Question

Block A, as shown in the figure weighs $2N$ and block B weighs $6N$. The coefficient of kinetic friction between all surfaces is 0.25. Find the magnitude of the horizontal force necessary to drag block B to the left at constant speed if A and B are connected by a light, inextensible cord passing around a fixed, frictionless pulley.

• A. $2N$
• B. $3N$
• C. $5N$
• D. $6N$

Answer 1

The correct option is B $3N$

Drawing FBD of the blocks,


Friction force on block A $f_1={\mu }_k{m}_{A}g=\left(0.25\right)\left(2\right)=0.5N$.
and friction force on block B $f_2={\mu }_k(m_A+m_B)g=\left(0.25\right)(2+6)=2N$.

From the FBD of A,
$T=f_1=0.5N$

From FBD of B,
$F-f_2-T-f_1=0$
$\Rightarrow F=f_2+2f_1$ ($\because T=f_1$)
$\Rightarrow F_2=2+1=3N$

The force F must then have magnitude $3N$