What is a Force? A force is a push or a pull causing a change in velocity or causing deformation.

Dynamics What is dynamics? Dynamics is the study of the relationship between force and motion.

How are contact forces different from long range forces? Contact forces - touching - example: hand on desk Long range forces - act at a distance - gravitational forces, electrostatic, magnetic

What is Newton’s First Law of Motion? Law of Inertia: tendency to resist change An object at rest remains at rest, and an object in motion remains in motion (same direction, constant speed) unless acted upon by an unbalanced force. Forces are balanced: Equilibrium

Newton’s 1st Law - Types of Equilibrium 1. Static Equilibrium object is at rest 2. Dynamic Equilibrium object is moving at constant velocity

What is Newton’s Second Law of Motion? Unbalanced forces produce acceleration **Acceleration is directly proportional to force and inversely proportional to mass Fnet = ma a = Fnet/m in reference table Units 1 kgm/s2 = 1 Newton

Example: An artillery shell with a mass of 5.5 kg is fired from a gun with a velocity of 770 m/s. The barrel of the gun is 1.5 m long. Find the force on the shell.

Solution: m = 5.5 kg vf = 770 m/s vi = 0 m/s d = 1.5 m

Special Case - weight W = mg is a special case of F = ma, where weight is the force, and gravity is the acceleration (can be written as Fg) Example: What is the weight of a 5 kg object?

Two Kinds of Mass 1. Gravitational mass - using a balance - comparing the gravitational force on two objects (one has a known mass). 2. Inertial mass - using Newton’s 2nd law - find the force necessary to produce a specific acceleration for a given mass Gravitational mass = inertial mass

Graph: Inertial mass F Slope is mass a

Free Body Diagrams What is Fnet? Used to show forces on an object Sketch and Equations: What is Fnet? Fnet is the sum of the forces acting in the direction of motion (vertical or horizontal)

Free Body Diagrams: Vertical  Lifted object (Ftens is tension)

Example:A 50 Newton force is used to lift a 2 kg object Example:A 50 Newton force is used to lift a 2 kg object. What is the acceleration of the object? Lift 50 N Weight

Example:A 4500 kg helicopter accelerates upward at 2 m/s2 Example:A 4500 kg helicopter accelerates upward at 2 m/s2. What lift force is exerted by the air on the propellers? Lift ? N Weight

Alternate Solution to helicopter problem:

What is Newton’s 3rd Law of Motion? For every action, there’s an equal and opposite reaction. The force on one object is equal and opposite to the force on the other. Object resting on a table: weight pushes back on table. Table pushes back with an equal and opposite force called Normal force (FN). If no other vertical forces are present: normal force equals weight

Falling objects: what are the forces on an object falling through the air? Object in freefall (no air resistance) Object in freefall (with air resistance)

Falling Objects: What are the forces on an object falling is the air? What happens when they are equal? Drag force (Fair) - air resistance - depends on size/shape of the object, air density, speed. When drag force = weight, forces are balanced (Fnet=0) No net force means no acceleration! You have reached TERMINAL VELOCITY. 

Free Body Diagrams Free body diagram - horizontal motion FN Ff FA Fg or W

What if…. FA is greater than Ff FA is equal to Ff then acceleration is positive FA is equal to Ff then no acceleration (constant velocity) FA is less than Ff acceleration is negative (you can slow down, but friction won’t make you move backwards!)

Free Body Diagrams Free body diagram - horizontal motion with no friction:

Example: If you apply a 50 Newton force to a mass of 5 kg, what is the acceleration?

Example (continued): What if a frictional force of 20 N opposes the applied force? Find a.

What is friction? Friction - force opposing motion between 2 surfaces in contact and parallel to the surface How can you calculate frictional force? Equation: Ff = frictional force (N) FN = normal force (N) coefficient of friction (no units)

What variables affect friction? Weight? YES Surface area? NO Type of surfaces in contact? YES Velocity? NO Normal force - force pushing objects together- is normal force always equal to weight? NO - they are not equal if other vertical forces are present.

What are two types of friction? 1. Static - objects are NOT in relative motion - static friction opposes the START of motion 2. Kinetic (sliding) - force between surfaces in motion - resists motion Which is greater? Static friction is greater - it is harder to start motion that it is to keep an object moving.

Example #1: A block is place on a table. It has a weight of 50 N. You must exert a force of 20 N to keep the block moving at a constant velocity. 1. What is coefficient of sliding friction?

2. Place a 10 N brick on the block 2. Place a 10 N brick on the block. What force is required to keep the block moving at constant velocity? Same surfaces, so  = 0.4

Example #2 A 10kg box made of wood is pushed on a wood floor with a force of 100 N. (a.) Will the box slide? (b.) What force must be applied to move the box at a constant velocity? (c.) What force must be applied for the box to accelerate at a rate of 5 m/s2?

Solution: (a.) Will it move? It will move if the applied force exceeds the static frictional force. From reference table: static = 0.42 Yes, 100N>41.2N, box will slide.

Solution: (b). To move box at a constant velocity….. Use KINETIC friction. From reference table: kinetic = 0.30 Since a = 0, then Fnet = ma =0

Solution: (c.) a = 5 m/s2, find FA