Register to reply 
Impulsive reaction 
Share this thread: 
#1
Nov1312, 01:45 PM

P: 3,807

1. The problem statement, all variables and given/known data
(see attachment) 2. Relevant equations 3. The attempt at a solution I am clueless here. I can conserve angular momentum but how will i find the "impulsive reaction"? 


#2
Nov1312, 03:57 PM

Homework
Sci Advisor
HW Helper
Thanks
P: 9,816

Let the impulsive reaction at A be I, a vector.
How will the rod move just after the impact? Put in an unknown for that. You can now write down three equations: conservation of linear momentum (one vertical, one horizontal) and conservation of angular momentum. 


#3
Nov1412, 01:59 AM

P: 3,807

mv=mv_{x}' (v_{x}' is the horizontal velocity of rod after impact) v_{x}'=v (is this correct?) I am not sure how conserving the linear momentum in vertical direction would help? Initially it is zero and after the impact, even if we assume that the rod has got some velocity in vertical direction, the velocity of rod in vertical direction turns out to be zero. 0=mv_{y}' (v_{y}' is the velocity of rod in vertical direction) I am still not sure how to proceed further. 


#4
Nov1412, 02:16 AM

Homework
Sci Advisor
HW Helper
Thanks
P: 9,816

Impulsive reaction



#5
Nov1412, 02:29 AM

P: 3,807




#6
Nov1412, 10:35 AM

P: 3,807

Anyone?
Are there any similar problems discussed here at PF? 


#7
Nov1412, 11:14 AM

HW Helper
Thanks
P: 10,551

The angular momentum is conserved as there is no external torque acting on the system rodparticle. But the linear momentum is not conserved, as there is a force at the hinge during the impact.
The change of linear momentum is m(rod) vcm(rod)mv=ΔI where ΔI is the impulse of the force at the hinge. You can call it "impulsive reaction". So find the angular velocity of the rod after the impact,, you get the linear velocity of the CM from it. ehild 


#8
Nov1412, 11:21 AM

P: 3,807




#9
Nov1412, 11:27 AM

HW Helper
Thanks
P: 10,551

Glad to hear. I never heard about "impulsive reaction" in this sense. Google gave such things as http://www.vsatbay.com/1/post/2012/0...reactions.html, for example
ehild 


#10
Nov1412, 11:32 AM

P: 3,807

But, is haruspex wrong with his/her suggestion of conserving linear momentum? 


#11
Nov1412, 03:12 PM

HW Helper
Thanks
P: 10,551

The change of linear momentum is equal to the impulse of the external force. Here the force comes from the hinge, but that is opposite to the force the rod exerts on the hinge. ΔP=F(external)Δt can also be written as Pi=Pf+F(system)Δt, and that looks as conservation of impulse or momentum, just like when they speak about conservation of energy when friction does work. I would not say it conservation of energy or conservation of momentum, but other people do. Haruspex wanted you to include the impulse from the hinge when you wrote the change of linear momentum, he only called the law ΔP=F(external)Δt "conservation of momentum".
ehild 


#12
Nov1412, 03:50 PM

Homework
Sci Advisor
HW Helper
Thanks
P: 9,816

Conservation of linear momentum (only need to consider horizontal since there is no vertical motion involved) gives you an equation involving the reactive impulse, I, and the speed of the rod directly after impact. The second equation is from conservation of angular momentum, but what equation you get will depend on where you take moments. If you take moments about the hinge it will not involve I; if you take them about the c of g of the rod it will. Either way, you end up with the same answer. 


#13
Nov1412, 04:18 PM

HW Helper
Thanks
P: 10,551

ehild 


#14
Nov1412, 05:27 PM

Homework
Sci Advisor
HW Helper
Thanks
P: 9,816




#15
Nov1412, 10:26 PM

P: 3,807

Thanks you both for the replies, i understand it better after this discussion.



#16
Nov1412, 10:28 PM

HW Helper
Thanks
P: 10,551

ehild 


#17
Nov1512, 07:53 AM

P: 758

Δp = _{t1} ^{t2}∫F_{ex}dt Where ∫F_{ex}dt is just impulse.... If impulse =0 , we get Δp=0 , which is law of conservation of linear momentum... 


Register to reply 
Related Discussions  
Impulsive Motion  Classical Physics  1  
Impulsive tension  Classical Physics  1  
Impulsive Tensions  Introductory Physics Homework  1  
Impulsive force  Introductory Physics Homework  10  
Impulsive Motion  Introductory Physics Homework  8 