How to Calculate an Arrow's Kinetic Energy

It's easy to take a bow and arrow at face value. You fire the arrow from the bow, and you either hit your target or you don't. However, much like anything, an arrow is a useful and interesting part of science. An arrow has many different scientific properties, despite often being just a long and thin piece of wood with a plastic or metal tip. For example, a fired arrow has a unique amount of kinetic energy. It may seem overwhelming and confusing at first, but calculating that kinetic energy is incredibly easy to do.

Difficulty: Easy

Instructions

Things You'll Need:

• Scale Calculator Stopwatch Tape measure

1. Weigh the arrow. To find out the arrow's kinetic energy, plug two properties of the arrow into a mathematical equation. The first is the weight. Use a scale to get an accurate reading and be sure to write it down for later.

2. Find the velocity of the arrow. You can get a rough estimate simply enough, using only a stopwatch and tape measure. Velocity is defined as "distance over time," often measured in meters/second. Fire your arrow and keep track of the time it takes to hit the ground, using your stopwatch. Next, measure the distance from the point you fired the arrow to the point it hit the ground. Write down the "distance/time," and you've just found the velocity.

3. Calculate the kinetic energy of the arrow. This can be done by taking the data you've collected and plugging it into the following equation:
   
   1/2 times Mass times Velocity Squared
   
   That is to say, multiply 0.5 by the arrow's mass by the squared velocity of the arrow when fired. The number you receive once the equation is calculated is the arrow's kinetic energy.

Tips & Warnings

• To get accurate readings of some of the data required for the kinetic energy equation, a partner may prove helpful.