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# Two cars collide at an intersection. One car has a mass of 1600 kg and is moving 8 m/s to the north, while the other has a mass of 1400 kg a

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Two cars collide at an intersection. One car has a mass of 1600 kg and is moving 8 m/s to the north, while the other has a mass of 1400 kg and is moving 12 m/s to the south. What is their combined momentum?

physics
Guest Feb 18, 2015

#4
+91471
+5

Yes i understand that as a Troll you feel the total need to say something snarky.

I assume that Heureka also understands this.

Yes I did notice your vector arrows, I'll have to add them to our very disorganised LaTex thread. :)

It is always great to get new commands.

I did not think that momentum and velocity were the same thing but the question asks for momentum and you answered with a velocity so I was confused.

So does that mean that the combined momentum is     $$1.\bar{3}*3000 = 4000\;kg\;m/s$$

Well i am glad that you did not want to start something that you could not finish but if you make a spelling mistake perhaps you should not blame others.  Your computer cannot even defend itself.

Melody  Feb 18, 2015
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#1
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## Solution

$$\small{\text{\boxed{\vec{v}_1 = \vec{v}_2 = \dfrac {(m_1\cdot v_1 - m_2\cdot v_2 )}{ (m_1+ m_2 ) } } \quad\begin{array}{rcl}m_1 &=& 1400\ \mathrm{kg} \\v_1 &=& 12\ \frac{\mathrm{m} }{ \mathrm{s} } \end{array}\quad\begin{array}{rcl}m_2 &=& 1600\ \mathrm{kg} \\v_2 &=& 8\ \frac{\mathrm{m} }{\mathrm{s}} \end{array}}}\\\\\\\small{\text{\vec{v}_1 = \vec{v}_2 = \dfrac {(1400\cdot 12 - 1600\cdot 8 )}{ (1400+ 1600 ) } \ \dfrac{\mathrm{m} }{\mathrm{s}} }}\\\\\small{\text{\vec{v}_1 = \vec{v}_2 = \dfrac { 4000 }{ 3000 } \ \dfrac{ \mathrm{m}}{\mathrm{s}} = 1.3333\dots\ \dfrac{ \mathrm{m} }{\mathrm{s} } }}\\\\\small{\text{m_1\cdot \vec{v}_1 + m_2\cdot \vec{v}_2 = 1400 * 1.3333\dots \;+ \;1600 * 1.3333\dots =\; 4000\ \frac{\mathrm{kg}\cdot \mathrm{m}}{\mathrm{s}}}}\\\end{array}}}\\ \small {\text{Velocity of combined cars = 1.33\overline 3(\dot 3)\; \dfrac{m}{s}\; south.}$$

Letex code stolen from Heureka (and vastly improved)

Nauseated  Feb 18, 2015
#2
+91471
+5

You have presented this beautifully Nauseated but

I see NO IMPROVEMENT on Heureka's presentation.

PLUS Heureka knows how to spell LaTex properly !

Is momentum and velocity the same thing?

Melody  Feb 18, 2015
#3
+1037
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I see NO IMPROVEMENT on Heureka's presentation.

There isn’t. The only difference is the use of arrow vectors.

I’m a troll, so my posts aren’t really complete without (a) snarky comment(s).

PLUS Heureka knows how to spell LaTex properly !

Considering his proficiency, I’m sure he does. However, I was using a company computer, and the command “Letex” is used to initiate Schematron-based XHTML table validation scripts for creating LaTeX formula images. D**k, a  company programming troll, used “LaTex” as a command to start a process to produce extra-large latex rubbers. The demand for these is small and I didn’t want to start something I couldn't finish.

Is momentum and velocity the same thing?

No. They are two different quantities.

Velocity is the speed with the direction.

Momentum is the product of mass and its velocity.

Nauseated  Feb 18, 2015
#4
+91471
+5

Yes i understand that as a Troll you feel the total need to say something snarky.

I assume that Heureka also understands this.

Yes I did notice your vector arrows, I'll have to add them to our very disorganised LaTex thread. :)

It is always great to get new commands.

I did not think that momentum and velocity were the same thing but the question asks for momentum and you answered with a velocity so I was confused.

So does that mean that the combined momentum is     $$1.\bar{3}*3000 = 4000\;kg\;m/s$$

Well i am glad that you did not want to start something that you could not finish but if you make a spelling mistake perhaps you should not blame others.  Your computer cannot even defend itself.

Melody  Feb 18, 2015
#5
+1037
0

. . . the question asks for momentum and you answered with a velocity so I was confused.

Actually, I answered with both momentum and velocity. Though not asked for, I included velocity because in dynamical systems, a mass’s position in space and rate of change of position in space are almost always useful pieces of information. This is especially so in situations involving vehicle crashes.

. . . but if you make a spelling mistake perhaps you should not blame others. Your computer cannot even defend itself.

True, but it doesn’t need to. I was blaming D**k, the programming troll. BTW my name is D**k, so either way, the blame is where it belongs. :)

Nauseated  Feb 18, 2015

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