How Much Elastic Potential Energy Was Stored in the Spring Before Release?

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The discussion centers on calculating the elastic potential energy stored in a spring that was compressed between two toy cars of different masses. When the string tying the cars is cut, the cars move apart, with the lighter car (0.112 kg) achieving a speed of 1.38 m/s. Participants express uncertainty about how to start the calculation and seek guidance on relevant physical principles. Key concepts include conservation of momentum and energy, which are crucial for solving the problem. The conversation emphasizes the need to apply these principles to determine the initial energy stored in the spring.
kevykevy
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Question-A child placed a spring of negligible mass between two toy cars of masses 0.112 kg and 0.154 kg. She compresses the spring and ties the cars together with a piece of string. When she cuts the string, the spring is released and the cars move in opposite directions. The 0.112 kg car has a speed of 1.38 m/s. What was the elastic potential energy stored in the spring before the string was cut?

Solution-I've tried to start this and I have no idea even where to begin. All I have so far is this picture I drew describing what's happening...

Spring Compressed
----

Spring Uncompressed (at rest)
- - - -

Before
Car1----Car2

After
Car1- - - -Car2
 
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kevykevy said:
Question-A child placed a spring of negligible mass between two toy cars of masses 0.112 kg and 0.154 kg. She compresses the spring and ties the cars together with a piece of string. When she cuts the string, the spring is released and the cars move in opposite directions. The 0.112 kg car has a speed of 1.38 m/s. What was the elastic potential energy stored in the spring before the string was cut?

Solution-I've tried to start this and I have no idea even where to begin. All I have so far is this picture I drew describing what's happening...

Spring Compressed
----

Spring Uncompressed (at rest)
- - - -

Before
Car1----Car2

After
Car1- - - -Car2
What physical quantities do you think are conserved in this process?
 
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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