Predict/Calculate A bullet with a mass of 4.0 g and a speed of 650 m / s is fired at a block of

Predict/Calculate A bullet with a mass of 4.0 g and a speed...

Predict/Calculate A bullet with a mass of 4.0 $\mathrm{g}$ and a speed of 650 $\mathrm{m} / \mathrm{s}$ is fired at a block of wood with a mass of 0.095 $\mathrm{kg}$ . The block rests on a frictionless surface, and is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is 23 $\mathrm{m} / \mathrm{s}$ . (a) What is the speed of the bullet when it exits the block? (b) Is the final kinetic energy of this system equal to, less than, or greater than the initial kinetic energy? Explain. (c) Verify your answer to part (b) by calculating the initial and final kinetic energies of the system.

Key Concepts

Conservation of Momentum

This concept states that in the absence of external forces, the total momentum of a system remains constant during any interaction, such as a collision. It is used to relate the velocities of different objects before and after the interaction, regardless of whether the collision is elastic or inelastic.

Kinetic Energy

Kinetic energy is the energy associated with the motion of an object and is calculated based on the mass and speed of the object. In collision problems, comparing initial and final kinetic energy helps determine if energy is conserved or transformed into other forms, such as heat or sound, especially in inelastic collisions.

Inelastic Collision

In an inelastic collision, while momentum is conserved, kinetic energy is not necessarily conserved. Some of the kinetic energy is converted into other forms of energy, leading to a decrease in the measurable kinetic energy of the moving objects after the collision.

Transcript

00:01 In question 32, we're presented with a problem that says a 4 gram or .004 kilogram bullet, traveling at 650 meters per second, strikes a block of wood, mass of 0 .095 kilograms, that is at rest.

00:12 The bullet penetrates the block, moves completely through it, and then exits the block.

00:18 The block is now moving at 23 meters per second, and the bullet is moving at some speed v.

00:23 We're asked to find what that final speed is.

00:25 We are asked in part b is the final kinetic energy of the system, equal to less than or greater than the initial kinetic energy and then c verify my answer to part b calculating the energies of the system.

00:39 Well first of all, this is an inelastic collision.

00:42 Elastic collisions, the two objects bounce apart, kinetic energy is conserved.

00:45 That didn't happen here.

00:47 One object passed completely through the other in this collision.

00:50 That's clearly going to convert some kinetic energy into thermal energy, and so this is inelastic, which means this is reduced ke.

00:59 And we will prove that right after we find the velocity.

01:02 Even though it's inelastic, momentum is still conserved.

01:05 So all we have to do to find this final momentum is, or this final velocity is find the momentum before, set it equal to the momentum after, and find our v.

01:13 So we can take our 650 times 0 .004 and add on to that the zero momentum of this object, which is just zero, and set that equal to the momentum afterwards, which is going to be that 23 meters per second that this block is moving times its mass of 0 .0 .0 .0 .5.

01:29 095 kilograms plus the final velocity of that bullet times its mass of 0 .004 kilograms...

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