Question Video: Determining the Drag Force at Terminal Velocity | Nagwa Question Video: Determining the Drag Force at Terminal Velocity | Nagwa

Question Video: Determining the Drag Force at Terminal Velocity Physics • First Year of Secondary School

A free diver of mass 65 kg 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 m/s².

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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.

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