The figure shows two boxes with mass M1 = 6.0kg and M2 = 4.0kg bound by a massle

Question

The figure shows two boxes with mass M1 = 6.0kg and M2 = 4.0kg bound by a massless wire that runs through a frictionless pulley with moment of inertia I = 0.005kg m2 and radius 5.0cm. The boxes are held so that they can not move. The friction coefficient between mass M1 and the substrate is 0.35. The boxes "loosen" at t = 0.

a) Calculate the acceleration of the boxes.

B) Determine the cord power to the box with mass 4.0kg.

c) Find the speed of the tiles after moving 2m.

d) What is the kinetic energy of the stage when the crates have moved 2m.

Explanation / Answer

given

M1 = 6 kg

M2 = 4 kg

I = 0.005 kg m^2

r = 5 cm

k = 0.35

a. let acceleration of the boxes be a

tension in the string attached to M2 be T2, and to M1 be T1

then

M2g - T2 = M2a

(T2 - T1)*r = Ia/r

T1 - k*M1*g = M1a

hence

M2g - (Ia/r^2) - k*M1*g = (M1 + M2)a

a = (M2g - k*M1*g)/(M1 + M2 + I/r^2) = 1.55325 m/s/s

b. Tension in cord connected to M2 = T2

T2 = M2(g - a) = 33.027 N

c. after 2 m, speed = v

2*a*2 = v^2

v = 2.492589 m/s

d. KE of the system at this moment = 0.5(M1 + M2 + I/r^2)v^2 = 37.278 J

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