What is the spring force constant k for a ball dropped onto a spring?

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To calculate the spring force constant k for a ball dropped onto a spring, the relevant equations involve gravitational potential energy and spring potential energy. The ball, weighing 142 g and dropped from 62.2 cm, compresses the spring by 4.35501 cm. The correct approach is to equate the gravitational potential energy (mgh) to the potential energy stored in the spring (1/2 kx^2). The discussion highlights the importance of using the correct formulas and considering the total distance the ball falls before coming to rest. The final calculation for k should reflect these principles accurately.
irbombardmnt
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Please help me out, I'm new here, and I only have one more attempt on this problem, totally lost.

Homework Statement



A(n) 142 g ball is dropped from a height of 62.2 cm above a spring of negligible mass. The ball compresses the spring to a maximum displacement of 4.35501 cm. The acceleration of gravity is 9.8 m/s^2 . Calculate the spring force constant k. Answer in units of N/m.

Homework Equations


F=-kx


The Attempt at a Solution


mgh=-kx
(.142)(9.8)(.622)=-k(0.435501)
k=19.875

?
 
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You're setting energy equal to force. Instead of the force of the spring, use the potential energy of the spring.
 
Hi irbombardmnt, welcome to PF.
Your relevant equation is not correct. mgh is the fall of potential. kx is not the energy.
What is the formula for the energy stored in a stretched spring?
In fact ball falls through h+x distance before it comes to rest.
 
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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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