Question

two boxes are placed side by side there is an applied force on the left box and frictional forces for both boxes what is the acceleration for both boxes

Answer 1

The acceleration of the left box is
`\(a_L = (F - f_(L))/(m_L)\),`and the acceleration of the right box is
`\(a_R = (f_(L) - f_(R))/(m_R)\),`where F is the applied force,
`\(f_(L)\)`is the frictional force on the left box, \
`(f_(R)\)` is the frictional force on the right box,
`\(m_L` is the mass of the left box, and
`\(m_R\)` is the mass of the right box.

Step-by-step explanation:

In the system with two boxes placed side by side, the left box experiences an applied force F and a frictional force
`\(f_(L)\).` The net force on the left box
`(\(F - f_(L)\))` divided by its mass
`\(m_L\)`gives the acceleration
`\(a_L = (F - f_(L))/(m_L)\)`. This equation is derived from Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

On the other hand, the right box, being in contact with the left box, experiences a frictional force
`\(f_(R)\)`opposing its motion. The net force on the right box
`(\(f_(L) - f_(R)\))`divided by its mass
`\(m_R\)` gives the acceleration
`\(a_R = (f_(L) - f_(R))/(m_R)\)`. This equation reflects the fact that the acceleration of an object is determined by the net force acting on it, in this case, the difference between the frictional forces on the left and right boxes, divided by the mass of the right box.

Understanding and calculating these accelerations allow us to analyze the motion of the boxes under the influence of applied and frictional forces, providing valuable insights into their behavior in a given physical scenario.