| Topic: |
Science > Physics |
| User: |
"wonda" |
| Date: |
04 Sep 2006 12:25:41 AM |
| Object: |
basic 2 dimensional motion question |
I saw a problem that says that two bullets fired simultaneously uphill
parallel to an inclined plane -with the bullets having different masses
and different initial velocities, will strike the plane at the same
time (as they fall after reaching their maximum heights). This does not
sound right to me. Is it true?
Thank you.
.
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| User: "Timo Nieminen" |
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| Title: Re: basic 2 dimensional motion question |
04 Sep 2006 01:01:56 AM |
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On Mon, 3 Sep 2006, wonda wrote:
I saw a problem that says that two bullets fired simultaneously uphill
parallel to an inclined plane -with the bullets having different masses
and different initial velocities, will strike the plane at the same
time (as they fall after reaching their maximum heights). This does not
sound right to me. Is it true?
Fire two bullets of different masses and initial velocities horizontally,
parallel to a horizontal plane, from the same height above the plane.
What happens?
Ignoring air resistance etc, the vertical motion and horizontal motion are
independent of each other. The horizontal motion is given by
x = v_h t, where v_h is the horizontal component of the initial velocity.
No horizontal acceleration, vertical acceleration is 9=9.8m/s^2 downwards,
both bullets have initial vertical velocity v_v = 0. Do they both hit the
horizontal plane at the same time?
Yes, of course. If you've gotten to your inclined plane problem through
the usual route, you'll already be familiar with this.
Now, do the inclined plane problem the _same_ way. Instead of of
horizontal and vertical, use parallel to and perpendicular to the plane.
What is the different between the horizontal and inclined plane problems?
Only the direction of acceleration due to gravity. Both bullets start with
the same v_perp = 0. Do both bullets have the same a_perp? This part is
still the same, except that a_perp < g. So will the result be any
different, qualitatively?
(The parallel motion is different, since before a_h was zero, and now
a_par is not zero.)
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "wonda" |
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| Title: Re: basic 2 dimensional motion question THANKS |
04 Sep 2006 02:02:59 AM |
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Hi, Thanks for a very clear explanation. So I see that what you have
suggested is to visualize the problem as along a horizontal plane and
the only difference in the vertical direction is that the effective
gravity is less than 9.8. Also, although this does not effect the
answer to the question, the horizontal acceleration will not be zero,
i.e. a_parallel will absorb some acceleration from the parallel
component of gravity. Is this right?
Thank you very much.
Timo Nieminen wrote:
On Mon, 3 Sep 2006, wonda wrote:
I saw a problem that says that two bullets fired simultaneously uphill
parallel to an inclined plane -with the bullets having different masses
and different initial velocities, will strike the plane at the same
time (as they fall after reaching their maximum heights). This does not
sound right to me. Is it true?
Fire two bullets of different masses and initial velocities horizontally,
parallel to a horizontal plane, from the same height above the plane.
What happens?
Ignoring air resistance etc, the vertical motion and horizontal motion are
independent of each other. The horizontal motion is given by
x = v_h t, where v_h is the horizontal component of the initial velocity.
No horizontal acceleration, vertical acceleration is 9=9.8m/s^2 downwards,
both bullets have initial vertical velocity v_v = 0. Do they both hit the
horizontal plane at the same time?
Yes, of course. If you've gotten to your inclined plane problem through
the usual route, you'll already be familiar with this.
Now, do the inclined plane problem the _same_ way. Instead of of
horizontal and vertical, use parallel to and perpendicular to the plane.
What is the different between the horizontal and inclined plane problems?
Only the direction of acceleration due to gravity. Both bullets start with
the same v_perp = 0. Do both bullets have the same a_perp? This part is
still the same, except that a_perp < g. So will the result be any
different, qualitatively?
(The parallel motion is different, since before a_h was zero, and now
a_par is not zero.)
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.
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| User: "Timo Nieminen" |
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| Title: Re: basic 2 dimensional motion question THANKS |
04 Sep 2006 02:13:46 AM |
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On Mon, 4 Sep 2006, wonda wrote:
Hi, Thanks for a very clear explanation. So I see that what you have
suggested is to visualize the problem as along a horizontal plane and
the only difference in the vertical direction is that the effective
gravity is less than 9.8. Also, although this does not effect the
answer to the question, the horizontal acceleration will not be zero,
i.e. a_parallel will absorb some acceleration from the parallel
component of gravity. Is this right?
Yes.
What you're interested in are the components of the velocity and
acceleration directly towards the surface. Choose your x and y axes to
match this, so you can separate this motion that you're interested in from
the rest of the motion. If you've done problems with blocks sliding down
inclined planes, you've probably done the same thing in them.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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