- #1
Eclair_de_XII
- 1,083
- 91
Homework Statement
"Figure 9-55 shows a two-ended "rocket" that is initially stationary on a friction-less floor, with its center at the origin of an x axis. The rocket consists of a central block C (of mass ##m_C=6kg##) and blocks L and R (each of mass ##m_L=2kg## and ##m_R=2kg##) on the left and right sides. Small explosions can shoot either of the side blocks away from block C and along the x axis. Here is the sequence:
(1) At time ##t_0=0##, block L is shot to the right with a speed of ##3\frac{m}{s}## relative to the velocity that the explosion gives the rest of the rocket.
(2) at time ##t_1=\frac{4}{5}s##, block R is shot to the right with a speed of ##3\frac{m}{s}## relative to the velocity that block C then has.
At ##t_f=\frac{14}{5}s##, what are (a) the velocity of block C and (b) the position of its center?"
Homework Equations
##p_i=p_f## at two different points in time, in a closed and isolated system
##m_C=6kg##
##m_L=2kg##
##m_R=2kg##
The Attempt at a Solution
Sequence (1):
##v_L-v_C=-3\frac{m}{s}##
##v_C-v_L=3\frac{m}{s}##
Sequence (2):
##v_R-v_C=3\frac{m}{s}##
##p_C-p_L=(m_C)(v_C)-(m_L)(v_L)=p##
##p_R-p_C=(m_R)(v_R)-(m_C)(v_C)=p##
##(m_C)(v_C)-(m_L)(v_L)=(m_R)(v_R)-(m_C)(v_C)##
##2(m_C)(v_C)=(m_L)(v_L)+(m_R)(v_R)##
##v_C=\frac{1}{2m_C}[(m_L)(v_L)+(m_R)(v_R)]##
So I got stuck here, not knowing what the actual velocities of the two side blocks were. These were just outlining the relationship between the momenta in the two sequences described. I've yet to come up with an equation for what the problem actually asks: the velocity and center of mass at ##t=\frac{14}{5}s##. I'm just guessing here, but I'm thinking that the momenta are dependent on time, since velocity is dependent on time. So, I'm just re-expressing the last equation in terms of t.
##v_C(t)=\frac{1}{2m_C}[m_Lv_L(t)+m_Rv_R(t-\frac{4}{5})]##
And that's as far as I can go without knowing the actual velocities of the two blocks. Can anyone help me understand this problem? I'm guessing that the absence of the actual velocities imply that they are not needed to calculate the velocity of the center block.