Video Transcript
A free diver of mass 65 kilograms
jumps from an aeroplane from a very high altitude. When the free diver reaches the
terminal velocity, meaning that he will fall at a constant speed, what is the drag
force due to air resistance equal to? Assume that the acceleration due to
gravity is constant and equal to 9.8 meters per second squared.
This question is asking us to
calculate the drag force due to air resistance that acts on a diver when he is at
terminal velocity. Let’s start by thinking about this
phrase “terminal velocity.” We’re told that when the diver is
at terminal velocity, he falls at a constant speed. But what does this mean for the
forces that act on the diver? Recall Newton’s second law of
motion. This tells us that the net force
acting on an object is equal to the mass of the object multiplied by the
acceleration of the object. 𝐹 net is equal to 𝑚𝑎.
When the diver is at terminal
velocity, he has a constant speed. If an object has a constant speed,
its acceleration must be zero. If we substitute 𝑎 equals zero
into Newton’s second law, we see that this means the net force acting on the object
is also zero. So, when the diver is at terminal
velocity, the net force on the diver is zero.
To understand this, let’s draw a
diagram. The diver has a weight due to the
gravitational force acting on him. The diver’s weight acts vertically
downwards and pulls the diver towards the Earth. At the instant when the diver first
leaves the plane, his weight causes him to accelerate downwards at 9.8 meters per
second squared. This is the acceleration due to
gravity.
However, as the diver falls, he
also experiences a drag force due to air resistance. Air resistance acts in the opposite
direction to an object’s motion. The faster an object moves, the
greater the air resistance that it experiences. The diver is moving downwards, so
the air resistance acts upwards. At first, the drag force is
small. But as the speed of the diver
increases, so does the air resistance.
Eventually, the diver will reach a
speed called the terminal velocity. At the terminal velocity, the air
resistance that acts on the diver has become equal in magnitude to the diver’s
weight. So, the downwards force of the
weight is exactly balanced by the upwards drag force due to the air resistance. There is no net force acting on the
diver, and the diver no longer accelerates. Instead, the diver falls at a
constant speed.
To answer this question, we need to
find the value of the drag force due to air resistance. Since this is equal to the diver’s
weight, all we need to do is calculate the weight of the diver. Recall that the weight of an object
is equal to the mass of the object, 𝑚, multiplied by the acceleration due to
gravity, 𝑔. Here, we’re told that the mass of
the diver is 65 kilograms and that the acceleration due to gravity is 9.8 meters per
second squared. Substituting these values into the
formula, we see that the weight of the diver is equal to 65 kilograms multiplied by
9.8 meters per second squared. This gives us a value of 637
newtons.
So, if the weight of the diver is
637 newtons and the air resistance is equal to the weight when the diver is at
terminal velocity, then the drag force acting on the diver must be equal to 637
newtons. This is the final answer to this
question.
