Force Diagrams Introduction Poes

Introduction to Forces and Free Body Diagrams (FBDs)

 There are four fundamental forces of nature that are responsible for all of the interactions that can occur between objects.

Force Relative Strength Description Acts at any distance but gets weaker as the distance between the objects involved increases. Gravity 1 Exists between any two objects that have a non-zero mass. Attraction only. Acts at any distance but gets weaker as the distance between the objects involved increases. Includes the electric force (like that involved in static electricity), as well as the magnetic force (like that which affects a compass needle).

36 Attraction and repulsion, therefore on average the forces tend to cancel each other Electromagnetic 10 out. If not, this force would overpower gravity. Holds atoms together by electrons being attracted to the nucleus. Hold objects together by its atoms being attracted to each other. (London dispersion forces / van der Waals forces – complicated) Is the root cause of most large-scale forces we experience every day. Acts only when distance between two objects is less than 10-15m.

38 Holds the nucleus together due to an attraction between the protons and neutrons, Strong Nuclear 10 even though the protons have an electric repulsion of each other. Attraction and repulsion. Acts only when distance between two objects is less than 10-18m. Particles like neutrons (and many other elementary particles), can break apart into Weak Nuclear 1025 smaller particles. This force is responsible for these particles being held together and being pushed apart. Attraction and repulsion.

 The forces listed above are typically at work “behind the scenes” of what we experience during everyday life. In the study of motion, we are often more concerned with describing forces in a way that is consistent with what we observe. The most common forces that we encounter on a daily basis are as follows:

Force Description Notation Caused by the mutual attraction of two objects that have a non-zero mass. However, this force is only Gravity F typically considered when there is one much larger g object (like the Earth) ‘pulling’ on a smaller object. When an object that is moving is in contact with another object (like the ground, or even the air), the F (or sometimes more specifically Friction f force of friction acts in the opposite direction to the Ff,ground, or Ff,air) object’s motion. Applied by one object to or on another object. For F (or sometimes more Applied example a wagon can be pushed by a hand, or app specifically F , or F ) pulled by a rope.* hand rope * As you will soon learn, there are other specific kinds of applied forces called Tension and the Normal Force, but for now I would like you to write every applied force by specifically stating the object that produces it.  One of the most important things to keep in mind during this unit is that FORCES CAUSE CHANGES IN MOTION (NOT MOTION ITSELF)!!! In the absence of forces, the motion of an object remains unchanged (i.e. it keeps moving as it was, or it keeps staying still)!

 To correctly analyze or predict the motion of an object, the first thing that a physicist must usually do is think of all the different forces that are acting on it.

 A Force Diagram (also called a Free Body Diagram, or FBD) is a diagram that depicts the object in question as a single dot and includes all of the forces acting on that object drawn as arrows (or vectors) pointing away from the dot. The rules for drawing a FBD are: - arrows are drawn with their ‘tail end’ attached to the dot, and pointing in the same direction that the force they represent is acting on the object - The relative strengths of the forces (if known) are indicated by the relative lengths of the arrows

 The following is a FBD for an asteroid in the middle of outer space between planet Earth and planet Mars, but significantly closer to planet Earth. Since the force of gravity gets stronger the closer you are to an object, the force vector for Earth’s gravity on the asteroid is larger than the force vector for Mars’ gravity.

. Fg,Earth Fg,Mars

 Try drawing a FBD for an asteroid in between Planet X (on the left) and Planet Z (on the right), where the planets are the same size but the asteroid is much closer to Planet Z.

 If the force Fg,x had a value of 100 N (for “Newtons”) and the force Fg,z had a value of 900 N what do you think is the overall/resultant/net amount of force that the asteroid feels?

Def’n: The net force, Fnet, is the vector addition/subtraction of all forces acting on an object. Exercise: Find the net force in each of the following situations.

9 N 12 N

10 N 7 N

6 N 11 N

5 N 8 N

6 N Free Body Diagram Predictions For each of the situations below, draw a FBD of the object in bold. A mass on a metre stick suspended across a valley A puck on a table being pushed to the right at a constant speed

A mass sitting on top of a table A puck on a table being pushed to the right and accelerating

A mass suspended by a spring A puck on a table sliding to the right after being let go from a push

A mass suspended by a rope A sled being pulled by a girl at an angle of 35˚ above the horizon and a constant speed of 1.5 m/s Newton’s Laws of Motion

 Building on the ideas from the early 1600s of French scientist/mathematician Rene Descartes, in the late 1600s English physicist Sir Isaac Newton proposed his famous three laws of motion to “perfectly” describe how the world worked (according to the best measurements that could be made at the time).

