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?

To solve this problem, we need to apply the principles of Newton's laws of motion and the concept of conservation of energy.

First, let's set up the problem:

Given:
Mass of block 1 (m1) = 3.8 kg
Mass of block 2 (m2) = 9.2 kg
Initial height of block 2 (h) = 140 cm = 1.4 m

Now, let's analyze the forces acting on the system:

1. Tension in the cord (T): The tension force acts in upward direction on block 1 and downward direction on block 2.

2. Gravitational force (mg): The weight of each block acts downward.

Considering the motion of block 2, we can set up the following equations:

1. The net force acting on block 2 in the downward direction is given by the difference between the gravitational force and the tension force:

F_net = mg - T

2. According to Newton's second law (F = ma), the above equation becomes:

m2 * g - T = m2 * a

Since the pulley is assumed to be frictionless, the acceleration of both blocks will be the same and can be represented as 'a.'

Now, let's examine the energy transformation in the system:

At the initial position, block 2 has gravitational potential energy due to its height above the floor. As it falls, this energy gets converted into kinetic energy.

The change in potential energy is given by:

ΔPE = m2 * g * h

This energy gets converted into kinetic energy, given by:

KE = (1/2) * m2 * v^2

Where v is the velocity of block 2 just before it reaches the floor.

Since the total mechanical energy of the system remains constant, we can equate the change in potential energy to the kinetic energy:

ΔPE = KE

m2 * g * h = (1/2) * m2 * v^2

Simplifying this equation, we get:

v^2 = 2 * g * h

Now, to find the time taken by block 2 to reach the floor:

1. Calculate the velocity (v) using the above equation.

v = √(2 * g * h)

2. Using the following kinematic equation, relate the velocity, acceleration, and time:

v = u + a * t

Since block 2 starts from rest, the initial velocity (u) is 0.

0 = a * t

t = 0

Therefore, the time taken by block 2 to reach the floor is 0 seconds.

Note: This result indicates that the problem is idealized, assuming no friction or other external forces that could slow down or stop the motion of the blocks. In reality, factors such as air resistance and imperfections in the pulley system would affect the actual time it takes for block 2 to reach the floor.