Hi Guys,
I just did a practical based on launching marbles at a certain launch angle and measuring the time and the horizontal distance it covers. We used a piece of equipment to measure the time the marble was in flight. However, when I calculated the time theoretically(without air resistance), the time was in fact greater than the practical time(obtained by the equipment). My question is why would this be the case and what does this suggest? I thought I would get the complete opposite with the theoretical time being lower than the practical time as the theoretical time is calculated without the presence of air resistance whilst the practical time(time obtained by the equipment) takes into account the presence of air resistance.
All replies will be much appreciated
Thanks
Let's break the problem up into 2 parts. One when the projectile is going up, and another while its going down.
Air resistance is a function of v^2. Therefore we can say that a projectile will experience greater air resistance the faster it is moving.
Now let's look in the horizontal direction. Air resistance doesn't just act in the y direction, but in the x direction as well. This means that by the time the projectile reaches its peak, its x component of velocity would've decreased by heaps.
Now in the y direction while the projectile is going up, it will experience a force of the form kv^2 opposing it's motion. This means the max height that the projectile reaches will be less than if there was no air resistance.
As the projectile starts it's descent the air resistance will resist it's downward motion thus increasing time of flight, but since it's velocity is less, the amount of air resistance it experiences is less, thus it wont increase the time of flight as much as it decreases it upon going up. This means the total time of flight will be less for air resistance.
Now what I've said above will vary and really depends on the specific scenario. Really it depends on the specific projectile and hard to just generalize to one scenario. I've only just used it to explain your experimental results.
For example an interesting scenario is if you throw the projectile at a velocity greater than it's terminal velocity, then it experiences much greater air resistance going up than it ever can going down, thus reducing the time of flight.