The 28-g rifle bullet has a mass of 0.028 kg and is traveling at a speed of 190 m/s. When it embeds itself in the pendulum, it transfers its momentum to the pendulum.
To find the velocity of the pendulum after the bullet embeds itself, we can use the principle of conservation of momentum. The initial momentum of the bullet is given by mass of the bullet (0.028 kg) multiplied by its velocity (190 m/s). The final momentum of the pendulum and the bullet together is equal to the mass of the pendulum (3.1 kg) multiplied by the final velocity of the pendulum.
Since the bullet embeds itself, we can assume that the final velocity of the bullet and the pendulum is the same. Therefore, we can set up the equation:
Initial momentum of bullet = Final momentum of pendulum and bullet
(0.028 kg) * (190 m/s) = (3.1 kg + 0.028 kg) * (final velocity)
Simplifying the equation, we find:
(0.028 kg) * (190 m/s) = (3.128 kg) * (final velocity)
final velocity = (0.028 kg * 190 m/s) / (3.128 kg)
final velocity ≈ 1.70 m/s
So, the pendulum swings up with a velocity of approximately 1.70 m/s after the bullet embeds itself.
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