Momentum Problems: Help with 2 Problems and Energy Stored in Spring

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The discussion revolves around two momentum problems involving a child in a sled and a spring system. In the first problem, the child throws a snowball, and participants suggest using conservation of momentum to find the sled's new velocity after the throw. The second problem involves a clay ball impacting a block attached to a spring, with discussions on calculating the energy stored in the spring and the initial speed of the clay ball. Key concepts include the transformation of kinetic energy into elastic energy and the importance of considering the system's initial and final momentum. The original poster successfully completed the homework with assistance from peers.
lucifer
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momentum problems

it's be really cool if someone could help me out with the following two momentum problems. nothing much just enough to get me started. i have ideas but I'm not quite sure about what's the right way to go about doing them. also want to say hi to all the people here. must say the whole homework help thing is a very neat concept. :biggrin:

problem 1- A 25 kg child is in a 10 kg sled that travels 1m/s east on ice. The child throws a 3 kg snowball at 40m/s at an angle of 50 degrees north of east. Find the velocity of the sled after the snowball leaves the child's hand.



problem 2- A 2kg block and an 8-kg block are both attached to an ideal spring (for which k=200 N/m) and both are initially at rest on a horizontal frictionless surface.

In an initial experiment, a 0.1 kg ball of clay is thrown at the 2kg block. The clay is moving horizontally with speed v when it hits and sticks to the block. the 8-kg block is held still by a removable stop. As a result, the spring compresses a maximum distance of 0.4 meters. Find:

a) the energy stored in the spring at max compression.

b) speed of the clat ball and 2-kg block immediately after the clay sticks to the block but before the spring compresses significantly.

c) the initial speed v of the clay.
 
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lucifer said:
problem 1- A 25 kg child is in a 10 kg sled that travels 1m/s east on ice. The child throws a 3 kg snowball at 40m/s at an angle of 50 degrees north of east. Find the velocity of the sled after the snowball leaves the child's hand.
Use conservation of momentum. I think you have to assume the 3 kg snowball was part of the sled+child system before the kid threw it.
The initial momentum is (25+10)1=35 kg m/s in the (say) x-direction.
The final momentum is equal to this.
Find the momentum of the snowball and the sled+kid which now weighs 32 kg together.
 
problem 2

a) it's just E = 1/2kx^2 = 1/2k(0.4)^2 J
b) & c) I couldn't really understand the question but I think it has something to do with the Kinetic Energy being transformed into Elastic Energy which means that 1/2kx^2 = 1/2mv^2
 
thanks a lot for the replies, Galileo and futb0l. it was due today and i got it done(eventually) but i had to ask my friend to help me out in lunch.
 
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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