What would be the appearance of the speed-time curve if the fallng body where so light that the effect of air friction could not be neglected?
It would start out as a linear relationship
v = g t,
but the curve would eventually flatten out to a horizontal asymptote at the limiting velocity, V
The v(t) relationship is approximately:
v = V [ 1 - e^-(gt/Vlim)]
Actually, this assumes that the drag force is proportional to velocity and that the body is not an irregular shape that tumbles
If the effect of air friction cannot be neglected, the appearance of the speed-time curve of a falling body would be different compared to a situation where air friction is negligible.
Typically, without air friction, the speed of a falling body would increase continuously at a constant rate. However, when air friction comes into play, it opposes the motion of the falling body, resulting in a change in the speed-time curve.
In the presence of air friction, the speed-time curve would show a different behavior. Initially, as the object starts falling, its speed would increase at a decreasing rate compared to a frictionless scenario. This is because the air friction will provide a resisting force that limits the acceleration of the object.
As the object gains speed, the air friction will have a greater impact, eventually reaching a point where the air friction force equals the force of gravity (weight) acting on the object. At this point, the speed of the object will become constant, meaning that the resistance offered by air friction matches the force of gravity, resulting in no further acceleration.
Therefore, in the presence of air friction, the speed-time curve would show an initial increase in speed at a decreasing rate, followed by a plateau where the speed remains constant.
To understand the appearance of the speed-time curve for a falling body in the presence of air friction, we need to consider the forces acting on the body.
When an object falls through the atmosphere, it experiences two main forces: gravity pulling it downward and air friction or drag acting in the opposite direction.
Initially, as the body starts to fall, the force of gravity is greater than the force of air friction. Therefore, the body accelerates downwards, and its speed increases. However, as the speed of the body increases, the force of air friction also increases.
There comes a point where the force of gravity and the force of air friction balance each other out. This is known as terminal velocity. At this stage, the net force on the body becomes zero, and the speed remains constant.
So, in the speed-time curve, when air friction cannot be neglected, we would observe the following behavior:
1. Initially, the curve will show an increasing speed, as the body accelerates due to gravitational forces.
2. As air friction starts to have an impact, the rate of increase in speed will decrease.
3. Eventually, the speed will reach a maximum value, representing the terminal velocity, and it will remain constant thereafter.
The curve will become horizontal at the level of the terminal velocity, indicating that the speed is no longer changing. This is because the gravitational force and air friction force are equal and opposite, resulting in zero net force, and therefore, no further acceleration.
It's important to note that the exact shape of the curve may vary depending on the specific object's properties and the atmosphere through which it is falling. Factors such as shape, surface area, and density of the object, as well as the density and viscosity of the air, can all affect the appearance of the speed-time curve.