Forces and Newton’s Laws of Motion To explain all nature is too difficult a task for any one man or even for any one age. `Tis much better to do a little with certainty, and leave the rest for others that come after you, than to explain all things. -Isaac

Objectives – What You Should Know about Forces Describe how forces affect the motion of objects. Interpret and construct free-body diagrams. Explain the relationship between the motion of an object and the net force acting on it. Determine the net external force on an object. Predict the direction and magnitude of the acceleration caused by a known net external force. Recognize the conditions required for equilibrium. Identify action-reaction pairs.

A Very Brief History of Statics and Dynamics The idea that a force causes motion goes back to the 4th century B.C., when the Greeks were developing ideas about science. Aristotle (384-332 BC) studied motion, and divided it into two types, natural and violent.

Natural Motion Natural motion was thought to be straight up or straight down on earth. Objects would seek their natural resting places: heavy things would fall to the ground, light things (like smoke) would rise. The heavens’ natural motion was circular. Since these motions were considered “natural”, they were not thought to be caused by forces. Newtonian Aristotelian

Violent Motion Violent motion was imposed motion. It was the result of forces that pushed or pulled. A cart moved because it was pulled. Violent motion had to have a cause. For nearly 2000 years, it was commonly believed that an object on earth moved “against its nature”.

Galileo Galilei (1564-1642) Until Galileo Galilei, the premier scientist of the 17th century, “common sense" told people that heavier objects fall faster. Galileo showed the power of experiment over logic.

Enter Newton In 1668, Newton built the first reflecting telescope. During his lifetime he was involved in the development of the calculus AND the laws of motion. Neither are small accomplishments. Newton struck upon the laws of motion and the law of gravitation. Newton was one of the greatest scientists the world has known for his ability to explain seemingly dissimilar phenomena by the formulation of a coherent system of laws.

Forces A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force.

Forces Force is a vector quantity. Forces cause changes in velocities (accelerations)… more specifically, unbalanced forces cause changes in velocities. Balanced Forces No Acceleration Force (cow on chair} Unbalanced Forces = Acceleration Weight FN

SI Unit for Forces The newton (N) is the SI unit for force… the pound is the English unit for force. One newton is the force required to accelerate a mass of 1 kg at a rate of 1 m/s2

Free-Body Diagrams Free-body diagrams (FBDs) are graphical representations of objects where all forces acting ON the object are represented. Forces exerted by the object on other objects are not included in the diagram. FBDs are used to analyze situations. When you isolate an object, and identify all of the forces acting on it, you can predict how the object will move.

Newton’s First Law of Motion Newton’s First Law of Motion, also known as the Law of Inertia, states that a body in motion will remain in motion at a constant velocity, and a body at rest will remain at rest unless acted upon by an unbalanced force. Inertia is the resistance of an object to changes in its motion.

More on Inertia Galileo developed the concept of inertia. Galileo reasoned that moving objects eventually stop because of a force called friction. Mass is a measure of inertia.

Implications of Newton’s First A body in motion at constant velocity does not necessarily require a force to keep it in motion at constant velocity.

Galileo’s Thought Experiment More Implications Galileo’s Thought Experiment If there were no friction, objects moving along a horizontal surface would not slow down.

AND If an Object is at Rest… OR Moving with Constant Velocity All forces acting on that object must add (as vectors) to be zero. The object is said to be in equilibrium.

Equilibrium Fx = 0 Fy = 0

What If There Were An Unbalanced Force?

Newton’s Second Law Forces mass acceleration summation Is the product of a vector (acceleration) and a scalar (mass); the direction of the acceleration is ALWAYS in the direction of the net force.

Newton’s Second Law F is the summation of forces acting on the object under consideration. F may also be called the net force, or the unbalanced force. Let’s consider the scenario below: Friction Normal Weight F F

Newton’s Second Law If there is an unbalanced force acting on an object, the acceleration of the object is directly proportional to the unbalanced force and inversely proportional to the mass of the object F  a a 

Implications of Newton’s Second Bigger forces yield bigger accelerations. 10 N F = ma 10 N = 5 kg (a) a = 2 m/s2 m = 5 kg 50 N F = ma 50 N = 5 kg (a) a = 10 m/s2 m = 5 kg

Implications of Newton’s Second Forces accelerate smaller masses more than larger masses. F = ma 10 N = 2 kg (a) a = 5 m/s2 10 N m = 2 kg 10 N F = ma 10 N = 4 kg (a) a = 2.5 m/s2 m = 4 kg

More Implications If you know the mass of an object, AND it’s acceleration, you know the net force acting on it… even if you don’t know the nature of these forces:

Newton’s Third Law of Motion For every action, there is an equal and opposite reaction.

Implications of Newton’s Third If you push/pull on something, it pushes/pulls back on you with an equal but opposite force. Forces always occur in pairs.

Equal and Opposite/Action-Reaction Pairs The force the earth exerts on the dinosaur is equal but opposite to the force the dinosaur exerts on the earth. Let’s say the dinosaur weighs 33,000 N. The weight of the dinosaur is the gravitational force the earth exerts on the dinosaur, and that 33,000 N is the gravitational force the dinosaur exerts on the earth. 33,000 N

More Action Reaction

And Even More Why does anything move? These forces seem to cancel.

The Forces Acting ON an Object Determine its Motion The action/reaction pairs are forces that are exerted on two objects by each other.