Question #118166

In the system shown, a horizontal force Fx = 40 N acts on an object of mass m2 = 8.00 kg. A friction force fk = 5 N acts between object m2 and the table top, and m1 = 2.00 kg.

i) Calculate the acceleration of the masses.

ii) Calculate the tension in the string

i) Calculate the acceleration of the masses.

ii) Calculate the tension in the string

Expert's answer

Acceleration of the masses

"F_{1} = F_{x}-F_{k}"

"a_{2} = \\frac {(40-5)}{8} = 4.375 \\frac {m} {sec^{2}}"

"\\mu_{2} = \\frac {F_{k}} {N} = \\frac {5} {8\\times9.81}=0.064"

fraction is same "\\mu_{2}=\\mu{1}=0.064"

Friction force at mass 1 "F_{f} = 0.064\\times ((2+8)\\times 9.81) =6.28 N"

"a_{1} = \\frac {F_{f}} {m_2} = \\frac {6.28}{2}=3.14 \\frac {m} {sec^2}"

Tension in the string

"T = W_1+W_2 = 2\\times 9.81+8\\times 9.81 = 98.1 N"

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