 These theories stood up for centuries until a brilliant outside-of-the-box thinker named Albert Einstein came along and proved that Newton’s laws of motion were only a simplification of an even broader Theory of Relativity.

 At this very moment, scientists are in the midst of proving that some observable phenomena cannot be explained by Einstein’s theory, leaving the door open for the next young revolutionary physics mind…. Maybe it will be you???

“ Give me matter and motion, and I will construct the universe.” - Rene Descartes (1640)

“… from the phenomena of motions to investigate the forces of nature, and then form these forces to demonstrate the other phenomena: … the motions of the planets, the comets, the moon and the sea …” - Isaac Newton (1686)

“ No one must think Newton’s great creation can be overthrown by [Relativity] or any other theory. His clear and wide ideas will forever retain their significance as the foundation on which our modern conceptions of physics have been built .” - Albert Einstein (1948)

 Despite the inability of Newton’s laws to accurately describe high speed motion, they are very useful for describing every day motion in and around the surface of the Earth.

First Law: “Law of Inertia”

 An object will remain in its current state of motion (vconstant=0 or vconstant=some#) if the net force acting on it is zero.  Inertia describes an object’s resistance to changing it’s current state of motion. More mass means more inertia (e.g. car has high inertia, marble has low inertia).

Second Law: “Fnet = ma”  If there is a net force acting on an object, the object will accelerate in the direction of that net force, and at a rate defined by the equation: v F v av = net which is more commonly written as F= mav m net

Third Law: “Action-Reaction Forces”  When object A exerts a force on object B, object B exerts the same amount force in the opposite direction back onto object A.  Examples: - To walk forward you push back on the floor so it will push you forward - A mother gently pushing her daughter (both on skates) - both move away  IMPORTANT: These two forces can never be in the same FBD because they happen to different objects (and an FBD only shows all the forces acting on one object)! Free Body Diagram Answers Using your new knowledge of Newton’s Laws, draw the correct FBD of the object in bold. A mass on a metre stick suspended across a valley A puck on a table being pushed to the right at a constant speed

A mass sitting on top of a table A puck on a table being pushed to the right and accelerating

A mass suspended by a spring A puck on a table sliding to the right after being let go from a push

A mass suspended by a rope A sled being pulled by a girl at an angle of 35˚ above the horizon and a constant speed of 1.5 m/s Fnet Practice p 7, 8

Fan Cart Physics p 9, 10 Fnet Practice p 2

For each of the following situations, I would like you to draw your prediction of the correct FBD. Since we are always near planet Earth (and far away from all other planets), to denote the

force of gravity you only need to write Fg and not Fg,Earth as in the previous sample FBD.

Situation Predicted FBD of the Book Actual FBD of the Book Comments

A heavy book sitting on the table

A heavy book held on the hand (like a waiter holding a tray)

A heavy book hung from a spring

A heavy book sitting on a piece of foam

A heavy book sitting on a metre stick suspended between two bricks

A heavy book sitting on the table  As you saw on the previous page, anything that supports a motionless object that is being pulled on by gravity must produce this “push back” force to keep the object from falling under gravity’s influence. This often “invisible” force is called the Normal Force.

 Connection: What do you think is the cause of the Normal Force? Consider specifically the normal force produced by the metre stick in the fifth of our mini-POEs above.

 Connection: Come up with three other situations where one of these causes is the reason we experience an “applied force” that would not be considered a normal force.

 Extension: After hearing all of your classmates’ different ideas, what might you conclude?  Now try this next group of FBDs.

Predicted FBD of the Actual FBD of the Situation Comments Paper Paper A 1 cm by 1 cm piece of paper immediately after it has been dropped out of the hand of a student A 1 cm by 1 cm piece of paper that has been dropped out of the hand of a student when half way to the ground A 8½ x 11 sheet of paper immediately after it has been dropped out of the hand of a student A 8½ x 11 sheet of paper that has been dropped out of the hand of a student when half way to the ground A crumpled 8½ x 11 paper immediately after it has been dropped out of the hand of a student A crumpled 8½ x 11 paper that has been dropped out of the hand of a student when half way to the ground  Although it is not always easy to detect, any objects that move through the atmosphere surrounding our Earth experience some degree of what is called Air Friction. Typically, air friction is not significant for: - slow moving objects - objects with a small surface area - objects that are built aerodynamically (i.e. so that they ‘cut through’ the air effectively)

 Usually, the force of air friction is so minimal compared to the other forces involved in a particular situation that it can be ignored, but since the strength of air friction increases with the speed or surface area of an object, it can become significant enough to warrant consideration for very fast-moving or very large objects.

