Defining Potential Energy at Different Heights of a Block on a Vertical Spring

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A 0.240 kg block on a vertical spring, compressed by 0.080 m with a spring constant of 5e3 N/m, is analyzed for its maximum height after release. The potential energy stored in the spring is calculated as 16 joules, but clarification is needed on how mass and gravitational potential energy factor into the height calculation. The discussion emphasizes the conservation of energy principle, where the spring's potential energy converts to gravitational potential energy as the block ascends. The gravitational potential energy can be expressed as a function of height, and the relationship between the two forms of energy is crucial for determining the maximum height reached. Understanding how to incorporate gravitational effects is essential for solving the problem accurately.
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Can anyone help me with this question?

A 0.240 kg block on a vertical spring with a spring constant of 5e3 N/m is pushed downward, compressing the spring 0.080 m. When released, the block leaves the spring and travels upward vertically. How high does it rise above the point of release?

I know that PE= 1/2 kx^2
so I got .5 x 5e3 x .08^2=16 I'm not sure where the mass comes into this equation. I also know that you have to subtract your anser from the point of release so i tried 16-.08 but it didn't work...

Thank-you
 
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Is the answer you got (16) a height? What units does it have? What units should it have?

Secondly, if it reaches a maximum height while initially traveling upwards, then something must be pulling it down... what is it? (kinda obvious).
 
16 joules is the potential energy
where would you incorporate gravity or weight into the equation??
 
Think of this as a conservation of energy problem. Intially, you have spring potential energy, which ends up being transformed into gravitational potential energy. How do you express gravitational PE as a function of height?
 
doesn't the block have P.E. as it travels upto to its max height; how would you define the P.E of an object at a certain height?
 
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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