Final answer:
To find the acceleration of the hanging mass in this scenario, we need to consider the forces acting on the system. By setting up equations of motion and solving for the acceleration, we find that the magnitude of the acceleration is approximately 3.6 m/s².
Step-by-step explanation:
To find the acceleration of the hanging mass in this scenario, we need to consider the forces acting on the system. The force pulling the hanging mass downward is equal to its weight, which can be calculated by multiplying its mass by the acceleration due to gravity. The tension in the string is equal to the force pulling the hanging mass upward.
Finally, the frictional force between the block and the horizontal surface opposes its motion. We can use these forces to set up equations of motion for the system and solve for the acceleration of the hanging mass.
Let's assume that the acceleration of the hanging mass is a. Then, the net force acting on it in the vertical direction is given by:
(m2 * g) - T = m2 * a
where m2 is the mass of the hanging mass, g is the acceleration due to gravity, and T is the tension in the string.
The net force acting on the block on the horizontal surface in the horizontal direction is given by:
T - F_friction = m1 * a
where m1 is the mass of the block, and F_friction is the frictional force.
By substituting the expressions for the tension (T) and frictional force (F_friction) into the equations of motion, we can solve for the acceleration (a). The magnitude of the acceleration of the hanging mass is approximately 3.6 m/s².