 Try this next group of FBDs.

Predicted FBD of Actual FBD of the Situation Comments the Person Person

A person immediately after they have jumped out of a plane 5 km above Earth

A person several seconds after they have jumped out of a plane 5 km above Earth

A person with a broken parachute just before they hit the ground after jumping out of a plane 5 km above Earth

 You might have heard the expression “terminal velocity” when people talk about skydiving. What do you think this term means, and why do you think it happens?  In the following situations, there may be more than one force acting in the same direction. When that is the case, the force vectors that act in the same direction are drawn “tip-to-tail” with each other. Consider the following FBD of a rocket ship in the same position as the asteroid mentioned earlier, but with an engine being used to propel it toward Mars

. Fg,Earth Fg,Mars Fengine

 Try this next group of FBDs.

Predicted FBD Actual FBD Situation Comments of the… of the… baseball baseball A baseball has just been thrown (to the right) by the pitcher and it is in mid-air on its way to home plate basketball basketball A basketball just after it has been released by a shooter during an NBA exhibition game on the Moon hockey puck hockey puck A hockey puck has just been shot along the ice (to the right) and it is sliding its way toward the net textbook textbook A textbook is being lightly pushed across a desk to the right by a student’s hand

textbook textbook A textbook is being pushed with a very strong force across a desk to the right by a student’s hand textbook textbook The textbook in the last situation just after the student stops applying the pushing force Introduction to Weight and Newton’s Second Law

To correctly interpret the various measurements of force (i.e. “weight”) that appear on the spring scale in the various situations investigated, it is important to realize that the reading on any weighing scale is a measurement of the upward force the scale is imparting on the object being weighed. In the situation where the object and scale are both at rest, the scale indicates how much force it needs to produce to counterbalance the downward force of gravity on the object – this is the scientific definition of the weight of an object. For the case of an everyday bathroom scale, this reading tells us how much ‘normal force’ the scale is pushing up on our body with. For the case of an object suspended by a spring scale and string we would say the reading is a measurement of either the ‘tension’ in the string or the ‘spring force’ in the spring that is pulling up on the object. Both kinds of scales, however, would produce the exact same amount of force to counterbalance the force of gravity on any one particular object, and therefore give a correct reading of that object’s weight.

Measured Weight Situation FBD of Object of Object Object is suspended (at rest) by a spring scale which hangs from a string that is attached to the ceiling

Prediction of FBD of Measured Situation Measured Weight Weight of Explanation Object of Object Object The string is hung over a pulley and Just as pulling pulled by the begins: teacher such that Less than initial weight the object moves Equal to initial weight upward at a Greater than initial weight constant speed

The string is hung over a pulley and Half way through the pulled by the ‘journey’: teacher such that Less than initial weight the object moves Equal to initial weight upward at a Greater than initial weight constant speed Prediction of FBD of Measured Situation Measured Weight Weight of Explanation Object of Object Object An object with the same mass of the original object is tied Less than initial weight to the opposite end Equal to initial weight of the string hung Greater than initial weight over a pulley and the system is let go from rest. An object with double the mass of the original object is Less than initial weight tied to the opposite Equal to initial weight end of the string Greater than initial weight hung over a pulley and the system is let go from rest. An object with half the mass of the original object is tied Less than initial weight to the opposite end Equal to initial weight of the string hung Greater than initial weight over a pulley and the system is let go from rest.

Nothing is tied to the opposite end of the Less than initial weight string hung over a Equal to initial weight pulley and the Greater than initial weight system is let go from rest.

 Connection: Why do you think astronauts are “weightless” in outer space?  Newton’s Second Law, the famous “F=ma”, can be seen in action here very well. It is

actually more accurate to write it as “Fnet=ma”, where ‘Fnet’ means the final resulting force after all the acting forces have been added/subtracted together. The ‘m’ stands for the mass of the object, and the ‘a’ stands for acceleration that the object will experience. It is often

more useful to think about this equation as “a=Fnet/m”, which tells us that the acceleration of an object is equal to the net force acting on it divided by its mass.

 If the mass of the object above was kg, try to complete the chart below.

Situation FBD of Object Net Force Acceleration

An object with the same mass of the original object is tied to the opposite end of the string.

An object with double the mass of the original object is tied to the opposite end of the string.

An object with half the mass of the original object is tied to the opposite end of the string.

Nothing is tied to the opposite end of the string.