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+1 vote
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in Work, Energy and Power by (20 points)
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A spring gun of spring constant 90 *10 ^2N /M is compressed 4cm by a ball of mass 16g. If the trigger is pulled, calculate the velocity of the ball.

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1 Answer

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by (541 points)

HELLO,

This is a question from simple use of conservation of energy,

Here, Initial energy = Potential energy stored in compressed spring = \(\frac{kx^2}{2}\), where k= spring constant of spring and x is compressed length.

Final energy = Kinetic energy of the ball = \(\frac{mv^2}{2}\), where m is the mass of the ball and \(v \)  is velocity of the ball.

Applying energy conservation,

Initial energy = Final energy

\(\frac{kx^2}{2} = \frac{mv^2}{2}\) 

\(kx^2 = mv^2 \)

Now, putting the value of \(k=9000N/m , x = 4cm = 0.04m , m=16g=0.016kg\) we get, 

\(v^2 = 900 m^2/s^2 \)

\(v=30m/s\) 

I HOPE YOU WILL UNDERSTAND.smiley

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