# Kinetic enengy needed to break a board

• Howlin
In summary, kinetic energy is the energy an object has due to its motion. It is calculated using the formula KE = 1/2 * m * v^2 and can be converted into other forms of energy. The amount of kinetic energy needed to break a board is affected by factors such as the type and thickness of the board, velocity and mass of the object, and material properties of the board. The required amount of kinetic energy can also vary depending on the martial arts technique used and the skill level of the practitioner.
Howlin

## Homework Statement

I need to get $E_{b}$ = .5(m*n*$V^{2}_{i}$)/(m+n) [eq 6]

where $E_{b}$ is the energy required to break the board, m is the mass of the object hitting the boards, n is the mass of the board and $V_{i}$ is the velocity of the object before hitting the board.

## Homework Equations

$K_{i}$=.5*m*$V^{2}_{i}$ [eq 1)
where $K_{i}$ is the initial kinetic energy, m is the mass of the object, $V_{i}$ is the inital velocity

$K_{f}$= $E_{b}$ + .5*(m+ n)*$V^{2}_{f}$ [Eq2]
$E_{b}$ is the energy required to break the board, m is the mass of the object hitting the boards, n is the mass of the board and $V_{i}$ is the velocity of the object before hitting the board.

momentum before = momentum after
m8$V_{i}$ = (m+n)*$V_{f}$

$V_{f}$=(m*$V_{i}$)/(m+n) [eq3]

## The Attempt at a Solution

I know make eq 1 and 2 equal (assuming no energy is lost) rearrange the equation to get E on its own

$E_{b}$ = .5*m*$V^{2}_{i}$ - .5*(m+ n)*$V^{2}_{f}$ [eq4]

Now i can sub in eq3 into eq 4

$E_{b}$ = .5*m*$V^{2}_{i}$ - .5*(m+ n)*[(m*$V_{i}$)/(m+n)$)^{2}$

$E_{b}$ = .5*m*$V^{2}_{i}$ - .5*[(m*$V_{i}$$)^{2}$/(m+n)]

This is where I am stuck, I cannot get to equation 6.
Can anyone help me?

##E_{b} = \frac{1}{2}mV^{2}_{i} - \frac{1}{2}\frac{(mV_{i})^{2}}{(m+n)}## - this is your last equation

##E_{b} = \frac{1}{2}mV^{2}_{i}\frac{m+n}{m+n} - \frac{1}{2}\frac{mmV_{i}^{2}}{(m+n)}##
##E_{b} = \frac{1}{2}mV^{2}_{i}\frac{m+n-m}{m+n}##
And the next step is the final result.
The idea was just to combine both terms.

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

## How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

## What factors affect the amount of kinetic energy needed to break a board?

The main factors that affect the amount of kinetic energy needed to break a board include the type and thickness of the board, the velocity and mass of the object hitting the board, and the material properties of the board.

## Can kinetic energy be converted into other forms of energy?

Yes, kinetic energy can be converted into other forms of energy, such as potential energy, heat, or sound.

## How does the amount of kinetic energy needed to break a board differ for different types of martial arts techniques?

The amount of kinetic energy needed to break a board can vary depending on the technique used and the skill of the practitioner. Techniques that involve a larger surface area of contact or use the full body's momentum will require more kinetic energy than techniques that use a smaller surface area or only a specific body part.

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