Question

Consider a force of 28 m g pulling two blocks connected by inextensible strings (which can be considered massless) in the vertical direction, where the masses are a multiple of a given mass m. 18 m 9 m f = 28 m g g t a find the acceleration a of this system of blocks.

Answer 1

To find the acceleration of the system, divide the force acting on the system by the total mass. The tension in the rope is the same on both blocks. To find the force needed to give the second block the same acceleration as the system, rearrange the equation for acceleration.

Step-by-step explanation:

To find the acceleration of the system of blocks, we can use Newton's second law of motion. The net force acting on the system is equal to the mass of the system times its acceleration. In this case, the net force is the force of 28 m g minus the force of friction between the blocks. We can assume that the force of friction is negligible, so the net force is simply 28 m g. Therefore, the acceleration of the system is equal to the force divided by the total mass of the system.

To find the tension in the rope, we can consider the forces acting on each block. The block with mass 18 m has a downward force of 18 m g and an upward tension force from the rope. The block with mass 9 m has a downward force of 9 m g and an upward tension force from the rope. Since the blocks are connected by the rope, the tension force is the same on both blocks.

By using the equation for the acceleration of the system and the tension in the rope, we can find the acceleration and the tension when the second block is separated and a different force is applied. The force needed to give the second block the same acceleration as the system can be found by rearranging the equation for acceleration.