Laws of Motion

A 4 kg block rests on top of a 6 kg block, which lies on a frictionless floor. The coefficient of friction between the two blocks is 0.3. A horizontal force F is applied to the TOP (4 kg) block. Find the maximum F for which both blocks move together. (g = 10 m/s²)

A 3 kg block rests on a frictionless 37° incline, connected by a string over a pulley at the top to a 2 kg block hanging vertically. Find the acceleration of the system and the tension. (Use sin37° ≈ 0.6, g = 10 m/s²)

A block rests on a frictionless 45° incline fixed inside a truck. Find the horizontal acceleration the truck must have so the block stays at rest relative to the incline (without sliding down). (g = 10 m/s²)

Two blocks of mass 2 kg and 3 kg are connected by a spring of force constant 500 N/m on a frictionless table. A force of 50 N is applied to the 3 kg block, pulling it away from the 2 kg block. Find the spring's extension once both blocks move with the same (steady) acceleration.

A uniform string of mass 2 kg and length 2 m hangs vertically, with an 8 kg block tied to its bottom end. The string is pulled upward from the top with a force of 120 N. Find the tension at the midpoint of the string. (g = 10 m/s²)

Three blocks of mass 2 kg, 3 kg, and 5 kg are connected in a line by two strings on a frictionless table. A force of 50 N is applied to the 5 kg block (at the far end), pulling all three. Find the tension in each connecting string.