Question

Two crates are connected by a rope lying on a horizontal surface. Crate 𝐴 and 𝐵 has a mass of 𝑚𝐴, and 𝑚𝐵, respectively. The coefficient of kinetic friction between each crate and the surface is 𝜇k. The crates are pulled to the right at a constant velocity by a horizontal force.  In terms of 𝑚𝐴, 𝑚𝐵, and 𝜇𝑘, calculate a) the magnitude of the force 𝐹; b) the tension in the rope connecting the blocks. Include the free-body diagram or diagrams you used to determine each answer.

Answer 1

(a) Determine the magnitude of the force using Newton's second law:

$$F-f_A-f_B=0,\\ f_A=\mu_km_Ag,\space f_B=\mu_km_Bg,\\ F-\mu_km_Ag-\mu_km_Bg=0,\\ F=\mu_kg(m_A+m_B).$$

(b) Determine the tension considering blocks B (the rear one) and A as an isolated system:

$$A:T-\mu_km_Bg=0,\\ T=\mu_km_Bg.$$

The free-body diagram: