Prepared by Dedra Demaree, Georgetown University

Prepared by Dedra Demaree, Georgetown University
Newtonian Mechanics Prepared by Dedra Demaree, Georgetown University © 2014 Pearson Education, Inc.

Newtonian Mechanics Why do seat belts and air bags save lives?
If you stand on a bathroom scale in a moving elevator, does its reading change? Can a parachutist survive a fall if the parachute does not open? © 2014 Pearson Education, Inc.

Be sure you know how to: Draw a motion diagram for a moving object (Section 1.2) Determine the direction of acceleration using a motion diagram (Section 1.6) Add vectors graphically and by components for one-dimensional motion (Section 1.2 and Appendix B) Last chapter: learned to describe motion This chapter: learn why an object has a particular acceleration © 2014 Pearson Education, Inc.

2.1 Describing and representing interactions
© 2014 Pearson Education, Inc.

Describing and representing interactions
Objects can interact directly, when they touch each other—for example, in a push or a pull. Objects can interact at a distance—for example, when a magnet attracts or repels another magnet without touching it. © 2014 Pearson Education, Inc.

Choosing a system to describe interactions
We choose one particular object for analysis; this object is called the system. All objects not part of the system can interact with it (touch it, pull it, and push it) and are in the system's environment. Interactions between the system object and objects in the environment are called external interactions. External interactions can affect the motion of the system. © 2014 Pearson Education, Inc.

Using a system when sketching a process
Make a light boundary (a closed dashed line) around the system object to emphasize the system choice. Any parts of an object that are inside the system can have internal interactions. We will model an object such as a car as point-like and ignore internal interactions. © 2014 Pearson Education, Inc.

Choosing a system to describe interactions (Cont'd)

Representing interactions
Make a light boundary (a closed dashed line) around the system object to emphasize the system choice. Draw an arrow to represent interactions between the system and the environment, such as the arrow in the figure showing the hands pushing upward on each ball. © 2014 Pearson Education, Inc.

Force Force is a vector quantity that characterizes how hard (magnitude) and in which direction an external object pushes or pulls on the system object. The symbol for force has subscripts identifying the external object that exerts the force and the system object on which the force is exerted. The SI unit for force is the newton (N). © 2014 Pearson Education, Inc.

What Do Forces Do? As the block starts to move, in order to keep the pulling force constant you must move your hand in just the right way to keep the length of the rubber band—and thus the force—constant. © 2015 Pearson Education, Inc.

Force Body Diagrams (FBD)
Used with the point-like model The system object is represented by a dot. Arrows used to represent the forces Length of the arrow relates to the strength of the force. Direction the arrow points relates to the direction in which the force is exerted on the system object. Includes forces exerted on the system object Shows the forces at a single instant © 2014 Pearson Education, Inc.

Free Body Diagrams A free body diagram is a drawing that is used in order to show all the forces acting on an object. Drawing free body diagrams can help when trying to solve for unknown forces or determining the acceleration of the object.

Drawing force body diagrams (FBD)
Sketch the situation. Circle the system. Identify external interactions. Place a dot at the side of the sketch representing the system object. Draw force arrows to represent the external interactions. Label the forces with a subscript containing two elements. © 2014 Pearson Education, Inc.

Constructing force diagrams
Example: a rock sinking into sand © 2014 Pearson Education, Inc.

Free Body Diagrams 1. Draw and label a dot to represent  the box. See, you don't even have to be able to draw a stick figure to do free body diagrams. 2. Draw an arrow from the dot  pointing in the direction of one of the  forces that is acting on that object.  Label that arrow with the name of the  force. 3. Repeat for every force that is acting  on the object. Try to draw each of the  arrows to roughly the same scale,  bigger forces getting bigger arrows. Fg Fg FN Fapplied

6. Repeat this process for every object in your sketch. Fg FN
Free Body Diagrams 4. Once you have finished your free body diagram, recheck it to make sure that you have drawn and labeled an arrow for every force. This is no time to forget a force. 5. Draw a separate arrow next to your free body diagram indicating the likely direction of the acceleration of the object. This will help you use your free body diagram effectively. 6. Repeat this process for every  object in your sketch. Fg FN Fapplied a Remember - the acceleration found does NOT tell you which way the object is moving - it only tells you how the velocity is changing!

