Dynamics/Kinetics

Newton’s First Law of Inertia states,” An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless enacted upon by an unbalanced force.” (Newton’s First Law of Motion). In relation to archery, once an arrow is nocked and drawn, it is at rest, with only the Force of Tension (on the string), the Force of Gravity (Fg) and the Normal Force (FN) acting upon it. The Normal Force is the force which a surface applies to an object resting upon it. This force is equal to the force of gravity, and is what allows objects to remain stationary when resting on a surface. In this case, the surface is the arrow rest. Without any additional force acting on the arrow, it will remain stationary. However, once the string is released, there is an unbalanced force being applied to the projectile; an applied force with a magnitude that exceeds the force of friction. This force causes the arrow to fly at roughly the same velocity (drag effecting velocity) until it reaches the target. Upon striking the target the velocity reaches zero, demonstrating the presence of another unbalanced force; one which exceeds the applied force of the arrow.

-Example of Inerta using a wagon and some blocks

Newton’s Law 1: Inertia

Newton’s Second Law states, “The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.” (Newton’s Second Law of Motion). As previously mentioned, for there to be acceleration present during a projectile’s flight, an unbalanced force- or a Net Force (FNET)- must be applied to the object in question. In addition to Net Force, the mass of the projectile also affects its acceleration. The Net force on the object is directly proportionate to the acceleration while the mass is inversely proportionate. This means that’s the stronger the Net Force, the greater the acceleration and the greater the mass the smaller the acceleration. As an archer, one is faced with a few decisions that will impact their performance in the sport- the most prevalent being which bow and arrows to use. When selecting a bow, many consider the draw weight in their decision. The draw weight describes the amount of force stored in fully drawn bow. Therefore, the higher the draw weight, the more powerful the shot and the more force applied to the arrow, resulting in a greater acceleration. Next, the type of arrow also impacts the effectiveness the archer. Arrows are most popularly comprised of a carbon, due to its high durability and its low mass. While considering Newton’s Second Law, these arrows are ideal in maximizing strength and density without having to sacrifice acceleration for greater mass.

Newton’s Second Law: F=mxa

Newton’s Third Law states that for every action force, there is an equal and opposite reaction force. For example, when you sit in your chair, you are exerting a downward force on the chair while it exerts and upward force on you. In archery, once the bow is drawn, the archer is applying a force backwards (drawing the bowstring). Once the string is released, the same force applied backwards is now being exerted on the arrow. This reaction force is evident when when observing the recoil a bow encounters upon firing. In addition, despite the fact that the arrow and the archer are experiencing the same amount of force applied to them, only the arrow will be propelled. This is because while the arrow is very light, the archer is too heavy to feel the effect of the force on him.

Newton’s Third Law: Action/ Reaction Forces

-The "Newton's Cradle" is a prime example of action/reaction forces; when the outermost ball strikes the group, the force of the impact is transferred to the opposite outermost ball,causing it to bounce and repeat the cycle.

Archery, like many projectile-based sports, is heavily affected by several different forces. These forces are present throughout the entire process of firing a bow, and are even prevalent as the arrow takes flight. The role each force plays can be described as such:
The first thing an archer does is nock the arrow, fitting it into the bow string and placing the arrow on its rest. Now, there is a Normal Force (FN) acting on the arrow, as the rest is now exerting an upwards force on the arrow to support it.Next, the string is drawn (pulled back) in preparation of the shot. At this point, an Applied Force (FApp ) is being exerted backwards on the string, which results in a Force of Tension (FTen). This tension is obvious as the bow begins to bend from the stress. A recurve bow derives its name from this unique function. When it is drawn, the string itself is not being stretched; the limbs bend, changing the shape (or “recurving”) the bow. This turns the bow into a sort of “spring”, ready to release the stored energy. This type of force is known as the Spring Force (FSpring). It is responsible for applying force (FApp ) from the bow to the arrow. As a result of this applied force, the arrow is now in flight where it is influenced by the Force of Air Resistance (FAir).This form of friction opposes the forward motion of the arrow, causing it loose velocity or “decelerate”. Finally, as is the case with any launched projectile, the Force of Gravity (FGrav) begins to pull the arrow towards the earth which ultimately dictates the object’s motion.

Forces Involved

-Free Body diagram demonstrating the forces at work during the drawing of the bow

-Free Body Diagram demonstrating the forces acting on the arrow once it is placed on the arrow rest.

-Free Body Diagram demonstrating the forces acting on the arrow once it is in flight.

Forces Involved in Archery.