Question

Blocks A, B, and C are placed as in the figure below and connected by ropes of negligible mass. Both A and B weigh 25.0N each, and the coefficient of kinetic friction between each block and the surface is 0.35. Block C descend with constant velocity. a) Draw separate free-body diagrams showing the forces acting on each block. b) Find the tension in the rope connecting blocks A and B. c) What is the weight of block C? 45°

Answer 1

(a) Let's draw the free-body diagram:

(b) Let's write the forces acting on the block A in projections on axis $x$ and $y$:

$$T_1-F_{frA}=0,$$ $$N_A-W_A=0.$$

Then, we get:

$$T_1=F_{frA}=\mu_kN_A=\mu_kW_A,$$ $$T_1=0.35\cdot25.0\ N=8.75\ N.$$

(c) Let's write the forces acting on the block C in projections on axis $y$:

$$T_2-W_C=0,$$ $$W_C=T_2.$$

Let's find $T_2$. Let's write the forces acting on the block B in projections on axis $x$ and $y$:

$$T_2-T_1-W_Bsin\theta-F_{frB}=0,$$ $$N_B-W_Bcos\theta=0.$$

Then, we get:

$$W_C=T_2=T_1+W_Bsin\theta+\mu_kN_B,$$ $$W_C=T_1+W_Bsin\theta+\mu_kW_Bcos\theta=T_1+W_B(sin\theta+\mu_kcos\theta),$$ $$W_C=8.75\ N+25.0\ N\cdot(sin45^{\circ}+0.35\cdot cos45^{\circ})=32.61\ N.$$