What is the difference between instantaneous speed and terminal speed?

Instantaneous speed is the velocity of an object at a specific moment in time, which may be changing. Terminal speed is the specific constant instantaneous speed reached when the drag force exactly balances the weight, resulting in zero acceleration.

How does the terminal speed of a heavy object compare to a light object of the same size and shape?

The heavy object will have a higher terminal speed. Because it has more weight, it must reach a higher speed to generate a large enough air resistance force to balance that weight.

When should you use a 'pointer' in a terminal speed experiment?

A pointer should be used to mark the start of the timed distance. It must be placed low enough that the object has already finished accelerating and reached a constant speed before passing it.

What error occurs if the drop height above the pointer is too small?

The object may still be accelerating when it passes the pointer. This results in an underestimation of the true terminal speed because the average speed measured over the distance will be lower than the final constant speed.

Why is it incorrect to say 'gravity' is the force pulling an object down?

'Gravity' refers to the phenomenon or the field strength ($g$). The actual force acting on the object's mass is called 'weight' ($W = mg$). Using the correct terminology is essential for clarity in force diagrams.

What is a common mistake when timing the fall of light objects like paper cases?

Human reaction time error is significant. This is mitigated by taking multiple repeat readings (e.g., 5 trials) and calculating a mean, or by using electronic gates/video analysis for higher precision.

What is the formula for weight, and what do the variables represent?

The formula is $W = mg$, where $W$ is the weight in Newtons (N), $m$ is the mass in kilograms (kg), and $g$ is the gravitational field strength (approx. $9.81$ N/kg on Earth).

What is meant by 'Resultant Force' in the context of terminal velocity?

The resultant force is the vector sum of all forces acting on the object. At terminal velocity, the upward drag and downward weight are equal and opposite, so the resultant force is exactly zero.

Why does air resistance increase as an object falls faster?

As speed increases, the object collides with more air molecules per second and with greater force. This increased rate of momentum transfer from the air to the object results in a larger resistive force.

Library Podcasts

Courses

Referral & Rewards

2. Forces, Space & Radioactivity

Investigating Terminal Speed

Summary

Terminal speed is the constant maximum velocity achieved by an object falling through a fluid when the upward resistive force (drag) exactly balances the downward force of gravity (weight). This investigation explores the relationship between an object's mass and its terminal speed by measuring the time taken for objects of varying mass to fall a fixed distance once equilibrium is reached.

1. Definition & Core Concepts

Terminal Speed is the steady, constant speed reached by an object when the resultant force acting on it is zero. For a falling object, this occurs when the upward air resistance (drag) equals the downward weight.

Weight ( $W$ ) is the force of gravity acting on the object's mass, calculated as $W = mg$ , where $g$ is the gravitational field strength. Unlike air resistance, weight remains constant throughout the fall.

Air Resistance ( $F_D$ ) is a resistive force that opposes motion through the air. It is not constant; it increases as the object's speed increases until it matches the weight of the object.

A graph showing speed increasing over time until it reaches a horizontal asymptote (terminal speed), accompanied by a free-body diagram showing balanced upward drag and downward weight forces.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions

Investigating Terminal Speed

Q: Define Terminal Speed.

Terminal speed is the constant maximum speed reached by an object falling through a fluid when the upward drag force equals the downward weight of the object.

Summary

1. Definition & Core Concepts

Air Resistance ( $F_D$ ) is a resistive force that opposes motion through the air. It is not constant; it increases as the object's speed increases until it matches the weight of the object.

A graph showing speed increasing over time until it reaches a horizontal asymptote (terminal speed), accompanied by a free-body diagram showing balanced upward drag and downward weight forces.

2. Underlying Principles

According to Newton's Second Law ( $F = ma$ ), an object accelerates as long as there is a non-zero resultant force. Initially, as an object is dropped, its speed is low, air resistance is negligible, and it accelerates at approximately $g$ .

As speed increases, the number of air molecules colliding with the object per second increases, causing the upward air resistance to grow. This reduces the resultant force ( $W - F_D$ ), which in turn decreases the acceleration.

When $F_D = W$ , the resultant force becomes zero ( $a = 0$ ). At this point, the object continues to move at a constant velocity, which is the terminal speed.

3. Methods & Techniques

To investigate the relationship between mass and terminal speed, use objects with high surface area and low mass (like paper filters) so they reach terminal speed quickly within a short vertical distance.

Experimental Setup: Position a pointer at a fixed height above the ground. Drop the object from a point significantly higher than the pointer to ensure it has reached terminal speed before it passes the timing zone.

Data Collection: Measure the time ( $t$ ) it takes for the object to fall from the pointer to the floor over a known distance ( $d$ ). Calculate terminal speed using $v = \frac{d}{t}$ .

Varying Mass: Increase the mass by stacking multiple identical objects together. This keeps the surface area and shape constant while changing the weight, allowing for a fair test of how mass affects speed.