Did anyone work on sample problem 26? I cant figure out how we can use the conservation of angular momentum formula. What would be Rb? And after that, how do we combine this with the equation for Vn's (coming from coefficient of restitution) ?
Thanks
5 comments:
1. FBD's of A, B and A+B
2. From FBD of A+B, angular momentum about O is conserved. (Since B is small, you can assume that r_B/O is the same as r_A/O in calculating angular momentum.) From FBD of B, linear momentum in t-direction conserved.
3. Kinematics: You know path of A before and after impact. You will need to resolve the initial and final velocity directions of A into n- and t-components so that you can use the COR equation (where you use only n-components).
4. Solve
So what difference does it make if linear momentum is conserved on t direction for B ?
Vb1=0 anyway.
So how do we use this? mVa is not included in this equation since conservation of linear momentum along t-direction applies just for B right?
Conservation of linear momentum in the t-direction for B tells us that B will move in only the n-direction after impact (since B initially has no t-component of linear momentum prior to impact).
You are correct -- linear momentum in the t-direction is NOT conserved for particle A (since the force of the rod on A has a t-component). You do not need this equation for finding the velocity of A after impact. Using A+B you can see that angular momentum is conserved. This, along with the kinematics of A and the COR equation, can be used to find vA2.
Does this help?
Actually yes it does..sorry about that.
No need to be sorry. These are good questions!
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