| Topic: |
Science > Physics |
| User: |
"James Stokes" |
| Date: |
09 Sep 2003 07:20:38 PM |
| Object: |
Tangential acceleration |
Suppose that a ball rolls down a slope inclined at an angle of a to the
horizontal. The tangential acceleration is thus
a_T = g sin[a] - k g cos[a]
where k is the coefficient of kinetic friction, N1 = g cos[a] is the
normal force exerted by the slope. Suppose further that as the ball rolls
down the slope, it is pressed against a vertical wall which exerts a normal
force N2 perpendicular to N1. Is the tangential acceleration now
a_T = g sin[a] - k(N1 + N2) ?
or
a_T = g sin[a] - k sqrt(N1^2 + N2^2) ?
Or something completely different?
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| User: "John C. Polasek" |
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| Title: Re: Tangential acceleration |
09 Sep 2003 08:42:36 PM |
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On Wed, 10 Sep 2003 00:20:38 GMT, "James Stokes"
<james.stokes@mailNOSPAM.com> wrote:
Suppose that a ball rolls down a slope inclined at an angle of a to the
horizontal. The tangential acceleration is thus
a_T = g sin[a] - k g cos[a]
where k is the coefficient of kinetic friction, N1 = g cos[a] is the
normal force exerted by the slope. Suppose further that as the ball rolls
down the slope, it is pressed against a vertical wall which exerts a normal
force N2 perpendicular to N1. Is the tangential acceleration now
a_T = g sin[a] - k(N1 + N2) ?
or
a_T = g sin[a] - k sqrt(N1^2 + N2^2) ?
Or something completely different?
Completely different. Friction has no effect on a rolling ball. Only
the side friction counts. You need a sliding block.
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
.
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| User: "James Stokes" |
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| Title: Re: Tangential acceleration |
10 Sep 2003 02:58:18 AM |
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"John C. Polasek" <jpolasek@cfl.rr.com> wrote
Completely different. Friction has no effect on a rolling ball. Only
the side friction counts. You need a sliding block.
Okay, let k be the coefficient of rolling friction. Now which equation is
appropriate?
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
.
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| User: "Paul R. Mays" |
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| Title: Re: Tangential acceleration |
10 Sep 2003 03:11:35 AM |
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"James Stokes" <james.stokes@mailNOSPAM.com> wrote in message
news:uQA7b.92111$bo1.80297@news-server.bigpond.net.au...
"John C. Polasek" <jpolasek@cfl.rr.com> wrote
Completely different. Friction has no effect on a rolling ball. Only
the side friction counts. You need a sliding block.
Don't mean to butt in But.... They are not Completly different and
friction Does have and effect on a rolling ball.... And you Don't need
a sliding block.. ( makes it much easer problem but you don't need it)
Okay, let k be the coefficient of rolling friction. Now which equation
is
appropriate?
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
.
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| User: "John C. Polasek" |
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| Title: Re: Tangential acceleration |
10 Sep 2003 08:25:00 AM |
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On Wed, 10 Sep 2003 04:11:35 -0400, "Paul R. Mays"
<simatar1@hotmail.Com> wrote:
"James Stokes" <james.stokes@mailNOSPAM.com> wrote in message
news:uQA7b.92111$bo1.80297@news-server.bigpond.net.au...
"John C. Polasek" <jpolasek@cfl.rr.com> wrote
Completely different. Friction has no effect on a rolling ball. Only
the side friction counts. You need a sliding block.
Don't mean to butt in But.... They are not Completly different and
friction Does have and effect on a rolling ball.... And you Don't need
a sliding block.. ( makes it much easer problem but you don't need it)
Okay, let k be the coefficient of rolling friction. Now which equation
is
appropriate?
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
Butt in, butt in. A ball rolls holonomically. There is no relative
motion. Yes if its rolling in mud or on a carpet, etc. but then it's
hard to make it proportional to velocity.
Other than that, it's much more complicated.
You should be dealing in rotation rates, not velocity. The frictional
forces act as torques, the carpet one about the horizontal, and the
side one about the inclined vertical. Take the vector sum.
Have fun with it.
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
.
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| User: "Paul R. Mays" |
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| Title: Re: Tangential acceleration |
10 Sep 2003 03:33:19 PM |
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"John C. Polasek" <jpolasek@cfl.rr.com> wrote in message
news:3f5f24c8.472987@news-server...
On Wed, 10 Sep 2003 04:11:35 -0400, "Paul R. Mays"
<simatar1@hotmail.Com> wrote:
"James Stokes" <james.stokes@mailNOSPAM.com> wrote in message
news:uQA7b.92111$bo1.80297@news-server.bigpond.net.au...
"John C. Polasek" <jpolasek@cfl.rr.com> wrote
Completely different. Friction has no effect on a rolling ball. Only
the side friction counts. You need a sliding block.
Don't mean to butt in But.... They are not Completly different and
friction Does have and effect on a rolling ball.... And you Don't need
a sliding block.. ( makes it much easer problem but you don't need it)
Okay, let k be the coefficient of rolling friction. Now which
equation
is
appropriate?
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
Butt in, butt in. A ball rolls holonomically. There is no relative
motion. Yes if its rolling in mud or on a carpet, etc. but then it's
hard to make it proportional to velocity.
Other than that, it's much more complicated.
You should be dealing in rotation rates, not velocity. The frictional
forces act as torques, the carpet one about the horizontal, and the
side one about the inclined vertical. Take the vector sum.
Have fun with it.
All that sounds valid and the math has been done a gazillion times
so I would not even try or actually much care except for general
concepts... My only But was that friction does have an effect on
the ball going roundy, roundy .. cause if it didn't it would not Roll
down the incline... And the frictional impact of the ball and the
incline and the block and an incline is exactlly the same thing acting
upon different structural designs... And you very well can calculate
the frictional loses, movement direction and values and total system
energy conversion with a ball instead of a block... It ,just as you
said, just gets a bit more complicated because of the inducement of the
energy conversions into rotational velocities of said ball....
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
.
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| User: "Starblade Darksquall" |
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| Title: Re: Tangential acceleration |
11 Sep 2003 01:36:00 AM |
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(John C. Polasek) wrote in message news:<3f5e820d.29009166@news-server>...
On Wed, 10 Sep 2003 00:20:38 GMT, "James Stokes"
<james.stokes@mailNOSPAM.com> wrote:
Suppose that a ball rolls down a slope inclined at an angle of a to the
horizontal. The tangential acceleration is thus
a_T = g sin[a] - k g cos[a]
where k is the coefficient of kinetic friction, N1 = g cos[a] is the
normal force exerted by the slope. Suppose further that as the ball rolls
down the slope, it is pressed against a vertical wall which exerts a normal
force N2 perpendicular to N1. Is the tangential acceleration now
a_T = g sin[a] - k(N1 + N2) ?
or
a_T = g sin[a] - k sqrt(N1^2 + N2^2) ?
Or something completely different?
Completely different. Friction has no effect on a rolling ball. Only
the side friction counts. You need a sliding block.
That's not true. What about traction? What about the deformation of
the ball that occurrs because of rolling?
Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).
(...Starblade Riven Darksquall...)
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