A 15 g bullet is fired at 610 m / s into a 4.0 kg block that sits at the edge of a 75-cm -high t

step 1 In this problem, we're going to talk about conservation of momentum. So remember that the moment

A 15 g bullet is fired at 610 m / s into a 4.0 kg block that...

A 15 g bullet is fired at $610 \mathrm{m} / \mathrm{s}$ into a $4.0 \mathrm{kg}$ block that sits at the edge of a $75-\mathrm{cm}$ -high table. The bullet embeds itself in the block and carries it off the table. How far from the point directly below the table's edge does the block land?

Key Concepts

Conservation of Momentum

This concept states that in the absence of external forces, the total momentum of a system remains constant. In collision problems, especially in cases where two objects stick together after impact, the momentum of the initial moving object is transferred to the combined system, despite possible energy transformations.

Inelastic Collision

An inelastic collision is one in which the colliding objects stick together after impact, meaning kinetic energy is not conserved because it is partially transformed into other forms of energy such as heat or deformation. However, momentum remains conserved, making it essential for determining the post-collision velocity of the combined mass.

Projectile Motion

Projectile motion deals with the motion of an object that is launched into the air and is subject only to gravitational acceleration, with air resistance often neglected. In such problems, the horizontal and vertical components of motion are analyzed separately, where the horizontal component has constant velocity and the vertical component experiences uniform acceleration due to gravity.

Transcript

00:01 In this problem, we're going to talk about conservation of momentum.

00:05 So remember that the momentum of a particle is equal to the mass of the particle times its velocity.

00:11 And the total momentum of a system is conserved, as long as there are no external forces acting on the system.

00:22 So the initial momentum pi is equal to the final momentum p .f.

00:27 So the individual momentum of the particles can change, but the initial momentum, the particles, the total momentum cannot.

00:35 Okay, so now we can move on to our exercise.

00:38 So what we have is a bullet that has a mass of 15 kilograms, sorry, 15 grams, so 0 .015 kilograms, and is fired with a speed of 610 meters per second.

00:55 And the bullet sticks to a block that has a mass of 4 kilograms.

01:02 And then the block starts to move since the bullet transfers part of its momentum to the block.

01:14 Okay, then we have to consider that the block slides in the table frictionlessly, and then it falls from the table, given that the table has a height of 75 centimeters above the ground.

01:34 And with this information i go is to find how far from the table horizontally the block lands.

01:42 I say horizontally because the exercise tells us to find the point, the distance between the point where the object lands and the point directly below the edge of the table.

01:56 The first thing i'm going to do is to find what is the speed of the block.

02:00 And in order to find that, i'm going to use conservational momentum...

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