Answer to Question #254992 in Physics for Jan Plaza

Question

A block of m1 = 9 kg rests on a horizontal table, attached to another block of m2 = 3 kg by a light string as shown in the figure below

A. What is the minimum coefficient of static friction such that the objects remain at rest?

B. If the coefficient of static friction is less than that found in part (a), and if the coefficient of kinetic friction between the block and the table is 0.15find the time it takes for the 3kg mass to fall 4 m to the floor if the system starts from rest?

Answer 1

$(a)\ \ T=m_2g=3\cdot9.8=29.4\ (N)$

$F_f=\mu N=\mu m_1g=T\to$

$\mu =T/(m_1g)=29.4/(9\cdot9.8)=0.33$

$(b)\ \ h=at^2/2\to t=\sqrt{2h/a}$

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

$=(3-0.15\cdot9)\cdot9.8/(9+3)=1.35\ (m/s^2)$

$t=\sqrt{2\cdot4/1.35}=2.43\ (s)$ . Answer