Physics of Freefall and Terminal Velocity

Freefall and Terminal Velocity

• Objects falling near Earth's surface accelerate at approximately 9.8 m/s².
• Objects falling through fluids eventually reach terminal velocity.
• Terminal velocity is the maximum speed where the forces acting on the object are balanced. The resultant force is zero. This means the object falls at a steady speed.
• Skydivers reach a terminal velocity of about 53 m/s when falling spread-eagled.
• Terminal velocity occurs when the forces acting on the object are balanced; the resultant force is zero.
• Stopping distances depend on speed, mass, road surface, and reaction time.
• Falling objects eventually reach terminal velocity.

Falling Through Fluids: Stages

• Initial Acceleration: The object accelerates due to gravity, its speed increases, and the resultant force acts downwards (weight > friction).
• Decreasing Acceleration: Speed increases, but acceleration decreases as air resistance (friction) increases. The resultant force is still downwards (weight > friction).
• Terminal Velocity: The object's speed levels off at a constant speed as the resultant force becomes zero. This means the weight force is eventually equal to the air resistance. The object does not stop falling unless it hits something.

Skydiving Example

• Weight remains constant during freefall.
• Parachute opening: Air resistance dramatically increases, causing a decrease in speed until a new, lower terminal velocity is reached. This does not cause the skydiver to rise.
• The visual illusion of upward movement during parachute opening is due to the timing difference between the falling camera and the falling sky diver.

Velocity-Time Graph (Fluid Falling Object)

• Initial acceleration: Speed increases, acceleration is high.
• Decreasing acceleration: Speed increase is less, but still increasing, acceleration decreases.
• Reaching terminal velocity: Speed is constant, no acceleration, Forces are balanced.

Newton's First Law and Resultant Force

• Newton's First Law: An object remains in the same state of motion unless a resultant force acts on it.
• Uniform Motion (Constant Velocity): If the resultant force is zero, an object's speed and direction remain constant (e.g., constant speed car, balanced forces).
• Non-Uniform Motion: If the forces are not balanced, the resultant force is not zero, and the speed, direction, or both can change.
• Resultant force: The single force that could replace all the forces acting on an object, found by adding these together.
• Newton's Second Law: Acceleration is directly proportional to the resultant force and inversely proportional to the mass. (F = ma)
• Inertial mass: A measure of how difficult it is to change the velocity of an object; calculated as the ratio of force over acceleration.

Balanced Forces (Example of a Submarine)

• Balanced Forces: Horizontal or Vertical forces equal in size and opposite in direction will result in zero resultant force.
• Horizontal Forces: Balanced forces mean zero horizontal acceleration for a submarine.
• Vertical Forces: Balanced forces mean zero vertical acceleration for a submarine.
• Object continues at same speed and in same direction(stationary, constant speed, straight line).

Calculating Forces and Accelerations

• Force (F) = mass (m) × acceleration (a)
• Example: To accelerate a 22 kg cheetah at 15 m/s², the force needed is ~330 N.
• Example: To accelerate a 15 kg gazelle at 10 m/s², the force needed is ~150 N.
• Estimating forces for road vehicles: Use estimated values of mass and acceleration to calculate force.
• Example: Force to accelerate a family car (~1600 kg) to its top speed (~3 m/s²) is approximately ~4800 N.
• Example: Force to accelerate a lorry (~36000 kg) to its top speed (~0.4 m/s²) is approximately ~14400 N.

Investigating Force and Acceleration

• Varying the force on an object affects its acceleration.
• Acceleration is directly proportional to the force applied.
• The relationship is linear where acceleration increases proportionally with the applied force.
• This relationship can be confirmed by plotting a graph with acceleration on the vertical axis and force on the horizontal axis, and observing whether the data points fall on a straight line passing through the origin.

Investigating Mass and Acceleration

• Experiment: Investigating the effect of varying mass on acceleration using a constant force (0.98 N).
• Method: Increase the mass of an object while keeping the applied force constant, and measure the acceleration.
• Data Collection: Record total mass (glider + added masses), calculate 1/mass, and plot acceleration vs. 1/mass.
• Analysis: Plot a graph of acceleration against 1/mass. The results should show an inverse proportionality: decreasing mass leads to increasing acceleration. A straight line graph through the origin confirms this relationship. Analyze any deviations.
• New Information: In this experiment, use 0.98 N force with increasing masses, and plot acceleration against 1/mass. Expected result: A straight line through the origin.

Reaction Time and Stopping Distances

• Reaction time varies from 0.2 s to 0.9 s.

• Longer reaction times increase thinking distance at a given speed.

• Reaction time can be measured using standardized methods like dropping a ruler.

• Braking distance is influenced by friction between brakes and wheels, reducing kinetic energy and increasing brake temperature.

• Faster vehicles require greater braking force for a given stopping distance.

• High deceleration can lead to overheating or loss of vehicle control.

• Thinking distance is directly proportional to speed (speed = distance × time with constant reaction time).

• Braking distance increases fourfold when speed doubles.

Explore the principles of freefall and terminal velocity as objects fall through Earth's atmosphere. Understand how forces like gravity and air resistance interact to influence the motion of falling objects, including the concept of terminal velocity and its significance for skydivers. This quiz covers key stages of falling through fluids, making it an essential resource for physics students.