Newton’s 1 st Law of Mechanics A particle will continue is a straight line at constant speed unless acted upon by a net push or pull (i.e. force). The property of a body to continue in a straight line at constant speed is called Inertia. Mass is the measure of a body’s inertia. Thus, a 2 kilo- gram object has twice the inertia of a 1 kilo-gram object.

Newton’s 1 st Law of Mechanics Newton’s 1 st Law tells us a couple of things: 1) The natural state of mater is a straight line at constant speed. 2) If an object is not moving in a straight line and/or if it is speeding up or slowing down then a net push or pull must be acting upon the body.

Newton’s 2 nd Law of Mechanics The direction of the acceleration of a particle will be in the direction of the net external force applied to the particle. The magnitude of the particle’s acceleration will be proportional to the magnitude of the net external force applied to the particle and inversely proportional to the mass of the particle. A F1F1 F2F2 F3F3 F 1 +F 2 +F 3

Newton’s 2 nd Law of Mechanics This is a vector equation. Each direction (x, y, and z) can be solved independently!!

Solving Newton’s 2 nd Law The mass of the particle is usually given or it can be obtained using a scale. Thus, in theory all problems in Newtonian Mechanics reduce to one of two types: 1) You have the acceleration and solve Newton II for the forces. 2) You have the forces and solve Newton II for the particle’s acceleration.

Free Body Diagrams Solving Newton’s 2 nd Law often requires us to identify all of the forces acting upon a body. Identifying the forces is not always obvious so physicist have devised a graphical trick called a Free Body Diagram to solve the left hand side of Newton’s 2 nd Law.

Drawing Free Body Diagrams Step 1: Isolate the body Step 2: Inventory the forces using WANTf Step 3: Draw a coordinate axis Step 4: Identify any critical angles or dimensions (Our problems will generally have no angles or critical dimensions!!)

Drawing Free Body Diagrams Step 1: Isolate the body Step 2: Inventory the forces using WANTf Step 3: Draw a coordinate axis Step 4: Identify any critical angles or dimensions (Our problems will generally have no angles or critical dimensions!!)

WANTf Weight Applied (springs, electric forces, etc.) Normal (Force of contact) Tension (strings or ropes) Friction (sliding friction, air drag, etc.) These are the only type of forces that exist in mechanics!!!

Drawing Free Body Diagrams Example: Draw the free body diagram for a ball falling on the Earth with no air resistance.

Drawing Free Body Diagrams Example: Draw the free body diagram for a ball falling on the Earth with no air resistance. Step 1: Isolate the body (Our body is a ball).

Drawing Free Body Diagrams Example: Draw the free body diagram for a ball falling on the Earth with no air resistance. Step 1: Isolate the body (Our body is a ball) Step 2: Inventory the forces W

Drawing Free Body Diagrams Example: Draw the free body diagram for a ball falling on the Earth with no air resistance. Step 1: Isolate the body (Our body is a ball) Step 2: Inventory the forces Step 3: Draw a coordinate axis W x y

Drawing Free Body Diagrams Example: Draw the free body diagram for a ball falling on the Earth with no air resistance. Step 1: Isolate the body (Our body is a ball) Step 2: Inventory the forces Step 3: Draw a coordinate axis Step 4: Critical Angles & Dimensions (None) W x y

Reading Your Free Body Diagrams Example: Use your Free Body Diagram and your knowledge of falling bodies to find a formula relating weight and mass of an object. Solution: From reading our Free Body Diagram, we have We know that acceleration of a free falling object is

Reading Your Free Body Diagrams Combining our results, we have Thus, we have a relationship between the magnitude of the weight of an object and the object’s mass:

Weight VS Mass As we learned earlier, mass is an intrinsic property of a body that describes a bodies resistance to acceleration. Weight doesn’t belong to a body. It is a gravitational force of attraction between the Earth and the body. Without the Earth, the ball would have no weight, but it still would have mass!! Forces act upon bodies! They are not part of the body!

Drawing Weight Arrows The arrow should start in the center of the body (this point is called the “center of gravity”) and should point straight downward toward the Earth. Drawing Normal Force Arrows A normal force is a force of contact between two bodies. The force should be drawn on the free body at the contact interface and in the direction that would push the objects apart.

Problems 1) A TSU dorm has caught fire and a TSU student is headed for safety by climbing down a rope. If the students is climbing down the rope as shown below at a decreasing speed A. Draw the student’s Free Body Diagram B. Determine if the student’s weight is greater or less than the force the rope applies on the student V

Problems 2) A bathroom scale actually reads the normal force applied by the scale to you and not your weight. The reading on the scale is sometimes called your “apparent weight. a) Describe a situation when the magnitude of your apparent weight is more than the magnitude of your actual weight. b) Describe a situation when the magnitude of your apparent weight is less than the magnitude of your actual weight.

Problems 3) When a rock falls near the Earth its speed will increase until it reaches some maximum value called its terminal speed. After this time the air drag will prevent the rock from gaining speed. a) Draw a Free Body diagram for a rock that is falling at its terminal speed. b) Determine the air drag if the rock has a mass of 2.5 kg.

Problems 5) Use Newton’s 2 nd Law to determine what the scale will read in each of the problems below: a)b) 2 kg

Newton’s 3 rd Law of Mechanics If body A applies a force of some type upon body B then body B must apply the same type of force upon body A that is equal in magnitude and opposite in direction. F BA F AB Body A Body B

Newton’s 3 rd Law of Mechanics Forces always come in pairs!! If we take the entire universe as our system then the sum of these forces always adds up to zero!!! Thus, the total motion of the universe is always conserved. Physicists call this quantity related to motion the Linear Momentum which is defined by the equation:

Conservation of Linear Momentum The linear momentum of a system is conserved (i.e. constant) if the system is isolated (i.e. there is no net external force) or if the time in which any forces occur is approximately zero (collisions, and explosions)!!

Conservation of Linear Momentum Example: A gun with a mass of two kilograms fires a bullet of mass kg with a speed of 180 m/s as seen by an observer. What is the speed of the recoiling gun as seen by the observer? Solution: Considering the gun + bullet as the system, the linear momentum just before and after the firing of the gun is conserved. x y Initially Final

Conservation of Linear Momentum Solution (continued): The initial linear momentum in the x-direction is The final linear momentum is found by x y Initially Final

Conservation of Linear Momentum Solution (continued):