| Problem statement Solution video |
DISCUSSION THREAD
Ask and answer questions here. You learn both ways.
DISCUSSION and HINTS
This is a standard problem for the central impact of two bodies.
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw three free body diagrams (FBDs): one of A alonw, one of B alone and one of A+B. Identify the n- and t-directions on your FBDs.
Step 2: Kinetics (linear impulse/momentum)
- In which directions, if any, is linear momentum conserved for A alone? For those direction(s), write down the appropriate momentum conservation equation.
- In which directions, if any, is linear momentum conserved for B alone? For those direction(s), write down the appropriate momentum conservation equation.
- In which directions, if any, is linear momentum conserved for A+B? For those direction(s), write down the appropriate momentum conservation equation.
- Recall that you also have the coefficient of restitution (COR) equation at your disposal. Keep in mind that the COR equation is valid for only the n-components of velocity.
Step 3: Kinematics
None needed here.
Step 4: Solve
From your equations solve for the n- and t-components of velocity of A and B.
When solving the system of equations, I feel like I am missing an equation to solve the system, I have V_b2, V_a2, and Θ_b as variables, and the equations I am using are the COR equation and momentum in the n direction. I need one more equation, can we use the COR to relate the kinetic energies before and after the collision?
As with most planar central impact problems, you have four unknowns: v_B2t, v_B2n, v_A2t and v_A2n.
And, you have four equations:
* LIM for A in the t-direction
* LIM for B in the t-direction
* LIM for A+B in the n-direction
* COR that relates the normal components of velocity for A and B
Four equations. Four unknowns. Solve
The COR equation is not for relating kinetic energies.