Two blocks are connected by a string that passes over a massless, frictionless p

Question

Two blocks are connected by a string that passes over a massless, frictionless pulley, as shown in the figure. Block A, with a mass m_A = 4.00 kg, rests on a ramp measuring 3.0 m vertically and 4.0 m horizontally. Block B hangs vertically below the pulley. When the system is released from rest, block A accelerates up the slope and block B accelerates straight down. When block B has fallen through a height h = 2.0 m, its speed is v = 6.00 m/s. Assuming that no friction is acting on block A, what is the mass of block B? If, instead, there is friction acting on block A, with a coefficient of kinetic friction of 5/8, what is the mass of block B?

Explanation / Answer

angle = tan^-1(3/4) = 37

change in energy = mA*g*h*sin37 + mB*g*h

change in KE = 0.5*mA*v^2 + 0.5*mB*v^2

from energy conservation

U1 + K1 = U2 + K2

dU = dK

4*10*2*sin37 + mB*10*2 = 0.5*4*6^2 + 0.5*mB*6^2

mB = 11.92 kg <<,---------answer

(b)

uk = 5/8 = 0.4

dU - Wf = dK

mA*g*h*sin37 + mB*g*h - Wf = 0.5*mA*v^2 + 0.5*mB*v^2

Wf = uk*mA*g*cos37

4*10*2*sin37 + mB*10*2 - 0.4*4*10*cos37 = 0.5*4*6^2 + 0.5*mB*6^2

mB = 18.31 kg

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