Question

Two objects are connected by a light string that passes over a frictionless pulley. The coefficient of sliding friction between the 4kg object and surface is 0.30. Find the acceleration of the two object and tension in the string, other object is 10kg

Answer 1

We write the equations of motion for each body in projections on the coordinate axes

на ось x

$-F_{fr}+T=m_1a$ (1)

на ось y

$m_2g-T=m_2a$ (2)

$m_1g-N=0$ (3)

given that $F_{fr}=\mu N$ from the equation (3) we write $F_{fr}=\mu m_1g$

add (1) to (2)

$m_2g-F_{fr}-T+T=m_2a+m_1a$

or

$m_2g-\mu m_1g=m_2a+m_1a$

$g(m_2-\mu m_1)=(m_2+m_1)a$

Then the acceleration is

$a=\frac{g(m_2-\mu m_1)}{m_2+m_1}=\frac{9.81(10-0.3 \cdot 4)}{10+4}=6.166 m/s^2$

from (2) we determine the string tension

$T=m_2g-m_2a=m_2(g-a)=10(9 .81-6.166)=36.44 N$