| Topic: |
Science > Physics |
| User: |
"Mark Folsom" |
| Date: |
05 Mar 2005 12:39:28 AM |
| Object: |
Collision quiz |
Hi Guys,
Long time no post--long time no read. But, now I thought I would bless you
with another elastic collision problem, since I've been thinking about this
one...
In a vacuum, with no gravitational effects of any importance, an initially
unstressed steel cylinder 3 cm in diameter and 10 cm long with flat ends,
collides squarely endwise with an unsupported "stationary" aluminum bar of
the same diameter but 5 km long, and also with flat ends. No adhesive or
other tensile force acts at the interface. The impact velocity is low
enough so that all deformation is in the linear elastic range.
Questions:
1. How much time passes from initial contact to separation of the two
cylinders?
2. Does the steel cylinder reverse direction?
3. Given V as the initial impact velocity, what is the pressure versus time
on the contact surface?
4. What is the coefficient of restitution?
Ciao,
Mark Folsom
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| User: "Mark Folsom" |
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| Title: Re: Collision quiz |
09 Mar 2005 01:35:26 AM |
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Okay, so you're lame...
I'll answer them myself.
"Mark Folsom" <folsom_snip_man@redshift.com> wrote in message
news:112ilbopk6opq0e@corp.supernews.com...
Hi Guys,
Long time no post--long time no read. But, now I thought I would bless
you with another elastic collision problem, since I've been thinking about
this one...
In a vacuum, with no gravitational effects of any importance, an initially
unstressed steel cylinder 3 cm in diameter and 10 cm long with flat ends,
collides squarely endwise with an unsupported "stationary" aluminum bar of
the same diameter but 5 km long, and also with flat ends. No adhesive or
other tensile force acts at the interface. The impact velocity is low
enough so that all deformation is in the linear elastic range.
Questions:
1. How much time passes from initial contact to separation of the two
cylinders?
About two seconds.
2. Does the steel cylinder reverse direction?
No.
3. Given V as the initial impact velocity, what is the pressure versus
time on the contact surface?
Initially, it's .71*V*sqrt(10000000*0.101/386) = 36*V (units are psi, if V
is in inches per second). After about 44 microseconds, it drops to .71
times that value; after another 44 microseconds, it drops to .71 times
*that* value, etc. After about two seconds it drops to zero.
4. What is the coefficient of restitution?
Very nearly zero.
Ciao,
Mark Folsom
.
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| User: "Mark Folsom" |
|
| Title: Re: Collision quiz |
10 Mar 2005 01:01:53 AM |
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Continuing with my monologue...
"Mark Folsom" <folsom_snip_man@redshift.com> wrote in message
news:112t9qdefu62rdd@corp.supernews.com...
Okay, so you're lame...
I'll answer them myself.
"Mark Folsom" <folsom_snip_man@redshift.com> wrote in message
news:112ilbopk6opq0e@corp.supernews.com...
Hi Guys,
Long time no post--long time no read. But, now I thought I would bless
you with another elastic collision problem, since I've been thinking
about this one...
In a vacuum, with no gravitational effects of any importance, an
initially unstressed steel cylinder 3 cm in diameter and 10 cm long with
flat ends, collides squarely endwise with an unsupported "stationary"
aluminum bar of the same diameter but 5 km long, and also with flat ends.
No adhesive or other tensile force acts at the interface. The impact
velocity is low enough so that all deformation is in the linear elastic
range.
Questions:
1. How much time passes from initial contact to separation of the two
cylinders?
About two seconds.
If the short cylinder was magnesium, they would separate smartly at
40-something microseconds, with the mg piece reversing at a decent fraction
of its original speed. If it were aluminum, the force would go to zero at
that time, but the cylinders would remain next to each other for about 2
seconds, after which the long cylinder would move away at a slow average
speed.
2. Does the steel cylinder reverse direction?
No.
3. Given V as the initial impact velocity, what is the pressure versus
time on the contact surface?
Initially, it's .71*V*sqrt(10000000*0.101/386) = 36*V (units are psi, if V
is in inches per second). After about 44 microseconds, it drops to .71
times that value; after another 44 microseconds, it drops to .71 times
*that* value, etc. After about two seconds it drops to zero.
4. What is the coefficient of restitution?
Very nearly zero.
Ciao,
Mark Folsom
.
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