Newton’s Laws!!

When one object or system interacts externally with another, we describe that interaction as a force. When two objects touch, they push or pull on one another. A push or pull is a common way to describe a force. Forces allow us to predict the future motion of objects or systems!! A force is a vector, which means it has magnitude and direction.

Newton’s First Law (N1L)!!

The Law of Inertia refers to an object’s tendency to resist changes in its motion. That is, an object at rest will remain at rest unless acted upon by an external force. Also, an object in motion will tend to stay in motion with the same speed until acted upon by an external force. We quantify the inertia of an object by the object’s mass!!

Mind the differences between mass, weight and inertia. Mass is the quantity of material in an object; no matter where in the universe you take the object, it’s mass remains the same. Weight is the magnitude of the gravitational force (Fg) on an object. It is proportional to mass but depends on the the value of ‘g’ at the object’s location. Inertia is the tendency of all objects to maintain the same motion!

#dyk that N1L contradicts the older theories of motion developed by ancient Greeks like Aristotle?

Newton’s Second Law!!

F = ma

The most commonly used notion to describe the relationship between force and motion. In words; if a net external force is exerted on an object, the object’s accelerates in the direction of the force. The net external force is equal to the product of the object’s mass and acceleration.

Remember that acceleration is due to the sum of all the forces exerted on an object. It sometimes beneficial to think of N2L in terms of acceleration.

a = F/m

In words; the acceleration of an object is proportional to and in the same direction as the net external force exerted on the object and inversely proportional to the mass of the object.

So, a net external force on an object causes the object to accelerate in the same direction. If you double the net external force on an the object the acceleration also doubles. If you apply the same net force to an object with double the mass the acceleration is half as great.

The SI unit of force is the Newton (N). A net external force of 1 N applied to an object with a mass of 1 kg gives the object an acceleration of 1 m/s^2. A Newton is also equal to .225 lb, so about 1/4 pound.

Ultimately, N2L tells us that a net external force is required to cause an object to accelerate, that is, change it’s velocity. If we push the paper football so that the football’s velocity is constant, it simply means that the force exerted is balanced by the force of kinetic friction the table exerts on the football. What happens if you stop applying the force on the football?

a: the net external force now points backwards and therefore acceleration is now pointing backwards and is now opposite motion. The football slows down!!

We say that an object is in equilibrium if the net external force on an object is zero. A hanging Halloween spider decoration is on equilibrium just the same as Mario moving along at a constant velocity!!

Newton’s Third Law (N3L)!!

This is the law of action/reaction pairs. Or, every action has an equal and opposite reaction. This relates the forces that two object’s exert on each other. You can feel the slap of the basketball against your hand as you push down on it!

So, if object A exerts a force on object B, object B exerts a force on object A that has the same magnitude but opposite direction.

You need the right recipe to make those perfect chocolate chip cookies. Now, The key that unlocks physics problems involving forces and the recipe that allows you to navigate these problems in the Free Body Diagram (FBD)!! The FBD is a graphical representation of all the external forces exerted ON an object. It’s useful because N2L and N1L both involve the sum of all the external forces on an object. The term “free body” mans that we draw only the object on which the forces are exerted and not the other objects that exert those forces!!

In the same sense, the Center of Mass (CoM) of a system moves as though all of the system’s mass were concentrated there. If every object in a system moves with the same acceleration as the CoM, then the entire system can be modeled as an object.

FBDs help connect the “real world” with “pen and paper” problems. They are an essential tool to solve most N2L problems. The FBD represents each external force on an object by a vector that originates on the object and points in the direction of the force. Remember to draw a simple representation of the object of interest. Here are the rules of drawing FBDs!!

1.) Sketch a simplified version of the object on which the forces are exerted. A dot, a small circle or a square is perfect. Something where you can easily place your arrow tails for your vectors. Remember we are representing the CoM so shape does not make a difference!!

2.) Identify what other objects exert a force on this object. This includes Earth, which exerts the force of gravity (Fg) and anything else that touches the object.

3.) For each force exerted on the object, draw a force vector with its tail at the center of the object. Don’t include forces the object may exert in other objects!

4.) Label each force properly with its symbol. Be sure to identify what other object exerts each force. Be sure it’s a real force.

5.) Choose, draw and label the directions of the positive (x) and (y) axes. Choose the axes so that as many force vectors as possible lie along one of the axes. That is, it might be advantageous to try your axes for objects on an incline!!

Look here for an simple example of the FBDs for the small block on a table! Remember to be able to draw the force vectors to scale to estimate the size of forces, particularly relative to one another. We also unambiguously label the vectors using a capital F and a subscript describing the force, that is, Fg.

Ramps and Inclines

Like Josh Neuman cruising down the Swiss Alps we always manipulate the rules of nature and apply Newton’s Laws in practice. If we analyze any sort of motion down a hill the most important aspect is to, of course, draw an FBD.

When we draw an FBD for an object accelerating down a hill there are a few things to keep in mind.

(1) Use a straight edge to draw a diagonal line from the horizontal.

(2) Label the angle between the incline and the horizontal, theta.

(3) Draw the Normal Force perpendicular to the contact surface.

(4) Draw the Force of Gravity pointing straight down!!

(5) Tilt your coordinate plane so that the x-axis is parallel to the ramp and the y-axis is parallel to the Normal Force. This means that Fg is the only force not directed along one of the axes.