Short Catalog of Forces
Types of Forces Short Catalog of Forces

Forces Commonly imagined as a push or pull on some object
Vector quantity May be a contact force or a field force Contact forces result from physical contact between two objects Field forces act between disconnected objects

Fundamental Forces Types Characteristics Strong nuclear force
Electromagnetic force Weak nuclear force Gravity Characteristics All field forces Listed in order of decreasing strength Only gravity and electromagnetic in mechanics Section 4.1

Weight The gravitational pull of the earth on an object on or near the surface of the earth is called weight. The agent for the weight forces is the entire earth. An object’s weight vector always points vertically downward, no matter how the object is moving.

Weight and Mass Mass is measured in kilograms and weight is measured in Newtons because it is a force. Labled: Weight or W or Fg 𝑜𝑟 𝑚𝑔 Does the value of the mass or the weight of an object change depending on where it is?

Spring Force Springs come in in many forms. When deflected, they push or pull with a spring force.

Normal Force The force exerted on an object that is pressing against a surface is in a direction perpendicular to the surface. The normal force is the force exerted by a surface (the agent) against an object that is pressing against the surface.

Microscopic Model Springy Atomic Model for Solids
Consider a solid object to be made of atoms Connected by bonds that are like springs. We can now understand how the table knows how much to push back. When the an object (in this case a book) is placed on the table it only feels its weight so it starts to accelerate downward. This deforms the table bringing upward spring forces into play. The table deforms until the forces are enough to cancel the weight.

Normal Force The normal force is responsible for the “solidness” of solids. The symbol for the normal force is I will also write as Fn Perpendicular touching forces are called normal forces. Normal forces are not always vertical.

Tension Force When a string or rope or wire pulls on an object, it exerts a contact force that we call the tension force. The direction of the tension force is always in the direction of the string or rope.

Ropes provide tension (a pull)
In physics we often use a “massless” rope with opposing tensions of equal magnitude

Friction Friction, like the normal force, is exerted by a surface.
The frictional force is always parallel to the surface. Kinetic friction, denoted by , acts as an object slides across a surface. Kinetic friction is a force that always “opposes the motion.” Static friction, denoted by , is the force that keeps an object “stuck” on a surface and prevents its motion relative to the surface. Static friction points in the direction necessary to prevent motion. © 2015 Pearson Education, Inc.

Drag The force of a fluid (like air or water) on a moving object is called drag. Like kinetic friction, drag points opposite the direction of motion. You can neglect air resistance in all problems unless a problem explicitly asks you to include it. © 2015 Pearson Education, Inc.

Thrust Thrust is a force that occurs when a jet or rocket engine expels gas molecules at high speed. Thrust is a force opposite the direction in which the exhaust gas is expelled. © 2015 Pearson Education, Inc.

Electric and Magnetic Forces
Electricity and magnetism, like gravity, exert long-range forces. The forces of electricity and magnetism act on charged particles. These forces—and the forces inside the nucleus—won’t be important for the dynamics problems we consider in the next several chapters. © 2015 Pearson Education, Inc.

2.2 Adding and Measuring Forces

Adding forces graphically
Draw the vectors head to tail. Draw the vector that goes from the tail of the first vector to the head of the second vector. This is the sum vector, also called the resultant vector. In this case this vector is the net force (it is not a new force, but rather the combined effect of all the forces being exerted on the object). © 2014 Pearson Education, Inc.

Adding forces graphically (Cont'd)

Example: Lifting a suitcase
The upward force you exert on the suitcase is larger than the downward force Earth exerts on the suitcase. The net effect is a 50-N force pointed straight up. © 2014 Pearson Education, Inc.

Adding forces graphically (Cont'd)
If several object in the environment exert forces on the system object. Use vector addition to find the sum Σ of the forces exerted on the object © 2014 Pearson Education, Inc.

Draw FBD for these exercise

Measuring force magnitudes
Force is a vector quantity with both magnitude and direction. One method to measure an unknown force is to calibrate a spring in terms of some standard force. This calibrated spring can then be used to measure other forces. A spring scale is the simplest instrument to measure forces. © 2014 Pearson Education, Inc.

Measuring force magnitudes (Cont'd)

Physics language: Force
Force is a physical quantity characterizing an interaction between two objects. Always identify the two interacting objects. Force includes both the magnitude and the direction of the interaction. The word "force" in physics is more precisely defined than how we use it in everyday life. The definition of "force" in physics has also been refined through history. © 2014 Pearson Education, Inc.

Draw FBD…do not forget about the Normal Force

2.3 Conceptual Relationship between force and motion

Conceptual Relationship between force and motion
Question: Is there a relationship between the forces that are exerted on an object and the way the object moves? Lets take a look © 2014 Pearson Education, Inc.

