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

step 1 First part here it is given. Mass of bullet 4 into 10 to the power minus 3 kg. Initial speed of

A bullet with a mass of 4.0 g and a speed of 650 m / s is...

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 it 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 greater than, less than, or equal to the initial kinetic energy? Explain. (c) Verify your answer to part (b) by calculating the initial and final kinetic energies of the system.

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 it 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 greater than, less than, or equal to the initial kinetic energy? Explain. (c) Verify your answer to part (b) by calculating the initial and final kinetic energies of the system.

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Key Concepts

Collision Dynamics

Collisions can be categorized based on the conservation of kinetic energy. Elastic collisions conserve kinetic energy along with momentum, while inelastic collisions conserve momentum but not kinetic energy. In many practical scenarios, such as an object passing through another, the collision is inelastic, meaning that some energy is lost to other forms even though momentum remains conserved.

Conservation of Momentum

This principle states that in the absence of external forces, the total momentum of a system remains constant throughout an interaction. It is a foundational concept in mechanics that is applicable to impacts and collisions, where the sum of the momenta of all objects before the event equals the sum afterwards, regardless of whether the collision is elastic or inelastic.

Kinetic Energy and its Transformation

Kinetic energy, defined as one half the mass times the square of the velocity, is a measure of motion energy. In collision problems, kinetic energy is not always conserved; particularly in inelastic collisions, some kinetic energy is transformed into other forms of energy such as heat or sound. Understanding how kinetic energy changes offers insights into the efficiency of energy transfer during collisions.

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