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Old Sep 15th 2008, 04:03 PM   #1
Raj
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Momentum (two variables)

A car at rest, Mass 1850kg, is hit from behind by a truck, travelling at 65.1km/h. After impact they lock together and travel at 26.2km/h. What is the mass of the truck?

I came up with this equation:

m1v1 + m2v2 = (m1+m2)v3
65.1m = 26.2m1 + 26.2m2

Stuck and need help =\
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Old Sep 15th 2008, 04:17 PM   #2
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Originally Posted by Raj View Post
A car at rest, Mass 1850kg, is hit from behind by a truck, travelling at 65.1km/h. After impact they lock together and travel at 26.2km/h. What is the mass of the truck?

I came up with this equation:

m1v1 + m2v2 = (m1+m2)v3
65.1m = 26.2m1 + 26.2m2

Stuck and need help =\
You've got the right idea, but I'm not clear on your notation.

So let's define $\displaystyle m_1$ to be the mass of the car at rest, $\displaystyle m_2$ the mass of the truck, $\displaystyle v_{10}$ the speed of the car before the collision, $\displaystyle v_{20}$ the speed of the truck before the collision, and v the speed of the combined mass after the collision. Then by conservation of momentum:
$\displaystyle m_1v_{10} + m_2v_{20} = (m_1 + m_2)v$

Plugging in what we know gives us
$\displaystyle 1850(0) + m_2(61.5) = (1850 + m_2)(26.2)$

$\displaystyle m_2(61.5) = (1850 + m_2)(26.2)$

Now solve for $\displaystyle m_2$.

Note that this is not an elastic collision since the two masses are stuck together after the collision, so we can't use conservation of energy here.

-Dan
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