Question

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

Answer 1

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

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