Two Masses, a Pulley, and an Inclined Plane?

Question

Block 1, of mass m1 = 0.650kg , is connected over an ideal (massless and frictionless) pulley to block 2, of mass m2, as shown. For an angle of θ = 30.0∘ and a coefficient of kinetic friction between block 2 and the plane of μ = 0.400, an acceleration of magnitude a = 0.600m/s2 is observed for block 2.Part AFind the mass of block 2, m2.

Bernhard White · 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 = maif the acceleration is down the slopem1g + μm2gcosθ - m2gsinθ = (m1 + m2)am1(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 kgif the acceleration is up the slopem1g - μm2gcosθ - m2gsinθ = (m1 + m2)am1(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

Bernhard White · Answer

Net force on the two blocks equals their combined mass * their common accelerationm1 g - m2 g sin(30) - mu m2 g cos(30) = (m1+m2) aAll is known except m2.

Mr. Ellis Hintz

Two Masses, a Pulley, and an Inclined Plane?

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