Question

Consider the situation depicted in this applet. The red block moves along a rough surface. The system begins at rest. You may assume that the pulley and rope are both massless and frictionless.

Find an expression for the acceleration a of the red block after it is released. Use mr for the mass of the red block, mg for the mass of the gray block, and uk for the coefficient of kinetic friction between the table and the red block. Express your answer in terms of mr, mg,uk, and g.

Answer 1

For a block of mass m _g ,tension in the string T = m _g gFor a block of mass m _r , T - f _k= m _r awhere f k = kinetic frictional force = μ_k m _rgsubstitue values wegetm _g g -μ _k m _rg = m _r afrom this accleration a = [m _g g -μ _k m _rg ] / m_r

Answer 2

for the red block:
T - ?_km_rg =m_ra               (1)
for the gray block:
m_gg - T =m_ga                    (2)
(1) + (2):
m_gg - ?_km_rg = (m_r+ m_g)a
?a = (m_g -?_km_r)g/(m_r +m_g)