Two blocks are connected by a lightweight, flexible cord that passes over a frictionless pulley. If m1 = 3.8 kg and m2 = 9.2 kg, and block 2 is initially at rest 140 cm above the floor, how long does it take block 2 to reach the floor?

Acceleration a = (m2 -m1)/(m2 +m1) * g

Solve for t:

(a/2)*t^2 = 0.140 meters

To calculate the time it takes for block 2 to reach the floor, we need to consider the forces acting on the system and apply Newton's laws of motion.

Let's start by analyzing the forces acting on the blocks. The force of gravity acts on both blocks, pulling them downward. Block 1 experiences a tension force from the cord that opposes its downward motion, while Block 2 only experiences the force of gravity.

Now, let's break down the problem step by step:

Step 1: Calculate the acceleration of the system:
Since the pulley is frictionless, the acceleration of both blocks will be the same and is determined by the net force acting on the system.

The net force is given by subtracting the force exerted by the lighter block from the force exerted by the heavier block.

F_net = m2 * g - m1 * g
= (9.2 kg) * (9.8 m/s^2) - (3.8 kg) * (9.8 m/s^2)

Step 2: Calculate the acceleration of the system:
The mass of the system is the sum of the masses of the two blocks.

m_system = m1 + m2 = 3.8 kg + 9.2 kg

Step 3: Calculate the acceleration of the system:
Using Newton's second law of motion, we can now calculate the acceleration of the system:

a = F_net / m_system

Step 4: Calculate the time taken for Block 2 to reach the floor:
We can use the kinematic equation:

d = v_i * t + (1/2) * a * t^2

Given that Block 2 is initially at rest, its initial velocity (v_i) is zero. The distance it travels is 140 cm, which we need to convert to meters:

d = 140 cm = 1.4 m

Rearranging the equation, we get:

t = sqrt((2 * d) / a)

Now, substitute the values for d and a from the previous steps, and you can calculate the time it takes for Block 2 to reach the floor.