - m2gsin30 - 0.3 m2g cos 30

3) let's find the accleration,

3a= 4.53- T -------eq (1) ( for mass 1)

3a= T - 22.338---------eq(2) ( mass 2)

4.53 -T = T - 22.338

T =13.434 N

a=- 2.968 m/s ^2 ( they are slowing down)

4)s( stopping distance) =0.5^2/ ( 2 x 2.968) =0.042 m apprx

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