Patterns observed in the experiments

Observational experiments for a bowling ball rolling on a very hard, smooth surface
In all experiments, the vertical forces add to zero and cancel. We consider only forces exerted in the horizontal direction. In the first experiment, the sum of the forces exerted on the ball is zero. The ball's velocity remains constant. When the ruler pushes the ball, the velocity change arrow points in the same direction as the sum of the forces. © 2014 Pearson Education, Inc.

Adding and Measuring Forces
Each of the experiments the ∆ 𝑣 arrow for the systems object and the sum of the forces Σ 𝐹 that external objects exert on that object are in same direction © 2014 Pearson Education, Inc.

Testing the relationship between the sum of forces and the motion of the system object

Relating forces and motion
What have we learned so far Δ 𝑣 always points in the same direction of the sum of forces Σ 𝐹 exerted on it We know from chapter 1 that the 𝑎 points in the same direction as the Δ 𝑣 . Thus we can say the ∆ 𝑣 arrow for the systems object and the sum of the forces Σ 𝐹 that external objects exert on that object are in same direction © 2014 Pearson Education, Inc.

Relating forces and motion
if the Σ 𝐹 is 0. the object continues with no change in velocity (is the velocity 0 or constant?) If Δ 𝑣 point in the same direction of the Σ 𝐹 the object speeds up (accelerates) If Δ 𝑣 point in the opposite direction of the Σ 𝐹 objects slows down (or accelerates in the opposite direction of the motion)

2.4 Reasoning without mathematical equations

Think about the options you have for Δ 𝑣 =_____

Reasoning without mathematical equations
Motion and force diagrams and the rule relating motion and force can be used to reason qualitatively about physical processes: To determine the relative magnitudes of forces if you have information about motion To estimate velocity changes if you have information about forces © 2014 Pearson Education, Inc.

2.5 Inertial reference frame and Newtons First Law

Inertial reference frame
Here the saying goes again: Again, Description of motion depends om the observers reference frame. So far in this chapter we have only talked about the observer standing on the Earth’s surface Determined that forces when all the sum of all Σ 𝐹 =0 the object moves at constant velocity or is stopped. © 2014 Pearson Education, Inc.

An inertial reference frame is one in which an observer: Sees that the velocity of the system object does not change if no other objects exert forces on it or Sees no change in the velocity if the sum of all forces exerted on the system object is zero In non-inertial reference frames, the velocity of the system object can change even though the sum of forces exerted on it is zero. © 2014 Pearson Education, Inc.

A passenger in a car or train that is speeding up or slowing down with respect to Earth is an observer in a non-inertial reference frame. When you are in a car that stops abruptly, your body jerks forward, yet nothing is pushing you forward. Observers in non-inertial reference frames cannot explain the changes in velocity of objects by considering the forces exerted on them by other objects. © 2014 Pearson Education, Inc.

Newton's First Law of Motion
For an observer in an inertial reference frame, the object continues moving at constant velocity (including remaining at rest): When no other objects exert forces on an system object or When the forces exerted on the object add to zero Inertia is the phenomenon in which an object continues to move at constant velocity when the sum of the forces exerted on it by other objects is zero. © 2014 Pearson Education, Inc.

Inertia Is the tendency of an object to continue in its original motion In the absence of a force Thought experiment Hit a golf ball Hit a bowling ball with the same force The golf ball will travel farther Both resist changes in their motion Think of mass as the unit of inertia….

Newtons 2nd Law So far we have learned about the relationship between Σ 𝐹 and Δ 𝑣 Δ 𝑣 and 𝑎 are related because they point in the same direction Now we need to figure out an equation so we can determine the 𝑎 of an object knowing Σ 𝐹 the exerted on it. © 2014 Pearson Education, Inc.

Newton's Second Law Of Motion
Observation experiments help us construct the following relationship between the sum of forces on a system object and the system object's motion: The symbol α means "is proportional to." For example, if the sum of the forces doubles, then the acceleration doubles. So is there another physical quantity that effects acceleration © 2014 Pearson Education, Inc.

What is easier to pull a bus or a small block of wood?
What is the physical quantity that seperate the wood from the bus? © 2014 Pearson Education, Inc.

The property of an object that affects its acceleration is called mass
From the pattern of the experiment we see that the greater amount of matter pulled the smaller the acceleration when the same amount of force is applied. The property of an object that affects its acceleration is called mass © 2014 Pearson Education, Inc.

