91Ó°ÊÓ

A free-body diagram is a simple yet essential tool in physics to visualize the forces acting on an object. Let's consider our two objects: the 15.0 kg load of bricks and the 28.0 kg counterweight.
For the load of bricks, the free-body diagram includes:

• The gravitational force (weight) acting downward, calculated as the mass of the bricks multiplied by the gravitational acceleration (\( m_1g \)).
• The tension in the rope acting upward, which is the force transmitted through the rope.

On the other hand, for the counterweight, the free-body diagram shows:

• The gravitational force (weight) acting downward (\( m_2g \)).
• The tension in the rope acting upward.

By creating these diagrams, we can clearly see all forces involved and set the stage for applying Newton's Second Law to solve for unknowns like tension and acceleration.

Tension in a rope is a force transmitted through a string, rope, cable, or similar when it is pulled tight by forces acting from opposite ends.
In this system involving a pulley, the tension remains constant throughout the rope because the pulley is frictionless and the rope's mass is negligible.
To find the tension while the brick load is moving, we applied Newton's Second Law. We used the equations:

• For the load of bricks: \( T = m_1g - m_1a \)
• For the counterweight: \( T = m_2g + m_2a \)

By solving these equations, we determined that the tension in the rope is approximately 100.95 N when the system moves.
It is crucial to compare this tension with the weights of both masses to understand its influence on the system dynamics.
The tension is less than both the weight of the bricks (\(147 ext{ N}\)) and the counterweight (\(274.4 ext{ N}\)), serving as a balancing force but not a complete one.

The acceleration of an object measures how quickly it changes velocity. When calculating the acceleration of objects connected by a rope over a pulley, we need to consider the difference in their weights.
Applying Newton’s Second Law to our scenario, we derived that:

• The net force acting on the entire system is the difference in gravitational forces of each mass (\((m_2g - m_1g)\)).
• Thus, the net effective force is used to calculate acceleration using the combined mass of both objects.

The formula is given as: \[ a = \frac{(m_2 - m_1)g}{(m_1 + m_2)} \]
Plugging in the values, we find the acceleration of the bricks is approximately 3.15 m/s².
This is a critical insight because it indicates how the difference in mass affects the motion, accelerating the smaller mass (bricks) upward as the heavier mass (counterweight) descends.