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vesna_86 [32]
3 years ago
7

"If a ball of mass M is dropped from a height h onto a spring with spring constant k (whose equilibrium positions is at height 0

), compresses the spring an additional distance (L/2), and then rebounds, what height will the ball reach? Express your answer symbolically."
So I was thinking something along the lines of h= M*k*(L/2) but I'm not sure :/ Any guidance?
Mathematics
1 answer:
bagirrra123 [75]3 years ago
7 0

Answer:h=\dfrac{kL^2}{8mg}

Step-by-step explanation:

Given

Mass of ball is M  is dropped from a height h

spring constant is k

Here we can use conservation of energy

Mass has a Potential energy of E=mgh

and when it falls on the spring then it compresses it a length of 0.5 L

Now potential energy is converted into Elastic potential energy and then spring unleashes this energy to the mass and again provide kinetic energy to mass to move upward .

In this way energy is conserved. So, mass must move to an initial  height h

mgh=\frac{1}{2}k(\frac{L}{2})^2

h=\dfrac{kL^2}{8mg}

considering h >> 0.5L

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