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power and distance (Read 6939 times)

Aussie

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Re: power and distance
Reply #15 - May 18^th, 2008 at 7:01pm

bigkahuna wrote on May 18^th, 2008 at 7:15am:

There is no terminal velocity if something is being acted upon by an outside force.

This "terminal velocity" notion can be a little confusing. It doesn't mean that an object cannot be thrown faster than this speed, only that a freefalling object will not go faster. Of course an object moving horizontally at this speed will be subjected to an instantaneous retardation of 1 g, ie. losing speed pretty quickly.

Cranks are little things that make revolutions.&&

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Thomas Senior Member Offline Rocks? Posts: 292 NORTHEAST OHIO Gender:	Re: power and distance Reply #16 - May 18^th, 2008 at 7:22pm Exactly, terminal velocity is just that. I don’t know what the golf ball terminal velocity is. tom
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Burner Interfector Viris Spurii Offline Take me out to the ball game........ Posts: 1238 Northeast Florida Gender:	Re: power and distance Reply #17 - May 18^th, 2008 at 9:47pm If you throw an object off a cliff,at a respectable angle(30-40 degrees),it will increase speed after it descends below the horizontal plane of takeoff.Is that not correct,assuming that the object will have sufficient enough time to fall far enough to reach its terminal velocity?
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Aussie

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Re: power and distance
Reply #18 - May 18^th, 2008 at 11:41pm

Burner wrote on May 18^th, 2008 at 9:47pm:

If you throw an object off a cliff,at a respectable angle(30-40 degrees),it will increase speed after it descends below the horizontal plane of takeoff.Is that not correct,assuming that the object will have sufficient enough time to fall up far enough to reach its terminal velocity?

The scenario you propose complicates things and there is no single yes or no answer. IN THEORY if there was no atmosphere the object would be losing speed until it reached the top of its trajectory. Once it started coming down again it would regain speed and be travelling at the same speed which it was originally thrown once it reached its original level. It would then continue accelerating until it hit the bottom of the cliff. With no atmosphere there is no such thing as terminal velocity. Of course atmosphere is always present and air drag is always directly opposing motion.

The best analogy I can think of is it's like riding a bike with the brake dragging. You can still ride it and it will even roll uphill a bit if your speed is high enough. But even downhill it won't go as fast as if the brake was off. It always opposes motion whichever way you're going. And there is going to be a speed beyond which you will not be able to go no matter how hard you pedal.

Whether or not your thrown object reaches terminal velocity depends on what it is, how hard you threw it and how high the cliff is etc. Also your projectile has a horizontal component to its velocity, ie. it's moving over the ground not only going straight up or down under the influence of gravity. Assuming your projectile is a baseball, it will reach terminal velocity if the vertical component of its velocity reaches the 97 mph quoted above. Because it also has a horizontal componenet to its velocity which is not affected by gravity its actual speed through the air may in fact be slightly higher.

However the horizontal componenet is also constantly being reduced by air drag. That's why a high arcing shot always hits the ground with a steeper angle than the one with which it as thrown. The ball's speed over the ground is constantly reducing so eventually it will be falling almost vertically.

Hope that helps.

Cranks are little things that make revolutions.&&

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wanderer

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Re: power and distance
Reply #19 - May 19^th, 2008 at 9:47am

bigkahuna wrote on May 18^th, 2008 at 7:15am:

There is no terminal velocity if something is being acted upon by an outside force.

At the terminal velocity the gravitational force on the body is balanced exactly by the drag force, so the total force on the body is zero, and so it's velocity doesn't change.

The terminal velocity is a really helpful figure when we think about sling bullets. If we can sling at a speed say above half the terminal velocity, then we need to worry about loss of speed due to air resistance. Unfortunately although one can compute these things (there is a little bit on drag in the WIKI) the figures are unreliable because the fudge factors (drag coefficients) are very sensitive to circumstances.

A few figures I get are:

baseball ball	35.1m/s	78.9 mph	86.9m
cricket ball	37.0m/s	83.3 mph	96.8m
tennis ball	24.4m/s	55.0 mph	42.2m
golf ball	33.4m/s	75.2 mph	78.9m
50gm lead ball	73.0m/s	164.3 mph	376.9m
#2 birdshot	31.6m/s	71.0 mph	70.4m

The last column is the distance in metres that the projectile will travel to lose half it's speed just through air resistance. The last line on birdshot is there because I could find some ballistics information on shotgun pellets. The figures for this match very well with published figures.

It's clear that we are all affected pretty strongly by air resistance when we sling, except perhaps with lead glandes.

The figures assume all the projectiles are smooth spheres (drag coefficient 0.47 - OK I know that's debateable!) and are for sea level. I could well believe Thomas' value for terminal velocity of a baseball is correct even though the calculations above predict a lower value. If anyone is interested how these figures are gotten, PM me and I'll see what I can do.

Sorry about the units - but I'm darned if I'm going to work everything in feet per second, etc. Angry

To go back to Slingbadger's original question - the distances give you an idea of how fast these things fall off - clearly air resistance matters Wink

. Also, if one does the calculations for ellipsoidal shot of the same weights, the bullets travel nearly three times further before they lose half their speed - that's a big improvement for the likes of neolithic hunters with clay shot.

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