Question

Consider a force of 28 mg 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. Find the acceleration a of this system of blocks.

Answer 1

To find the acceleration of the system of blocks connected by inextensible strings, we can set up a system of equations and apply Newton's second law. The tension in the string can also be found using a separate equation. The speed with which the hanging mass hits the floor can be calculated using the equation for potential energy.

Step-by-step explanation:

To find the acceleration of the system, we need to consider the forces acting on the two blocks. The force pulling the blocks vertically is 28 mg, where m represents the mass of one block. Since the blocks are connected by inextensible and massless strings, the tension in the strings is the same. By applying Newton's second law to both blocks, we can set up a system of equations and solve for the acceleration. The tension in the rope can also be found using the equation T = m₁a, where T is the tension and m₁ is the mass of the block on the table.

Acceleration of the system (a) = 28g / (2m).
Tension in the rope (T) = m₁a = 2m * (28g / (2m)) = 28g.
Speed with which the hanging mass hits the floor = √(2gh), where g is the acceleration due to gravity and h is the height from which the mass is dropped.