Finding the Speeds of Objects in a Spring System

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To find the speeds of objects A and B in a spring system, the conservation of energy principle is applied, using the formula W=1/2kx^2 to calculate the potential energy stored in the compressed spring. The user attempts to set up the equation 1/2kx^2=1/2mv1^2+1/2mv2^2 but struggles with the calculations, leading to confusion about the correct values for v1 and v2. For part b, the user needs to consider the center of mass concept to relate the speeds of the two objects after accounting for friction on the surface. The discussion highlights the importance of understanding energy conservation and the effects of friction in determining object speeds. Assistance is requested to clarify these concepts and solve the problem accurately.
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Homework Statement


Object A (1 kg) and B (3 kg) are forced together,
initially compressing a spring S between them by 6 cm;
then the system is released from rest. The spring with
k=1250 N/m is not fastened to either block and drops to
the surface after it has expanded to its unstretched position.
a) By assuming frictionless surface, what are the speeds of objects after the spring has expanded
to its unstretched position?
b) Assume that the surface is frictional with s=k=0.1. If object B has speed of 0.2 m/s at 0.5 s
after the system is released from rest, what should the speed of object A be at this time instant?
(Hint: Consider “center of mass of a system” concep


Homework Equations



W=1/2kx^2
F=k.x
K=1/2mV^2

The Attempt at a Solution



i'm having trouble with this energy thing. i tried 1/2kx^2=1/2mv1^2+1/2mv2^2
i found 37,5=1/2v1^2 + 1/2v2^2
and i tried F=k.x=75 .
then used f=m.a formula both objects and found V1=3V2. so i solved equation but it seems all wrong.
can you help?
 
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and i have no idea what to do in part b :)
 
can anyone help ? :(
 
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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