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March 29, 2024, 06:46:12 am

Author Topic: Physics Question about the effect of air resistance  (Read 1272 times)  Share 

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dream chaser

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Physics Question about the effect of air resistance
« on: August 05, 2019, 06:43:04 pm »
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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  :)
« Last Edit: August 05, 2019, 06:45:29 pm by dream chaser »

DrDusk

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Re: Physics Question about the effect of air resistance
« Reply #1 on: August 05, 2019, 07:49:26 pm »
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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.
« Last Edit: August 05, 2019, 07:52:43 pm by DrDusk »

dream chaser

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Re: Physics Question about the effect of air resistance
« Reply #2 on: August 05, 2019, 08:02:39 pm »
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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.

Thanks DrDusk. Your reply is much appreciated.  :)

So you are saying that the horizontal velocity of the marble decreases as the time progresses of the marble in flight?

DrDusk

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Re: Physics Question about the effect of air resistance
« Reply #3 on: August 05, 2019, 08:21:58 pm »
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Most definitely. 

dream chaser

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Re: Physics Question about the effect of air resistance
« Reply #4 on: August 05, 2019, 08:32:24 pm »
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Most definitely.

Another question. Why is it that 45 degrees is the angle that gives the greatest theoretical(without air resistance) horizontal range when the vertical displacement is zero?

Bri MT

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Re: Physics Question about the effect of air resistance
« Reply #5 on: August 05, 2019, 08:43:47 pm »
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Another question. Why is it that 45 degrees is the angle that gives the greatest theoretical(without air resistance) horizontal range when the vertical displacement is zero?

You can derive this using the trig formulas and the range equation :) I.e. just put theta into the trig equations and solve for maximum range


DrDusk

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Re: Physics Question about the effect of air resistance
« Reply #6 on: August 05, 2019, 08:46:37 pm »
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Now lets suppose the projectile is launched at any arbitrary angle theta where theta is between 90 and 0 degrees. Lets also suppose its net velocity(the sum of its x and y components) is v.






If you sub this expression into the vtcos(theta), you can differentiate x with respect to theta and find that the maxima occurs at 45 degrees


I hope the VCE'rs don't mind a fellow NSW'er answering questions on here
« Last Edit: August 05, 2019, 08:50:12 pm by DrDusk »

dream chaser

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Re: Physics Question about the effect of air resistance
« Reply #7 on: August 05, 2019, 08:52:23 pm »
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Now lets suppose the projectile is launched at any arbitrary angle theta where theta is between 90 and 0 degrees. Lets also suppose its net velocity(the sum of its x and y components) is v.






If you sub this expression into the vtcos(theta), you can differentiate x with respect to theta and find that the maxima occurs at 45 degrees


I hope the VCE'rs don't mind a fellow NSW'er answering questions on here


Okay, thanks. Also, with the experiment I did, I forgot to mention that the launch angle of the marble was zero degrees(i.e no vertical velocity initially). Does the explanation you gave a couple of posts back still apply to this situation. Sorry for not mentioning this before

DrDusk

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Re: Physics Question about the effect of air resistance
« Reply #8 on: August 05, 2019, 08:56:15 pm »
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Okay, thanks. Also, with the experiment I did, I forgot to mention that the launch angle of the marble was zero degrees(i.e no vertical velocity initially). Does the explanation you gave a couple of posts back still apply to this situation. Sorry for not mentioning this before

Ooooooh no that's a completely different scenario then. All good for not mentioning it.

In that case your measurements are flawed, because for the projectiles entire journey the air resistance will resist it's downward motion. So you are right in saying the practical value should be greater.

By how much is it greater though? If it's like 1 or 2 seconds then that's normal because of error in the stopwatch or whatever you used to measure it and also because the marble is really small so the air resistance wouldn't make that much of a difference.
« Last Edit: August 05, 2019, 08:58:18 pm by DrDusk »

dream chaser

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Re: Physics Question about the effect of air resistance
« Reply #9 on: August 05, 2019, 09:00:37 pm »
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Ooooooh no that's a completely different scenario then. All good for not mentioning it.

In that case your measurements are flawed, because for the projectiles entire journey the air resistance will resist it's downward motion. So you are right in saying the practical value should be greater.

By how much is it greater though? If it's like 1 or 2 seconds then that's normal because of error in the stopwatch or whatever you used to measure it and also because the marble is really small so the air resistance wouldn't make that much of a difference.

Well the time I got according to the equipment(with air resistance) was 0.48 seconds and the time I calculated through formulas(without air resistance) is 0.5091 seconds

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Re: Physics Question about the effect of air resistance
« Reply #10 on: August 05, 2019, 09:02:52 pm »
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Well the time I got according to the equipment(with air resistance) was 0.48 seconds and the time I calculated through formulas(without air resistance) is 0.5091 seconds

Aha see. The difference in the measurement is so small that it doesn't matter. There's always a degree of error in any measurement tool. The time in reality should essentially be the same as the calculated value because the marble is so tiny in surface area that the air resistance it experiences will be quite negligible.

dream chaser

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Re: Physics Question about the effect of air resistance
« Reply #11 on: August 05, 2019, 09:05:42 pm »
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Aha see. The difference in the measurement is so small that it doesn't matter. There's always a degree of error in any measurement tool. The time in reality should essentially be the same as the calculated value because the marble is so tiny in surface area that the air resistance it experiences will be quite negligible.

That's true. The marble used only weighed 16.3 grams as well

blyatman

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Re: Physics Question about the effect of air resistance
« Reply #12 on: August 05, 2019, 09:11:25 pm »
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That's true. The marble used only weighed 16.3 grams as well
Yeah air resistance should be negligible in this situation, even if it was launched at an angle (unless you were using a trebuchet and launching them from the rooftops). For a 10g marble, k (from the kv^2 term) would be on the order of about 0.1, which wouldn't make much of a difference if it was a small-scale experiment.
« Last Edit: August 05, 2019, 09:14:05 pm by blyatman »
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