## Re: [SeattleRobotics] Rapidly moving objects Correction (1/2)mv^2

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• Hello SRS, Kinetic Energy = (1/2)mv^2 = one half m v squared The Kinetic Energy of a moving object increases (exponentially) as the square of the velocity of
Message 1 of 5 , Mar 1, 2001
Hello SRS,

Kinetic Energy = (1/2)mv^2 = one half m v squared

The Kinetic Energy of a moving object increases (exponentially) as the
square of the velocity of the moving object .

K.E. of one pound traveling at one mile per hour = (1/2) x .031081
(foot - lbs) x 1.4667 fps x 1.4667 fps = .03343085 foot-lbs K.E..

K.E. of one pound traveling at 5 miles per hour = .8357716 ft-lbs .

K.E. of one pound at 10 mph = 3.343085 ft-lbs .

K.E. of one pound at 20 mph = 13.372345 ft-lbs .

K.E. of one pound at 50 mph = 83.577 ft-lbs.

At 100 mph, or 146.67 feet per second, the K.E. of a one pound object is
334.3085 ft-lbs .

One pound falling (about 32 feet) for one second reaches a speed of about
32.174 feet per second in the first second or about 21.9 miles per hour.
It has an impact force of about 16.087 ft-lbs.

The acceleration due to gravity G varies with latitude. G = 32.174 feet per
second per second is a standard approximation correct in latitudes between 46
and 47 degrees. From a General Science reference table, G varies with
latitude from 32.08730 at the equator (0 degrees latitude) to 32.25744 at the
poles (90 degrees latitude).

Bryan E. Daniel
Bellevue, Washington

"Bryan E. Daniel" wrote:

> Hello SRS,
>
> Rapidly moving objects are very hazardous.
> This applies to moving robots and moving robot parts.
> Be careful.
>
> The Kinetic Energy of a moving object increases as the
> square of the velocity of the moving object (exponentially).
>
> The Kinetic Energy of a moving object increases directly
> with mass (directly proportional).
> The velocity of the moving object is the more significant
> term.
>
> m = mass = Weight / G G = acceleration of gravity
>
> Weight = 1 pound (example)
>
> G = 32.174 feet per second per second
> m = 1 / 32.174 = .031081 (slugs) mass
>
> K.E. = Kinetic Energy = mv^2 ( = mv squared )

***K.E. = (1/2)mv^2

>
>
> 1 mile per hour = 5280 feet per hour = 88 feet per minute =
> 1.4667 feet per second
>
> K.E.of one pound travelling at one mile per hour = .031081
> (foot - lbs) x 1.4667 fps x 1.4667 fps = .0668617
> foot-lbs K.E..

***half that or .03343085

>
>
> At 5 mph = 7.3335 feet per second,
> K.E. of one pound traveling at 5 miles per hour = 1.6715431
> ft-lbs .

***half that or .8357716

>
> That is 25 times as much kinetic energy as a one pound
> object moving at one mile per hour.
>
> At 10 miles per hour = 14.667 feet per second,
> K.E. of one pound at 10 mph = 6.68617 ft-lbs .

***half that or 3.343085

>
> That is one hundred times as much kinetic energy as one
> pound at 1 mph.
>
> At 20 miles per hour = 29.334 feet per second,
> K.E. of one pound at 20 mph = 26.744689 ft-lbs .

***half that or 13.372345

>
> That is 395.5 times as much kinetic energy as a pound at 1
> mph.
>
> At 50 miles per hour = 73.335 feet per second
> K.E. of one pound at 50 mph = 167.154 foot - lbs

***half that or 83.577

>
> That is 2,500 times as much kinetic energy as the same
> weight at 1 mph.
>
> At 100 mph, or 146.67 feet per second the K.E. of one pound
> object is 668.617 foot-lbs .

***half that or 334.3085

>
> That is 10,000 times as much kinetic energy as the one pound
> weight moving at one mile per hour.
>
> The weight merely acts as a scale multiplier.
> A 2,000 pound car crashes with 2,000 times as much energy at
> each of the speeds as does a one pound weight.
> A 1 ounce weight has one sixteenth the weight of a pound and
> therefore has one sixteenth the kinetic energy at each of
> the speeds.
>
> A 100 pound robot moving five miles per hour has over 167

***half that or over 83

>
> foot pounds of kinetic energy to expend if it runs into
> something.
> A 100 pound robot moving twenty miles per hour has over 2674

***half that or over 1337

>
> foot pounds of kinetic energy to expend if it runs into
> something.
>
> Bryan E. Daniel
> Bellevue, Washington
>
> To unsubscribe from this group, send an email to:
> SeattleRobotics-unsubscribe@egroups.com
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
• ... Slight correction here, even though velocity is ~32 ft/sec at the end of one sec it s zero at the beginning, accel is basically constant due to gravity so
Message 2 of 5 , Mar 1, 2001
> One pound falling (about 32 feet) for one second reaches a speed of about
> 32.174 feet per second in the first second or about 21.9 miles per hour.
> It has an impact force of about 16.087 ft-lbs.
>

Slight correction here, even though velocity is ~32 ft/sec at the end
of one sec it's zero at the beginning, accel is basically constant due
to gravity so average velocity over that second is 32+0/2= 16
feet/second and you only fall ~16 feet in the first second..

