Understanding the Setup

* Pulley: A pulley changes the direction of the force but doesn't change its magnitude.

* Frictionless: This means we don't have to consider any energy loss due to friction.

* Negligible Mass: The string has almost no mass, so we don't need to account for its inertia.

Forces Involved

* Gravity: Both masses experience a downward force due to gravity (m1g and m2g).

* Tension: The string exerts an upward force on both masses (T).

Newton's Second Law

We'll use Newton's Second Law (F = ma) to find the acceleration:

1. Free Body Diagrams: Draw separate free body diagrams for each mass:

* Mass 1 (m1):

* Downward force: m1g

* Upward force: T

* Mass 2 (m2):

* Downward force: m2g

* Upward force: T

2. Equations of Motion: Apply Newton's Second Law to each mass:

* Mass 1: T - m1g = m1a

* Mass 2: m2g - T = m2a

3. Solve for Acceleration (a):

* Add the two equations together to eliminate T:

m2g - m1g = (m1 + m2)a

* Simplify and solve for a:

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

Calculations

* m1 = 30 grams = 0.03 kg

* m2 = 40 grams = 0.04 kg

* g = 9.8 m/s² (acceleration due to gravity)

Substitute the values into the equation:

a = (0.04 kg - 0.03 kg) * 9.8 m/s² / (0.03 kg + 0.04 kg)

a ≈ 1.4 m/s²

Answer:

The acceleration of the system is approximately 1.4 m/s².