- FBD: Use pendulum and bullet TOGETHER as your system. Draw an FBD of this system.
- Impulse momentum equations: From your FBD, find a point about which angular momentum is conserved (no external moments acting on system about this point). [HINT: It is point O.] Recall the definitions of angular momentum for a particle (bullet) and for a rigid body (pendulum). Add these together to find the angular momentum for time 1 (before impact), HO1. Add these together to find angular momentum for time 2 (after impact), HO2. Equate: HO1 = HO2.
- Kinematics: After impact (time 2), the bullet is stuck to pendulum. Ignore the width of the pendulum, and assume that the embedded bullet is directly under G (at a distance of h from O) immediately after impact.
- Solve
Note that this problem is very similar to the angular impulse Problem 3/248 that we worked earlier in the semester. The difference here is that we treat the pendulum as a rigid body (HO = IO*omega) rather than as particles (HO = m*(rP/O x vP) ). See the solution of that problem on the Homework Page of the course site.
Let us know if you have any questions on this problem.
4 comments:
so i set up impulse equations one for the bullet hitting pendulum and then one for the pendulum rotating. since there are no external moments these equations are equal to zero.
Hox2 = Hox1, Iow2 = Iow1. if this is correct then i am having trouble on what i can assume to neglect. I am thinking in Hox2 that vb2 equals w*r since O is the instant center. I also thought Iow1 equaled zero because the pendulum is at rest when hit.
Nick I would recommend you watch the solution to 6/183. It is a similar problem and may provide you with some usefull insight.
I did it just like problem 3/248 but I did not use the moment of inertia part that is given in the problem description, so I am obviously doing something wrong. I assume that has to do with how the pendulums angular momentum works but I'm not sure what the equation is.
--to peter--
The two problems are similar in that you have a system of bodies which impact, and during impact angular momentum is conserved about point O.
In Problem 3/248 you determine angular momentum for each particle using HO = m*rP/O x vP and adding up the components.
In Problem 6/185 you determine the angular momentum for the bullet by using HO = m*rb/O x vb. For the pendulum (a rigid body) you use HO = IO*omega (as we discussed in lecture). You then add up the two components.
As Steve points out above, Problem 6/183 (a problem for which you have access to a solution video) is also very similar. In that problem, you have a rigid body for which HO = IO*omega in addition to a particle for which HO = m*rP/O x vP.
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