And from working with helis the real danger from rotating objects
isn't the KE in it's own right, that's the same as an object of same
weight moving in a line at same speed. But an object with high linear
velocity has a good chance of already being past you, or you getting
through it's line before it hits. Even when it hits something it stands
some chance of a glancing blow, with considerably less energy transfer.
Rotating objects on the other hand can have very high KE with no or
relatively low total displacement. People stand a much greater chance
of becoming lax around a rotating object than linear movement at same
energies because of this. And no matter how slow the relative
displacements, when something does come into contact with it, it tends
to hold it's position or velocity due to high apparent intertia from
gyroscopic effects, so there tend to be multiple to many hits, not just
one. Tends toward higher energy transfer, even for 'glancing' impacts.
People or animals or objects coming into the edge of a RC heli rotor
disc tend to get hit several times, the tip velocities are a large
fraction of the speed of a bullet, and it tends to have a similar effect
to getting several grazing gunshot wounds at once. One case comes to
mind off hand, he was lucky and it did only hit once, 56 stitches just
below the knee. If it'd hit any bone, whatever it hit would have
shattered. And that was a 'lucky' instance.
• This is not an exponential increase. It is a quadratic increase. If a parameter increased exponentially with velocity, then velocity would appear as an
Message 3 of 5 , Mar 2, 2001
This is not an exponential increase. It is a quadratic increase. If a
parameter increased exponentially with velocity, then velocity would appear
as an exponent in the expression for that parameter. In the expression for
kinetic energy, the exponent is the constant 2.

Doug Bell

----- Original Message -----
From: "Bryan E. Daniel" <bedaniel@...>
To: "SRS" <SeattleRobotics@yahoogroups.com>
Sent: Thursday, March 01, 2001 12:39 AM
Subject: Re: [SeattleRobotics] Rapidly moving objects Correction (1/2)mv^2

| Hello SRS,
|
| Kinetic Energy = (1/2)mv^2 = one half m v squared
|
| The Kinetic Energy of a moving object increases (exponentially) as the
| square of the velocity of the moving object .
|...
• Correction *** ... *** Distance s = 1/2 a t^2 where a = acceleration due to gravity multiplied by time squared. s = 1/2 (32.174 feet / sec^2) (1 sec)^2 =
Message 4 of 5 , Mar 7, 2001
Correction ***

"Bryan E. Daniel" wrote:

> Hello SRS,
>
> Kinetic Energy = (1/2)mv^2 = one half m v squared
>
> The Kinetic Energy of a moving object increases

***Correction -

> (exponentially)

***

> as the
> square of the velocity of the moving object .

***This is an exponential increase in velocity with the exponent being 2.

>
>
> K.E. of one pound traveling at one mile per hour = (1/2) x .031081
> (foot - lbs) x 1.4667 fps x 1.4667 fps = .03343085 foot-lbs K.E..
>
> K.E. of one pound traveling at 5 miles per hour = .8357716 ft-lbs .
>
> K.E. of one pound at 10 mph = 3.343085 ft-lbs .
>
> K.E. of one pound at 20 mph = 13.372345 ft-lbs .
>
> K.E. of one pound at 50 mph = 83.577 ft-lbs.
>
> At 100 mph, or 146.67 feet per second, the K.E. of a one pound object is
> 334.3085 ft-lbs .

>
> One pound falling (about 32 feet)

> for one second reaches a speed of about
> 32.174 feet per second in the first second or about 21.9 miles per hour.
> It has an impact force of about 16.087 ft-lbs.

*** Distance s = 1/2 a t^2 where a = acceleration due to gravity multiplied by
time squared. s = 1/2 (32.174 feet / sec^2) (1 sec)^2 = 16.078 feet .

