Pad * 69% + 4:53 AM learn.unt.edu 10. (7 points) A mass - 4.00 kg is connected,

Question

Pad * 69% + 4:53 AM learn.unt.edu 10. (7 points) A mass - 4.00 kg is connected, as shown, by a light cord to a mass M = 6.00 kg, which slides on a horizontal surface. The coefficient of kinetic friction between the mass M and the horizontal surface is 0.150. The pulley, which rotates about a frictionless axle and has a radius R = 0.120 m, may be treated as a uniform disk of mass mp-2.00 kg. The cord does not slip on the pulley. a) What is the magnitude of the acceleration of m? b) What is the tension in the horizontal section of the cord?

Explanation / Answer

Let tension in left bt T1 and tension in right be T2 and acceleration of masses be a.

Writing force on the masses,

T1 - uMg = Ma

mg - T2 = ma

Writing torque equation,

(T2-T1)r = i alpha where i= 0.5 mp r^2 and alpha = a/r

So T2-T1 = 0.5 mp a

so adding this equation to force equations,

mg - uMg = [M+m+ 0.5mp]a

a = [m-uM]g/ [M+m+ 0.5mp]

= [4-0.15*6]*9.8/[4+6+0.5*2]

= 2.762 m/s^2

b] T1 = Ma + uMg = 6*(2.762+0.15*9.8)

= 25.4 N answer

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