A 10-g bullet of unknown speed is shot horizontally into a 2-kg block of wood suspended from the ceiling by a cord. The bullet hits the block and becomes lodged in it. After the collision, the block and the bullet swing to a height 30cm above the original position. What was the speed of the bullet? (This device is called the ballistic pendulum). Take g=98ms−2

Question

zephyr141 · Answer

i just did this question on my homework. but i had a lot more information than this. like cord length and the tension of the cord at the height in question.

theeric · Answer

Yeah, and, like that problem, it seems that you're given a method to learn the momentum of the block-bullet combination so that you can find the momentum and therefore velocity of the bullet.

I would guess that you can examine the block-bullet system's mechanical energy. The system rises 30cm at its max, and you can calculate the work done. The forces are tension and gravity. However, tension is perpendicular to the displacement at each instant, so no work is done by tension. Then we can consider work done by gravity, right? This work is really taking the freshly shot block-bullet system's kinetic energy and changing it to gravitational potential energy.

So, considering that, finding the change in gravitational potential energy from bottom to top is like finding the kinetic energy at the bottom.

Then you can $\it find$ the system's momentum.

Then you $\it know$ the bullet's momentum beforehand.

Since you know the bullet's momentum and mass, it's nearly trivial to find the velocity with $p=mv$.