1.) An 8 g bullet is fired into a 9 kg cube of wood, which is at rest, and sticks in it. The cube is free to move and has a speed of 40 cm/sec after impact. Find the initial velocity of the bullet.
450.4 m/s
To find the initial velocity of the bullet, we can use the principle of conservation of momentum.
The law of conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting on it. In this case, we can consider the bullet and the cube as a closed system.
The momentum of an object is equal to its mass multiplied by its velocity. Therefore, we can write the equation for the conservation of momentum as:
(mass of bullet) * (initial velocity of bullet) + (mass of cube) * (initial velocity of cube) = (mass of bullet + mass of cube) * (final velocity of cube)
Now let's substitute the given values into the equation:
(8 g) * (initial velocity of bullet) + (9 kg) * (0) = (8 g + 9 kg) * (40 cm/sec)
Note that we converted the mass of the bullet to grams and velocity to centimeters per second for consistent units.
Simplifying the equation further:
(8 g) * (initial velocity of bullet) = (17 kg) * (40 cm/sec)
Now we can solve for the initial velocity of the bullet:
(initial velocity of bullet) = [(17 kg) * (40 cm/sec)] / (8 g)
Calculating this expression will give us the initial velocity of the bullet.