A bullet with momentum of $10 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$ embeds itself into a large, heavy block of wood: $m _ { \text {wood } } = 12.6 \mathrm {~kg}$ and $m _ { \text {wood } } m _ { \text {bullet } }$. The block of wood is tied to a string connected to the ceiling, forming a ballistic pendulum. The maximum (vertical) height that the block of wood + bullet rises to is
A) 8 cm.
B) 5 cm.
C) 3 cm.
D) 9 cm.

Question

A bullet with momentum of $10 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$ embeds itself into a large, heavy block of wood: $m _ { \text {wood } } = 12.6 \mathrm {~kg}$ and $m _ { \text {wood } } > > m _ { \text {bullet } }$. The block of wood is tied to a string connected to the ceiling, forming a ballistic pendulum. The maximum (vertical) height that the block of wood + bullet rises to is
A) 8 cm.
B) 5 cm.
C) 3 cm.
D) 9 cm.

Quizplus · Accepted Answer

The conservation of momentum and energy principles are used to solve this problem. Initially, the bullet's momentum is conserved when it embeds into the block of wood, allowing us to find the velocity of the wood+bullet system just after the collision. Then, using the conservation of energy, we can find the maximum height the system rises to by equating the initial kinetic energy to the potential energy at the maximum height. Given the momentum and masses, the calculations lead to a maximum height of 3 cm, making option C correct.

A Bullet with Momentum Of 10 kg⋅m/s10 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }10 kg⋅m/s

A Bullet with Momentum Of $10 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$