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The rod should rotate about the hinged point A.haruspex said: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.
Conserving linear momentum in horizontal direction:haruspex said:You can now write down three equations: conservation of linear momentum (one vertical, one horizontal) and conservation of angular momentum.
Yes, ultimately, but instantaneously what will be the motion of its c of g? Will it move horizontally, vertically, or somewhere between?Pranav-Arora said:The rod should rotate about the hinged point A.
No, you're still overlooking the reactive impulse at the hinge. You have to think of the rod as effectively struck by the hinge at the same instant in a way that leads to the expected subsequent motion. (If not, the top of the rod should move away from the hinge.) So in which direction will the reactive impulse act?Conserving linear momentum in horizontal direction:
mv=mvx' (vx' is the horizontal velocity of rod after impact)
vx'=v (is this correct?)
I suppose it should move somewhere between.haruspex said:Yes, ultimately, but instantaneously what will be the motion of its c of g? Will it move horizontally, vertically, or somewhere between?
I still don't get it. :(haruspex said:No, you're still overlooking the reactive impulse at the hinge. You have to think of the rod as effectively struck by the hinge at the same instant in a way that leads to the expected subsequent motion. (If not, the top of the rod should move away from the hinge.) So in which direction will the reactive impulse act?
ehild said:The angular momentum is conserved as there is no external torque acting on the system rod-particle. 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
ehild said:Glad to hear. I never heard about "impulsive reaction" in this sense. Google gave such things as http://www.vsatbay.com/1/post/2012/06/ten-ways-to-control-your-impulsive-reactions.html, for example
ehild
There are basically two ways of solving it:Pranav-Arora said:But, is haruspex wrong with his/her suggestion of conserving linear momentum?
haruspex said:There are basically two ways of solving it:
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.
Does it contravene standard terminology? If so, I apologise for any confusion. To me it's the same. Initial quantity of x + input quantity of x = resulting quantity of x is a conservation law, whether x be momentum, energy, charge...ehild said:Haruspex, why do you call the law "Change of momentum = impulse " "conservation of momentum"? There is an external force, so the momentum is not conserved.
haruspex said:Does it contravene standard terminology? If so, I apologise for any confusion. To me it's the same. Initial quantity of x + input quantity of x = resulting quantity of x is a conservation law, whether x be momentum, energy, charge...
ehild said:Well, I saw that at several places already that people speak about conversation of energy when there is work of friction, or work of a man, that is work of non-conservative forces. I also saw using the word "impulse" for momentum mv. Work and energy are different concepts, impulse and momentum are also different in principle, just like internal energy is different either from heat or work, although the impulse is "input" for momentum and work is "input" for energy. Physicist do not use "input" so frequently as engineers.
ehild
An impulsive reaction is a type of chemical reaction that occurs very quickly and is characterized by a sudden release of energy.
The rate of an impulsive reaction can be calculated by measuring the change in concentration of the reactants or products over time using the rate law equation.
The rate of an impulsive reaction can be affected by factors such as temperature, concentration of reactants, surface area, and presence of a catalyst.
An impulsive reaction is a type of chemical reaction that occurs quickly, while an explosive reaction is a type of chemical reaction that occurs very rapidly and with a large release of energy.
Yes, impulsive reactions can be controlled or modified by adjusting the factors that affect the rate of the reaction, such as temperature, concentration, or the use of a catalyst.