>
>
> The acceleration due to gravity G varies with latitude. G = 32.174 feet per
> second per second is a standard approximation correct in latitudes between 46
> and 47 degrees. From a General Science reference table, G varies with
> latitude from 32.08730 at the equator (0 degrees latitude) to 32.25744 at the
> poles (90 degrees latitude).
>
> Bryan E. Daniel
> Bellevue, Washington
>
> "Bryan E. Daniel" wrote:
>
> > Hello SRS,
> >
> > Rapidly moving objects are very hazardous.
> > This applies to moving robots and moving robot parts.
> > Be careful.
> >
> > The Kinetic Energy of a moving object increases as the
> > square of the velocity of the moving object (exponentially).
> >
> > The Kinetic Energy of a moving object increases directly
> > with mass (directly proportional).
> > The velocity of the moving object is the more significant
> > term.
> >
> > m = mass = Weight / G G = acceleration of gravity
> >
> > Weight = 1 pound (example)
> >
> > G = 32.174 feet per second per second
> > m = 1 / 32.174 = .031081 (slugs) mass
> >
> > K.E. = Kinetic Energy = mv^2 ( = mv squared )
>
> ***K.E. = (1/2)mv^2
>
> >
> >
> > 1 mile per hour = 5280 feet per hour = 88 feet per minute =
> > 1.4667 feet per second
> >
> > K.E.of one pound travelling at one mile per hour = .031081
> > (foot - lbs) x 1.4667 fps x 1.4667 fps = .0668617
> > foot-lbs K.E..
>
> ***half that or .03343085
>
> >
> >
> > At 5 mph = 7.3335 feet per second,
> > K.E. of one pound traveling at 5 miles per hour = 1.6715431
> > ft-lbs .
>
> ***half that or .8357716
>
> >
> > That is 25 times as much kinetic energy as a one pound
> > object moving at one mile per hour.
> >
> > At 10 miles per hour = 14.667 feet per second,
> > K.E. of one pound at 10 mph = 6.68617 ft-lbs .
>
> ***half that or 3.343085
>
> >
> > That is one hundred times as much kinetic energy as one
> > pound at 1 mph.
> >
> > At 20 miles per hour = 29.334 feet per second,
> > K.E. of one pound at 20 mph = 26.744689 ft-lbs .
>
> ***half that or 13.372345
>
> >
> > That is 395.5 times as much kinetic energy as a pound at 1
> > mph.
> >
> > At 50 miles per hour = 73.335 feet per second
> > K.E. of one pound at 50 mph = 167.154 foot - lbs
>
> ***half that or 83.577
>
> >
> > That is 2,500 times as much kinetic energy as the same
> > weight at 1 mph.
> >
> > At 100 mph, or 146.67 feet per second the K.E. of one pound
> > object is 668.617 foot-lbs .
>
> ***half that or 334.3085
>
> >
> > That is 10,000 times as much kinetic energy as the one pound
> > weight moving at one mile per hour.
> >
> > The weight merely acts as a scale multiplier.
> > A 2,000 pound car crashes with 2,000 times as much energy at
> > each of the speeds as does a one pound weight.
> > A 1 ounce weight has one sixteenth the weight of a pound and
> > therefore has one sixteenth the kinetic energy at each of
> > the speeds.
> >
> > A 100 pound robot moving five miles per hour has over 167
>
> ***half that or over 83
>
> >
> > foot pounds of kinetic energy to expend if it runs into
> > something.
> > A 100 pound robot moving twenty miles per hour has over 2674
>
> ***half that or over 1337
>
> >
> > foot pounds of kinetic energy to expend if it runs into
> > something.
> >
> > Bryan E. Daniel
> > Bellevue, Washington
> >
> > To unsubscribe from this group, send an email to:
> > SeattleRobotics-unsubscribe@egroups.com
> >
> >
> >
> > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
> To unsubscribe from this group, send an email to:
> SeattleRobotics-unsubscribe@egroups.com
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
• What kind of kinetic energy would we have to absorb were this thread to stop instantaneously? :-) Gary (did this in Freshman physics) Livick
Message 5 of 5 , Mar 7, 2001
What kind of kinetic energy would we have to absorb were this thread to stop
instantaneously? :-)

Gary (did this in Freshman physics) Livick

"Bryan E. Daniel" wrote:

