chiurox said:
I redid the problem and got two answers: 0.9 m/s or -13 m/s for the initial velocity of block B and two final velocities for both objects as 1.5 m/s or -9.5 It makes sense I guess, because block A is traveling about twice as faster and hits the bigger block B making Block B travel a bit faster while block A has energy dissipated due to the collision.
Is that what you got?
Not quite what I got. From a physical standpoint, you're right, the answers kind of make sense. In the first case, the big block is moving slowly to the right, and the small block comes up and hits it, and the two now move slightly faster than Block B, as expected. In the second case, the massive block flies in fast, to the left, strikes block A, reverses it, and they continue left more slowly. That's all well and good.
You can check, however, to see if your answers are correct or not. They have to satisfy your initial equations-- conservation of momentum, and your energy equation. Let's have a look:
First, vb = 0.9 m/s and vf = 1.5 m/s:
m_av_{ai} + m_bv_{bi} = (m_a + m_b)v_f
\ \Rightarrow (2){(4)} + (8){(0.9)} = (2 + 8){(1.5)}
\ \Rightarrow 8 + 7.2 = 15
\ \Rightarrow 15.2 = 15
So that's good, the slight difference is due to rounding. Now for the energy equation:
\frac{1}{2}m_a{v_{ai}}^2 + \frac{1}{2}m_b{v_{bi}}^2 = E_i
\frac{1}{2}(m_a + m_b){v_f}^2 = E_f
E_i - E_f = 30
\ \Rightarrow \frac{1}{2}m_a{v_{ai}}^2 + \frac{1}{2}m_b{v_{bi}}^2 - [ \frac{1}{2}(m_a + m_b){v_f}^2] = 30
\ \Rightarrow \frac{1}{2}(2){(4)}^2 + \frac{1}{2}(8){(0.9)}^2 - \frac{1}{2}(2 + 8){(1.5)}^2 = 30
\ \Rightarrow 16 + 3.24 - 11.25 = 30
\ \Rightarrow 19.24 - 11.25 = 30
\ \Rightarrow 7.99 \not= 30 So there's a problem here.
You can do the same kind of thing for your other set of answers, to see what fits and what doesn't.
