Question

26. 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 𝑚k. The crates are pulled to the right at a constant velocity by a horizontal force 𝐹. 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) The magnitude of F can be found by Newton's first law:

$$F=\mu_k m_Ag+\mu m_Bg=\mu_kg(m_A+m_B).$$

b) Determine the tension.

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