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physicsman23
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Homework Statement
A ball with mass 'm' is pushed against a spring (with a spring constant 'k') and causes a displacement 'x' on the spring. Once the force is released from, the ball is shot horizontally. What is the velocity 'v' horizontally?
Homework Equations
E(k) = 1/2 mv^2
E(s) = 1/2 kx^2
The Attempt at a Solution
I equated both of the relevant equations and get the result that:
v = [tex]\sqrt{k(x^2)/m}[/tex]
This answer seems right. However, when I use Newton's second law, it doesn't seem to work anymore. I state that:
kx = ma (Spring force = Net force) and therefore: a = kx/m
Substitute for a:
a = v^2/2x
equate a = a and get the result that:
v = [tex]\sqrt{2k(x^2)/m}[/tex]
Can anyone tell me where my logic is going wrong? My teacher said that the first one is correct. I don't understand why the second one is not.