Two Masses, a Pulley, and an Inclined Plane?

Question

Block 1, with a mass of m1 = 0.650 kg, is connected over an ideal (massless and frictionless) pulley to Block 2, which has a mass of m2, as illustrated in the accompanying diagram. Given an angle of θ = 30.0° and a coefficient of kinetic friction between Block 2 and the inclined plane of μ = 0.400, an acceleration of magnitude a = 0.600 m/s² is observed for Block 2. 
Part A: Determine the mass of Block 2, m2.

Anonymous · Accepted Answer

As we are not given the picture, or the assumed origin or direction of acceleration, there are two values available for m2 which will result in an acceleration of the magnitude given. This results from friction always opposing motion.
Fnet = ma
if the acceleration is down the slope
m1g + μm2gcosθ - m2gsinθ = (m1 + m2)a
m1(g - a) = m2(a + g[sinθ - μcosθ])
m2 = m1(g - a) / (a + g[sinθ - μcosθ]) 
m2 = 0.650(9.81 - 0.600) / (0.600 + 9.81[sin30 - 0.400cos30]) 
m2 = 7.94 kg
if the acceleration is up the slope
m1g - μm2gcosθ - m2gsinθ = (m1 + m2)a
m1(g - a) = m2(a + g[sinθ + μcosθ])
m2 = m1(g - a) / (a + g[sinθ + μcosθ]) 
m2 = 0.650(9.81 - 0.600) / (0.600 + 9.81[sin30 + 0.400cos30]) 
m2 = 0.662 kg

Anonymous · Answer

Net force on the two blocks equals their combined mass * their common acceleration
m1 g - m2 g sin(30) - mu m2 g cos(30) = (m1+m2) a
All is known except m2.

Ms. Katlynn Fadel

Two Masses, a Pulley, and an Inclined Plane?

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