Question

Two blocks made of different materials connected together by a thin cord, slide down a plane ramp inclined at an angle θ to the horizontal as shown in the figure(Figure 1)(block B is above block A). The masses of the blocks are mA and mB and the coefficients of friction are μA and μB.  

A) If mA=mB=5.2kg, and μA = 0.23 and μB = 0.33, determine the acceleration of the blocks for an angle θ = 34 ∘.

Answer 1

given
ma = mb = 5.2 kg
uA = 0.23
uB = 0.33
theta = 34 deg

now, acceleration of both the blocks will be the same if the string is taught
let tension in the string be T
acceleratrion = a
hence
by force balance

ma*g*sin(theta) - T - uA*ma*g*cos(theta) = ma*a
T + mb*g*sin(tehta) - uB*mb*g*cos(theta) = mb*a

(mb + ma)*g*sin(theta) - (uA*ma + uB*mb)*g*cos(theta) = mb*a + ma*a
a = g*sin(theta) - (uA*ma + uB*mB)g*cos(theta)/(ma + mb)
for ma = mb
a = g*sin(theta) - (uA + uB)gcos(theta) = 0.93 m/s/s