Maximum Projectile Speed for Safe Hanging: 20kg Wood Ball and 2m Long Wire

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To determine the maximum speed of a 1.0 kg projectile that can hit a 20 kg wood ball hanging from a 2.0 m wire without breaking it, conservation of momentum and centripetal force equations are essential. The maximum tension the wire can handle is 400N, which limits the speed of the projectile. After applying the relevant physics principles, the calculations reveal the largest permissible speed. The original poster expressed frustration but ultimately found the solution with assistance. This highlights the importance of understanding momentum and tension in solving physics problems involving hanging objects.
darkdryad
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Look I really need someone's help, I spent over 3 hours on this problem and can't figure it out. If anyone could tell me what to do (try being specific), I'd appreciate.

A 20kg wood ball hangs from a 2.0m longwire. The maximum tension the wire can withstand without breaking is 400N. A 1.0 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the largest speed this projectile can have without causing the cable to break?

Please anyone, I really need to get this.
 
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Use conservation of momentum to determine what speed the ball will have when it is struck by the projectile. Use the equation for centripetal force to determine the tension in the wire. You should be able to go from there.
 
Actually, I really can't figure it out, I read what you said, but nothing adds up.
 
I got it, OMG I got it, thank you sooooo much. God why didn't i think of that. Thx very much.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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