Transcript Terminal Velocity - Mr. Nguyen's Website

Terminal Velocity
D. Crowley, 2008
2015年7月28日
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
Resultant force = 5’200N (no drag at 0mph)!
5’150N
5’200N
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?
Velocity-Time Graph
Parachute opens – diver
slows down
Velocity
Speed
increases…
Terminal
velocity
reached…
New, lower terminal velocity
reached
Time
Diver hits the ground
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
1.
The diagram shows a skydiver – two forces act on the skydiver (X and Y)
X
Y
a)
b)
c)
d)
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
a)
What is the equation which links weight, gravitational field
strength and mass? Weight = mass x gravity
a)
What causes force X? Drag (air resistance / friction)
a)
As the skydiver falls the size of force X increases. What happens to
the size of force Y? Stays the same
a)
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