Terminal Velocity

Terminal Velocity D. Crowley, 2008

Terminal Velocity • To understand terminal velocity

Terminal Velocity • What are the forces on a skydiver? How do these forces change (think about when they first jump out; during free fall; and when the parachute has opened)? • What happens if the skydiver changes their position? • The skydiver’s force (W=mg) remains the same throughout the jump • But their air resistance changes depending upon what they’re doing which changes the overall resultant force

Skydiving • Falling objects are subject to the force of gravity pulling them down – this can be calculated by W=mg Weight (N) = mass (kg) x gravity (N/kg) • On Earth the strength of gravity = 10N/kg • On the Moon the strength of gravity is just 1.6N/kg

Positional • What happens when you change position during free-fall? • Changing position whilst skydiving causes massive changes in air resistance, dramatically affecting how fast you fall…

Skydiving Stages • Complete the skydiving stages worksheet • Label the forces • Draw correctly sized force arrows • Write a sentence explaining the forces experienced by the skydiver during the descent

Skydiving Stages • Stage 1 – after just jumping from the plane the skydiver is not moving very fast – their weight is a bigger force than their air resistance, so they accelerate downwards

Skydiving Stages • Stage 2 – eventually the force of the air resistance has increased so much that it is the same size as the skydiver’s weight – the forces are balanced and the speed remains constant (this is terminal velocity)

Skydiving Stages • Stage 3 – when the chute opens air resistance increases dramatically: the air resistance force is much greater than the weight force, so the skydiver slows down

Skydiving Stages • Stage 4 – as the skydiver slows, the air resistance force from the chute is reduced, until it is the same size as the weight force – the forces are balanced and the speed remains constant (this is a new terminal velocity)

Skydive

Terminal Velocity • When vehicles and free-falling objects first move they have much more force accelerating them than resistance which is trying to slow them • As speed increases resistance builds up – gradually reducing the acceleration • Eventually the resistance forces is equal to the accelerating force and the object remains at a constant speed (terminal velocity)

Resultant Force • In most real situations there are at least two forces acting on an object along any direction – the overall effect of these forces is the resultant force, and will decide the motion of the object (whether it accelerates, decelerates or stays at a constant speed) • E.g. a car of mass 1750kg has an engine producing a driving force of 5’200N, with a drag force of 5’150N at 70mph – what is its acceleration when setting off from rest & at 70mph?

Resultant Force • Initially work out the resultant force at rest and at 70mph… 5’200N 5’150N 5’200N Resultant force = 5’200N (no drag at 0mph)! Resultant force = 50N (5’200N – 5150N) Acceleration = force ÷ mass Acceleration = 5’200 ÷ 1’750 = 3.0m/s2 Acceleration = 50 ÷ 1’750 = 0.03m/s2

Velocity-Time Graph • Can you annotate what the velocity-time graph shows for a parachute jump?

Parachute opens – diver slows down Speed increases… Terminal velocity reached… New, lower terminal velocity reached Diver hits the ground Velocity-Time Graph Velocity Time

Fluids & Surface Area • How is the speed of an object and the terminal velocity it will reach affected by the fluid it its travelling through? • How does the shape and area of an object affect its terminal velocity?

Fluids & Surface Area • The speed an object can travel at through a fluid will vary depending upon the drag of the fluid – if the drag is high then this will affect the resultant force so that the terminal velocity of the object is low. If the drag is reduced then the resultant force will increase, allowing for an increased terminal velocity • The accelerating force acting on all falling objects is gravity – all objects would fall at the same rate if there was no drag (air resistance) • The drag is due to the area and shape of the object, which determines the terminal velocity – in skydiving the force of weight = mass x gravity pulls the skydivers towards the Earth • With the parachute open the same force of W=mg pulls the skydivers down, but the drag force is much greater, so the overall resultant force is reduced = reduced terminal velocity

Questions • The diagram shows a skydiver – two forces act on the skydiver (X and Y) X Y What is the equation which links weight, gravitational field strength and mass? What causes force X? As the skydiver falls the size of force X increases. What happens to the size of force Y? Describe the motion of the skydiver when force X is smaller than force Y; and when force X is equal to force Y

Answers What is the equation which links weight, gravitational field strength and mass? Weight = mass x gravity What causes force X? Drag (air resistance / friction) As the skydiver falls the size of force X increases. What happens to the size of force Y? Stays the same Describe the motion of the skydiver when force X is smaller than force Y; and when force X is equal to force Y. When force X is smaller than force Y the skydiver accelerates downwards. When the forces are equal the skydiver moves at a constant speed

Terminal Velocity