Problem 12 - Basic Physics: A Self-Teaching Guide

Question

The acceleration of gravity is \(9.8 \mathrm{~m} / \mathrm{s}^{2}\) downward. In actual practice, does an object continue to accelerate if dropped from a tall building? Explain. ___________

Step-by-Step Solution

Answer

No, it does not. The object reaches terminal velocity due to air resistance and then stops accelerating.

Step 1: Identify the Situation

An object is dropped from a tall building, and the acceleration due to gravity is given as 9.8 m/s^2 downward.

Step 2: Understand Free Fall

In a vacuum, an object in free fall continues to accelerate at 9.8 m/s^2 until it hits the ground, because there is no air resistance.

Step 3: Introduce Air Resistance

In actual practice, air resistance acts on the object as it falls. This resistance opposes the motion of the object.

Step 4: Explain Terminal Velocity

As the object falls faster, the air resistance increases. Eventually, the force of air resistance equals the force of gravity, causing the object to stop accelerating. At this point, the object falls at a constant speed known as terminal velocity.

Step 5: Conclusion

Therefore, in real-life conditions, an object does not continue to accelerate indefinitely when dropped from a tall building. It accelerates until it reaches terminal velocity.

Key Concepts

Free Fall

When we talk about free fall, we mean an object falling solely under the influence of gravity. In a vacuum, where there is no air resistance, an object in free fall will continue to accelerate at a rate of 9.8 m/s². This is because gravity is the only force acting on it.

In real-life conditions, other forces like air resistance come into play. Free fall is an idealized concept that helps us understand how gravity works without any other forces. It is important to understand this concept as a foundation for studying more complex cases, such as falling with air resistance.

Air Resistance

Air resistance, also known as drag, is the force that opposes the motion of an object through the air. When an object falls, it pushes against the air, and the air pushes back. This creates air resistance.

Several factors affect air resistance:

• Speed of the object: Faster objects face greater air resistance.
• Surface area: Larger surface areas increase air resistance.
• Shape of the object: Aerodynamic shapes reduce air resistance.

Initially, an object will accelerate due to gravity. However, as it speeds up, air resistance grows larger and begins to counteract the force of gravity, slowing down the acceleration.

Terminal Velocity

Terminal velocity is the constant speed an object reaches when the force of air resistance equals the force of gravity acting on it. At this point, the object stops accelerating and continues to fall at a steady rate.

Key points about terminal velocity:

• It depends on the mass, shape, and surface area of the object.
• It is lower for objects with larger surface areas and higher for more compact objects.

Once an object reaches terminal velocity, the forces acting on it are balanced, and it will not speed up any more as it falls. Understanding terminal velocity helps explain why objects with different shapes and masses fall at different rates in the presence of air resistance.