Introduction to Statics Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Introduction to Statics

Forces in Equilibrium Tall buildings are an impressive example of equilibrium, or the balancing of forces. A modern office tower is constructed of steel and concrete beams that are carefully designed to provide reaction forces to balance against wind, gravity, and people. All forces acting on the building must add up to zero.

Statics Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics The study of forces and their effects on a system in a state of rest or uniform motion ©iStockphoto.com ©iStockphoto.com ©iStockphoto.com Uniform motion means constant velocity. State of rest is constant velocity also, specifically v=0.

Equilibrium The concept of equilibrium is important to the design of bridges, buildings and virtually any technology invented by humans. In order for a bridge to stay in place, ALL the forces acting on the bridge must add up to produce a net force of zero.

Statics Principles Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Newton’s First Law of Motion (law of inertia): An object in a state of rest or uniform motion will continue to be so unless acted upon by another force. If the net force of an object is zero (equilibrium), an object at rest will stay at rest and an object in motion will stay in motion with constant speed and direction. Describes the relationship between velocity and forces.

Force = Mass x Acceleration Statics Principles Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Newton’s Second Law of Motion: The acceleration of an object is proportional to the net force acting on the object and inversely proportional to the object’s mass Force = Mass x Acceleration The acceleration of an object in equilibrium is zero because the net force acting on the object is zero. Zero acceleration means neither the speed or the direction of motion can change. Describes the acceleration of an object in the direction of the net force applied to it.

Free Body Diagrams Statics Principles Principles of EngineeringTM Unit 2 – Lesson 2.1 - Statics Newton’s Second Law of Motion: Any object at rest is in equilibrium and has a net force of zero acting on it. Imagine a book sitting on a table. Gravity pulls the book downward with a force equal to the books weight. But what force balances the weight? The table exerts an upward force on the book called the Normal Force. In mathematics, Normal means perpendicular. The force the table exerts is perpendicular to the table’s surface.

Free Body Diagrams Statics Principles Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Newton’s Third Law of Motion: For every action force, there is an equal and opposite reaction force Describes action-reaction pairs. ©iStockphoto.com

Statics Principles Newton’s Third Law of Motion: The third law explains why normal forces exist. The book pushes down on the table, so the table pushes up on the book. The book’s force on the table is the action force, and the table’s force on the book is the reaction force. These forces are equal in strength. If the book is at rest, these forces must be equal but opposite in direction.

Equilibrium Static Equilibrium: Free Body Diagrams Equilibrium Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Static Equilibrium: A condition where there are no net external forces acting upon a particle or rigid body and the body remains at rest or continues at a constant velocity ©iStockphoto.com

Equilibrium Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Translational Equilibrium: The state in which there are no unbalanced forces acting on a body ©iStockphoto.com ©iStockphoto.com Balanced Unbalanced

Equilibrium Rotational Equilibrium: Free Body Diagrams Equilibrium Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Rotational Equilibrium: The state in which the sum of all the clockwise moments equals the sum of all the counterclockwise moments about a pivot point Remember Moment = F x D ©iStockphoto.com

Statics Principles Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Scalar Quantities: A physical quantity that has magnitude only Examples: Mass, length, time, volume, temperature, pressure, and speed ©iStockphoto.com ©iStockphoto.com

Scalars Scalars have Magnitude A scalar is a quantity that can be completely described by a single value called a magnitude. Magnitude means the size or amount and always includes units of measurement Temperature is a good example of a scalar quantity. If you use a thermometer to check your temperature and it shows 101 F. The magnitude of your temperature is 101, degrees Fahrenheit is the unit of measurement. O

Statics Principles Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Vector Quantities: A physical quantity that has both a magnitude and direction Examples: Position, velocity, force, and moment ©iStockphoto.com ©iStockphoto.com

Vectors Vectors have direction If you are giving someone directions to your house, you could not just say drive 5 miles. You must also add the direction to drive those 5 miles. A force vector has units of Newtons, like all forces; the force vector also includes the direction of the force.

What Is a Force? The pushing or pulling interaction of objects Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics The pushing or pulling interaction of objects A vector quantity defined by its known magnitude, direction, and point of application A 45 lbf 21.8°NE A force vector is drawn as an arrow.

Force Units British System of Units International System of Units Free Body Diagrams Force Units Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics British System of Units Pound-force (lbf) International System of Units Newton (N) Conversions between Unit Systems 1lbf = 4.448 N 1N = 0.2248 lbf

Static Equilibrium Force Principles Free Body Diagrams Static Equilibrium Force Principles Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Forces always occur in pairs. Force pairs act in opposite directions and have the same magnitude.

