Serway & Jewett — The Laws of Motion: Problem 39

Two blocks of masses \(m_1\) and \(m_2\) are placed on a table in contact with each other as discussed in Example 5.7 and shown in Figure 5.13a. The coefficient of kinetic friction between the block of mass \(m_1\) and the table is \(\mu_1\), and that between the block of mass \(m_2\) and the table is \(\mu_2\). A horizontal force of magnitude \(F\) is applied to the block of mass \(m_1\). We wish to find \(P\), the magnitude of the contact force between the blocks. (a) Draw diagrams showing the forces for each block. (b) What is the net force on the system of two blocks? (c) What is the net force acting on \(m_1\)? (d) What is the net force acting on \(m_2\)? (e) Write Newton’s second law in the \(x\) direction for each block. (f) Solve the two equations in two unknowns for the acceleration \(a\) of the blocks in terms of the masses, the applied force \(F\), the coefficients of friction, and \(g\). (g) Find the magnitude \(P\) of the contact force between the blocks in terms of the same quantities.