> Correction ***
>
> "Bryan E. Daniel" wrote:
>
> > Hello SRS,
> >
> > Kinetic Energy = (1/2)mv^2 = one half m v squared
> >
> > The Kinetic Energy of a moving object increases
>
> ***Correction -
>
> > (exponentially)
>
> ***
>
> > as the
> > square of the velocity of the moving object .
>
> ***This is an exponential increase in velocity with the exponent being 2.
>
> >
> >
> > K.E. of one pound traveling at one mile per hour = (1/2) x .031081
> > (foot - lbs) x 1.4667 fps x 1.4667 fps = .03343085 foot-lbs K.E..
> >
> > K.E. of one pound traveling at 5 miles per hour = .8357716 ft-lbs .
> >
> > K.E. of one pound at 10 mph = 3.343085 ft-lbs .
> >
> > K.E. of one pound at 20 mph = 13.372345 ft-lbs .
> >
> > K.E. of one pound at 50 mph = 83.577 ft-lbs.
> >
> > At 100 mph, or 146.67 feet per second, the K.E. of a one pound object is
> > 334.3085 ft-lbs .
>
> >
> > One pound falling (about 32 feet)
>
>
> > for one second reaches a speed of about
> > 32.174 feet per second in the first second or about 21.9 miles per hour.
> > It has an impact force of about 16.087 ft-lbs.
>
> *** Distance s = 1/2 a t^2 where a = acceleration due to gravity multiplied by
> time squared. s = 1/2 (32.174 feet / sec^2) (1 sec)^2 = 16.078 feet .
>
> >
> >
> > The acceleration due to gravity G varies with latitude. G = 32.174 feet per
> > second per second is a standard approximation correct in latitudes between 46
> > and 47 degrees. From a General Science reference table, G varies with
> > latitude from 32.08730 at the equator (0 degrees latitude) to 32.25744 at the
> > poles (90 degrees latitude).
> >
> > Bryan E. Daniel
> > Bellevue, Washington
> >
> > "Bryan E. Daniel" wrote:
> >
> > > Hello SRS,
> > >
> > > Rapidly moving objects are very hazardous.
> > > This applies to moving robots and moving robot parts.
> > > Be careful.
> > >
> > > The Kinetic Energy of a moving object increases as the
> > > square of the velocity of the moving object (exponentially).
> > >
> > > The Kinetic Energy of a moving object increases directly
> > > with mass (directly proportional).
> > > The velocity of the moving object is the more significant
> > > term.
> > >
> > > m = mass = Weight / G G = acceleration of gravity
> > >
> > > Weight = 1 pound (example)
> > >
> > > G = 32.174 feet per second per second
> > > m = 1 / 32.174 = .031081 (slugs) mass
> > >
> > > K.E. = Kinetic Energy = mv^2 ( = mv squared )
> >
> > ***K.E. = (1/2)mv^2
> >
> > >
> > >
> > > 1 mile per hour = 5280 feet per hour = 88 feet per minute =
> > > 1.4667 feet per second
> > >
> > > K.E.of one pound travelling at one mile per hour = .031081
> > > (foot - lbs) x 1.4667 fps x 1.4667 fps = .0668617
> > > foot-lbs K.E..
> >
> > ***half that or .03343085
> >
> > >
> > >
> > > At 5 mph = 7.3335 feet per second,
> > > K.E. of one pound traveling at 5 miles per hour = 1.6715431
> > > ft-lbs .
> >
> > ***half that or .8357716
> >
> > >
> > > That is 25 times as much kinetic energy as a one pound
> > > object moving at one mile per hour.
> > >
> > > At 10 miles per hour = 14.667 feet per second,
> > > K.E. of one pound at 10 mph = 6.68617 ft-lbs .
> >
> > ***half that or 3.343085
> >
> > >
> > > That is one hundred times as much kinetic energy as one
> > > pound at 1 mph.
> > >
> > > At 20 miles per hour = 29.334 feet per second,
> > > K.E. of one pound at 20 mph = 26.744689 ft-lbs .
> >
> > ***half that or 13.372345
> >
> > >
> > > That is 395.5 times as much kinetic energy as a pound at 1
> > > mph.
> > >
> > > At 50 miles per hour = 73.335 feet per second
> > > K.E. of one pound at 50 mph = 167.154 foot - lbs
> >
> > ***half that or 83.577
> >
> > >
> > > That is 2,500 times as much kinetic energy as the same
> > > weight at 1 mph.
> > >
> > > At 100 mph, or 146.67 feet per second the K.E. of one pound
> > > object is 668.617 foot-lbs .
> >
> > ***half that or 334.3085
> >
> > >
> > > That is 10,000 times as much kinetic energy as the one pound
> > > weight moving at one mile per hour.
> > >
> > > The weight merely acts as a scale multiplier.
> > > A 2,000 pound car crashes with 2,000 times as much energy at
> > > each of the speeds as does a one pound weight.
> > > A 1 ounce weight has one sixteenth the weight of a pound and
> > > therefore has one sixteenth the kinetic energy at each of
> > > the speeds.
> > >
> > > A 100 pound robot moving five miles per hour has over 167
> >
> > ***half that or over 83
> >
> > >
> > > foot pounds of kinetic energy to expend if it runs into
> > > something.
> > > A 100 pound robot moving twenty miles per hour has over 2674
> >
> > ***half that or over 1337
> >
> > >
> > > foot pounds of kinetic energy to expend if it runs into
> > > something.
> > >
> > > Bryan E. Daniel
> > > Bellevue, Washington
> > >
> > > To unsubscribe from this group, send an email to:
> > > SeattleRobotics-unsubscribe@egroups.com
> > >
> > >
> > >
> > > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
> >
> > To unsubscribe from this group, send an email to:
> > SeattleRobotics-unsubscribe@egroups.com
> >
> >
> >
> > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
> To unsubscribe from this group, send an email to:
> SeattleRobotics-unsubscribe@egroups.com
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
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