Force Components Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics A single force can be replaced by component forces if their combination produces the same effect as the original force. a Fa Fay Fax a

Free Body Diagrams Resultant Force Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics A single force that has the same effect as two or more concurrent forces 7lbf Resultant = 2lbf 5lbf 3lbf Resultant 5lbf 2lbf =

Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Visual representation of force and object interactions Individual objects or members are isolated from their environment or system, illustrating all external forces acting upon them Every object exists surrounded by other objects, perhaps resting against something, perhaps moving through its surroundings. While an object is in a given environment, it interacts with other objects around it, exerting forces on those objects and having forces exerted upon it. A free body diagram isolates an object from its environment, or system, and symbolically examines all of the forces acting on the object. This allows engineers to focus on the forces acting upon the object. From the free body diagram, engineers develop equations which can describe equilibrium, motion, momentum, strength, and many other physical properties.

Free Body Diagram Components Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Components Force A straight line push or pull acting upon an object Vector quantity has direction and magnitude Direction is illustrated by arrowhead Magnitude is illustrated by length of line segment and is the amount of push or pull

Free Body Diagram Components Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Components Moment The twisting effort about a point or axis when a force is applied at a distance Arc with an arrowhead acting about a point indicating direction of CW or CCW

Moment Review Moment (M) = Force (F) x distance (d) Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Moment Review Moment (M) = Force (F) x distance (d) Distance (d) is called the moment arm. It must be measured perpendicular to the line of action of the force. Point of Rotation F d Line of Action

Free Body Diagram Procedure Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Procedure A stack of three books, each weighing 5 lb, is sitting on top of a table. Draw the Free Body Diagram (FBD) of the top book.

Free Body Diagram Procedure Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Procedure 1. Sketch the isolated object. What is the isolated object? Top Book Free body diagrams should be drawn completely isolated from all other objects. We “free” the body from its system. Instead of taking time to draw the object in detail, we substitute a simple geometric shape, such as a square or a circle. For these exercises the shape we draw is considered dimensionless.

Free Body Diagram Procedure Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Procedure 2. Sketch the applied and norm forces. When an object is in contact with and is supported by a second object, the second object can be replaced with a normal force which is perpendicular to the surface of the second object. Free body diagrams should be drawn completely isolated from all other objects. We “free” the body from its system. Instead of taking time to draw the object in detail, we substitute a simple geometric shape, such as a square or a circle. For these exercises the shape we draw is considered dimensionless.

Free Body Diagram Procedure Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Procedure 2. Sketch the applied force and norm forces. Normal Force Reaction force pushing up on the book, causing it not to fall Free body diagrams should be drawn completely isolated from all other objects. We “free” the body from its system. Instead of taking time to draw the object in detail, we substitute a simple geometric shape, such as a square or a circle. For these exercises the shape we draw is considered dimensionless. Applied Force Weight of top book

Free Body Diagram Procedure Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Procedure 3. Label objects and forces. N=5 lbf PLTW – DE book Free body diagrams should be drawn completely isolated from all other objects. We “free” the body from its system. Instead of taking time to draw the object in detail, we substitute a simple geometric shape, such as a square or a circle. For these exercises the shape we draw is considered dimensionless. Ask the question: Why are these two forces equal? A typical answer would be that they are not moving. Go a little bit further and ask what law of motion explains this situation. Answer=Newton’s Second Law, which is F=ma. If there is no acceleration, then there is no net force. W=5 lbf

Free Body Diagram Procedure Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Free Body Diagram Procedure 4. Label dimensions. For more complex free body diagrams, proper dimensioning is required, including length, height, and angles. N=5 lbf 45° 8 ft 10 ft 38.6° PLTW – DE book Free body diagrams should be drawn completely isolated from all other objects. We “free” the body from its system. Instead of taking time to draw the object in detail, we substitute a simple geometric shape, such as a square or a circle. For these exercises the shape we draw is considered dimensionless. W=5 lbf

Free Body Diagram Practice Free Body Diagrams Free Body Diagram Practice Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Create a FBD for the sled pictured below. Fapp Fapp θ FN θ Ff W Ff W FN

Free Body Diagram Practice Free Body Diagrams Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Create a FBD for the refrigerator pictured below. FN Fapp Fapp W W Ff θ FN Ff θ

Free Body Diagram Practice Free Body Diagrams Free Body Diagram Practice Principles of EngineeringTM Unit 4 – Lesson 4.1 - Statics Create a FBD for the pulley system pictured below. FT FBD of Mass 1: W1 FT FT FBD of the movable pulley: Free body diagrams are frequently used while solving pulley system problems. It is useful to isolate the parts of a pulley system to discover relationships between the parts. This pulley system consists of an upper fixed pulley, which is supporting block M1, and a lower movable pulley. The movable pulley is supporting block M2. A single rope or cord connects these pulleys. Both pulleys are considered mass-less and frictionless. A free body diagram of M1 would start with a small shape. Two forces are acting on M1: The weight of M1 and the tension force of the rope. We can also isolate the pulleys. Looking at the lower movable pulley, we draw the free body. The weight of the block M2 is pulling down on the pulley. Two strands of the rope are pulling up on the pulley, and each of the strands is exerting a tension force. The tension force in the rope is equal in each free body diagram within the system since there is a single tension force in the entire rope. W2 + W pulley M2 M1 Tension Forces (FT ) are equal throughout the system.