A4.8 kg block is suspended from a spring with a spring constant of 500 n/m. a 50 g bullet is fired into the block from directly below with a speed of 130 m/s and is embedded in the block. (a) find the amplitude of the resulting simple harmonic motion. m (b) what fraction of the original kinetic energy of the bullet appears as mechanical energy in the harmonic oscillator?

The fraction of the original kinetic energy of the bullet appears as mechanical energy in the harmonic oscillator is 0.00468.

Explanation:

Given that,

Mass of block = 4.8 kg

Mass of bullet = 50 g

Spring constant = 500 N/m

Speed of bullet = 130 m/s

(a). We need to calculate the velocity

Using conservation of momentum

Put the value into the formula

We need to calculate the amplitude of the resulting simple harmonic motion

Using formula energy

Put the value into the formula

(b). We need to calculate the kinetic energy

Using formula of kinetic energy

for harmonic oscillator,

The fraction of the original kinetic energy of the bullet appears as mechanical energy in the harmonic oscillator

Hence, The fraction of the original kinetic energy of the bullet appears as mechanical energy in the harmonic oscillator is 0.00468.

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