Two masses are sliding to the left on two separate inclines. The pulley connecti

Question

Two masses are sliding to the left on two separate inclines. The pulley connecting the left and the right sides is massless and frictionless. The surfaces of the inclines have kinetic friction. On the left m1 = 3kg is sliding to left initially at 0.5 m/s. The left slope is 20 degree and mu_k1 = 0.2. On the right m_2 = 3kg is sliding the left also at 0.5 m/s. The right slope is 30 degree and mu_k2 = 0.3. Make free body diagrams for both m_1 and m_2? Extract equation of motion for m_1 and 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 m_1? or they slow down, how far do they go before they come to rest? (Explain why each equation is used, Show all your work)

Explanation / Answer

Let the tension in rope = T

b) Equation for m1

m1a = m1gsin20 - T - 0.2 m1 g cos 20

3 (a) = 3 (9.8) sin 20 - T - 0.2 (3)(9.8 ) cos 20

3a= 10.055 - T - 5.5253

3a= 4.529 - T-----------eq(1)

equation for m2, m2 a = T - m2gsin30 - 0.3 (m2) g cos 30

3(a) = T - 3( 9.8) sin 30 - 0.3 (3) ( 9.8) cos 30

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

c) Let's find the accleration of masses,

T - 22.338= 4.529 - T

T = 13.433 N

a= - 2.968 m/s^2

slow down

4) let's find the retarding distance

s= 0.5^2 / 2( 2.968) =0.04211 m apprx

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