Problem

A 15.0-kg block is attached to a very light horiz…

12:09

Problem 43 Hard Difficulty

A 12.0-g rifle bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 6.00 kg, suspended from a cord 70.0 cm long (see Example 8.8 in Section 8.3). Compute (a) the vertical height through which the pendulum rises, (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the wood.

Answer

A. $2.93 \mathrm{cm}$
B. $866 \mathrm{J}$
C. $1.73 \mathrm{J}$

Related Courses

Physics 101 Mechanics

University Physics

Chapter 8

Momentum, Impulse, and Collisions

Section 3

Momentum Conservation and Collisions

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Video Transcript

problem. 8.43. We have 12 grand bullet hitting a ballistic pendulum. Six kilograms. It's going 380 meters per second. Immediately before the collision. The pendulum is suspended from a 70 centimeter cord, and the the first thing we want to find is through what height does the pendulum move? After the bullet hits, it swings back burden. The second thing we want to find is the initial kinetic energy of the bullet before the impact. And the third thing is, what is the total Connecticut Angie right before or right after the impact before the pendulum has started swinging and turning some of some of that kinetic energy into potential energy, and eventually it gets to the top of its wing. It all becomes a potential enemy. So if, like, a distant if we want to use the conservation of energy to figure out how high the pendulum goes. And, uh, we need to know what it's kinetic energy is, and in order to do that, we needed speed for which we can use the conservation of momentum. So the initial moment of just consists of the bullet moving and after is the bullet lodges into the pendulum and they both start moving together. So we have the combined mass hands. 11 bullet for the sake of brevity, will all the speed here the speed of the pendulum even though the bullet has also launched so speed that the pendulum is going to be equal to this ratio of the masses of the things that are moving before and after the collision times the initial speed of the bullet. I know this works out to be 0.75 eight meters per second and then we use the conservation of energy. So 1/2 the mass of the combined object he squared Answer the combined object again Scene h So it doesn't matter what the masses of the objects were and define that r h here, the square of the speed immediately after it starts moving, divided by two G and this is two points 993 70 meters. So I'm not especially Harvey we want was the kinetic energy of a bullet to begin and this is fairly simple. On half the mass of the bullet finds the speed of the bullet squared and this ends up being 800 and 66 Jules immediately after the collision. We need to know what the total energy is of the bullet and pendulum moving together. And because this collision is totally in elastic, our bidding is an elastic at all. But especially being totally an elastic, we expect that there's going to be a loss of kinetic energy because of it gets dissipated, deforming the material of the pendulum and it gets turned into heating. Sounded all sorts of things we might call this Spanish all this final that's sort of more like a intermediate, but that would also be a I. So you know. So here we have the total mass of both objects. The speed of hensel them with the bullet of it square before, is this seven, by the way, when it's a 0.758 meters per second and this works up to be 1.73 Jules, so you can see quite a lot of energy got lost and in the in elastic collision where the bullet was lodging into the pendulum, which again is sort of what you would expect to happen because it's a totally an elastic collision. And so a lot of the energy is going to go somewhere else, being converted into different forms

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