Some questions about momentum for SAT II Physics

<ol>
<li><p>A 1-kilogram object is moving with a velocity of 6 meters per second to the right. It collides and sticks to a 2-kilogram object moving with a velocity of 3 meters per second in the same direction. How much kinetic energy was lost in the collision? (I know the answer is D, but how it works?)
A.1.5J
B. 2J
C. 2.5J
D. 3J
E. 0J</p></li>
<li><p>A mass m is attached to a massless spring with a force constant k. The mass rests on a horizontal frictionless surface. The system compressed a distance x from the springs initial position and then released. The momentum of the mass when the spring passes its equilibrium position is given by (Please explain how it works out?)
A.x√mk
B. x√k/m
C. x√m/k
D. x√k²m
E. xmk</p></li>
<li><p>A 2-kilogram object is moving with a velocity of 7 meters per second collides elastically with a 4-kilogram mass moving in the opposite direction at 4 meters per second. The 2-kilogram mass reverses direction after the collision and has a new velocity of 3 meters per second. What is the new velocity of the 4-kilogram mass?(Please explain how it works out?)
A. -1m/s
B. 1m/s
C. 6m/s
D. 4m/s
E. 5m/s</p></li>
</ol>

<ol>
<li> (1/2)mv^2 So for the first mass (1/2)(1)(6^2) = 18 J
The second mass (1/2)(2)(3^2) = 9 J
9 + 18 = 27 J
After the collision, mv + Mv = (m + M)v, so (1)(6) + (2)(3) = (1+2)(v) v = 4
(1/2)(3)(4^2) = 24 J
27 - 24 = 3 J</li>
</ol>

<ol>
<li> 2 Kg object has momentum mv = 14 J
4 Kg object has momentum mv = 16 J
Because it is an elastic collision, all energy is conserved, therefore 14 + 16 = (2)(3) + 4(v).
30 = 6 + 4v v = 6 m/s, so I would say C</li>
</ol>

<p>Number 2 is tricky, but I would go with B, because (1/2)(m)(v^2) = (1/2)(k)(x^2)
mv^2 = kx^2
For some reason, it looks like you’re supposed to solve for v, which would give you square root of [ (kx^2)/m ], or x√(k/m)</p>

<p>I think you solved the no.2 partially right. The question was for the “momentum”, not “velocity”, so if you use m times x√(k/m), the answer would be A.</p>

<p>for Q3, 2kg object and 4kg object are moving in opposite direction, so you have to take negative sign into calculation, 14-16=-6 + 4v, so v is 1m/s, answer B.</p>

<p>Thanks. Got it</p>