Final answer:
The decelerating force that stopped a 1.8 g bullet traveling at 360 m/s after moving 10 cm into a block of wood was 1166.4 Newtons, acting in the direction opposite to the motion of the bullet.
Step-by-step explanation:
To calculate the decelerating force that stopped the bullet in the wood, we use the work-energy principle. The work done by the decelerating force is equal to the change in kinetic energy of the bullet. At the moment of impact, the bullet has initial kinetic energy, which is later dissipated completely as it comes to rest inside the block of wood.
Firstly, the initial kinetic energy (KE) of the bullet is given by:
KE = ½ mv²
Where m is the mass of the bullet and v is its velocity. Substituting the given mass (1.8 g = 0.0018 kg) and velocity (360 m/s), we have:
KE = ½ × 0.0018 kg × (360 m/s)²
KE = 116.64 J
Since the bullet comes to rest after penetrating 10 cm (0.1 m) into the wood, the work (W) done by the force (F) is equal to the kinetic energy, and is given by:
W = F × d
Where d is the distance over which the force is applied. Therefore:
F = W / d
F = 116.64 J / 0.1 m
F = 1166.4 N
The decelerating force that stopped the bullet is 1166.4 Newtons, acting in the opposite direction of the bullet's motion.