Question43. Two blocks are connected by a massless rope as shown below. The mass of the block on the table is 4.0 kg and the hanging mass is 1.0 kg . The table and the pulley are frictionless. (a) Find the acceleration of the system. (b) Find the tension in the rope. (c) Find the speed with which the hanging mass hits the floor if it starts from rest and is initially located 1.0 m from the floor.

Studdy Solution
Use kinematic equations to find the speed of the hanging mass when it hits the floor.
Use the equation $v^2 = u^2 + 2as$, where $u = 0 \, \text{m/s}$ (initial speed), $a = 1.96 \, \text{m/s}^2$, and $s = 1.0 \, \text{m}$:
$$v^2 = 0 + 2 \times 1.96 \times 1.0$$ $$v^2 = 3.92$$ $$v = \sqrt{3.92}$$ $$v \approx 1.98 \, \text{m/s}$$
The acceleration of the system is $1.96 \, \text{m/s}^2$, the tension in the rope is $7.84 \, \text{N}$, and the speed of the hanging mass when it hits the floor is approximately $1.98 \, \text{m/s}$.