Air Resistance and projectile motion

In summary, when dealing with projectile motion and air resistance, it is important to take into account the continuously changing drag force and its direction. This can be calculated using calculus or approximated through programming by calculating the forces acting on the projectile at small time intervals.
  • #1
mpm166
14
0
For projectile motion, how does one take air resistance into consideration?

I have constructed a device to launch a projectile and I know how to deal with projectile motion without any air resistance, but I am unsure how I determine the range (the distance the marble/object will go) in the real world (with air resistance).

can anyone help me out?

thanks
 
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  • #2
If you can do calculus, you can calculate the complete path of the object. The reason you need calculus is that the air resistance, or drag, is a continuously changing force (both in magnitude and direction), unlike gravity, which is fairly constant. The drag force usually goes like F(drag) = -cv, there v is the instantaneous velocity, and c is the drag coeeficient. The drag force always acts opposite to the direction of the instantaneous velocity, ie. always points backwards relative to the projectile. For a smooth, shiny marble, you might find that air resistance is so small that your standard result for the range wll be close enough. Try this and see how far you are off your calculated value. You could then, if necessary, tabulate the error as a function of the range (and height) for different ranges.

Another option, if you don't know calculus, but are good at programming, is the following :

Calculate the forces acting on the particle at the ends of tiny time intervals (like 1 ms). Assume the forces stay constant during the interval, and change only at the end of each interval. This way, you can construct the entire path of the projectile, given initial conditions.
 
  • #3


Air resistance plays a significant role in projectile motion and can greatly affect the trajectory and range of the projectile. In order to accurately calculate the range of a projectile with air resistance, you will need to take into account the drag force acting on the projectile. This drag force is caused by the air resistance and is dependent on the velocity and cross-sectional area of the projectile.

To incorporate air resistance into your calculations, you can use the drag equation, which states that the drag force is proportional to the velocity squared and the cross-sectional area. This equation can be used to determine the magnitude of the drag force and then incorporate it into the equations of motion for projectile motion.

Another approach is to use numerical methods, such as computer simulations, to account for air resistance. This involves breaking down the motion of the projectile into small time intervals and calculating the effects of air resistance at each interval. This can provide a more accurate prediction of the range of the projectile.

Overall, it is important to consider air resistance when dealing with projectile motion in the real world. Neglecting it can lead to significant errors in your calculations. So, whether using equations or simulations, make sure to account for air resistance to get a more precise result for the range of your projectile.
 

What is air resistance?

Air resistance is the force that acts against the motion of an object as it moves through the air. It is caused by the molecules in the air colliding with the object, creating a drag force that opposes the object's motion.

How does air resistance affect projectile motion?

Air resistance can significantly affect the trajectory of a projectile. As the object moves through the air, it experiences a drag force that slows it down and changes its direction. This can cause the object to travel a shorter distance and have a lower maximum height than it would without air resistance.

How can air resistance be reduced?

Air resistance can be reduced by making the object more aerodynamic. This means shaping the object in a way that minimizes the surface area in contact with the air and reduces the drag force. Additionally, increasing the velocity of the object can also decrease the effects of air resistance.

What is the difference between air resistance and terminal velocity?

Air resistance is the force that opposes the motion of an object through the air, while terminal velocity is the maximum speed that an object can reach when falling through the air. When the force of air resistance is equal to the force of gravity, the object will stop accelerating and reach its terminal velocity.

How does air resistance affect different objects?

Air resistance affects objects differently depending on their shape, size, and velocity. Objects with a larger surface area, such as a parachute, will experience a greater air resistance force than smaller objects. Additionally, objects with a higher velocity will experience a greater air resistance force than objects with a lower velocity.

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