Mass (another physical quantity)
Mass is a measure of the amount of matter. Mass is represented by the symbol m. To measure mass quantitatively, you first define a standard unit of mass. The SI standard unit of mass is the kilogram (kg). The kilogram standard is a cylinder made of a platinum-iridium alloy stored in a museum of measurements near Paris. © 2014 Pearson Education, Inc.

Mass Mass characterizes the amount of matter in an object.
When the same unbalanced force is exerted on two objects, the object with greater mass has a smaller acceleration. Mass is a scalar quantity, and masses add as scalars. MASS IS AN INHERENT PROPERTY OF AN OBJECT Mass and weight are different quantities; weight is usually the magnitude of a gravitational (non-contact) force. © 2014 Pearson Education, Inc.

Newton's second law of motion
Observation experiments help us construct the following relationship for the proportionality between the acceleration of a system object and the system object's mass: |a| m © 2014 Pearson Education, Inc.

Newton's second law of motion
Combining the results of our observational experiment findings, we have: Force is a ubiquitous quantity so it has a unit defined for it called a newton (N). Newton is about equivalent to the force generated by gravity (9.8 m/s2by a 0.1kg object. (Put the weight in your hand how does it feel) It feels like a 1 Newton!!!!!. About a 50KiloNewton required to break bone. A force of 1 newton (1 N) will cause an object with a mass of 1 kg to accelerate at 1 m/s2. About G (1 G equals 9.8m/s2) will cause a concussion. With an 80 kg person that about 78400N. It’s the acceleration that cause the force that cause concussions!!! 20% of all HS football players will get a concussion in a 3-4 year playing time.

Making sense of Newton's second law
The equation we deduced for Newton's second law is: If the mass is infinitely large, the acceleration is zero. If the mass is zero, the acceleration is infinitely large. Both of these extreme cases make sense. © 2014 Pearson Education, Inc.

Acceleration Formulas
Newtons 2nd law is called the cause and affect relationship Called the dynamics method 𝑎 = Δ 𝑣 Δ𝑡 is called the operational definition of acceleration. It tells us the quantity of acceleration but does not tell us WHY. This is the kinematics method © 2014 Pearson Education, Inc.

Force components used for forces along one axis
Our equation for Newton's second law can be written in vector component form. For example, in the x-direction we have: Identify the positive direction of the axis. Find the components of all the forces being exerted on the system. Forces that point in the positive direction have a positive component; forces that point in the negative direction have a negative component. © 2014 Pearson Education, Inc.

2.7 Gravitational Force Law

Gravitational force law (little g definition)
Objects falling in a vacuum (for instance, a tube with the air removed) show that all objects fall straight down with the same acceleration. This acceleration has a magnitude of 9.8 m/s2. Earth (E) exerts the only force on the falling object (O) (in a vacuum). FE on Oy = mOaOy = mO(9.8 m/s2) We define g such that: © 2014 Pearson Education, Inc.

Gravitational force law (little g definition)
Lots of names for little g Free Fall acceration Gravitational acceleration Gravitational constant Why is it the same for all objects? Force being applied by the Earth changes to accomadate the mass of an object so that a always equals g. Increase the Mass of an object by 10 the FEonO also increases by 10 so that g remains constant. © 2014 Pearson Education, Inc.

The trap is that the net force does NOT tell you how the object is moving - that is, it does not give you any information about its velocity or displacement. It only tells you the object's acceleration - its change in velocity. An object may be moving at 300 km/s, with zero external force on it, so it has zero acceleration - which just means it keeps a constant velocity of 300 km/s. ΣF =ma

2.8 Skills for applying Newtons 2nd Law for 1D processes

Skills for applying Newton's second law for one-dimensional processes
Sketch and translate. Sketch the process, choose the system object and coordinate system, and label the sketch with everything you know about the situation. © 2014 Pearson Education, Inc.

Weight The weight of the object on a planet is the force that the planet exerts on the object. In everyday language, the normal force that a scale exerts on you (which balances the downward force you exert on it) is your weight. We will not use the term "weight of an object" because it implies that weight is a property of the object rather than an interaction between two objects. Labeled as Weight/ W /Fg /mg More on weight later!!! © 2014 Pearson Education, Inc.

Elevator Problems Scales: What do they read!!!
TAKE NOTES: I am putting this on the board © 2014 Pearson Education, Inc.

Couple of Vocabulary Terms
Apparent Weight: The equation for measuring apparent weight is F = mg + ma. Its what a scale reads (Total Normal Force). No acceleration your weight will equal your weight… Acceleration… Fn = mg + ma=scale weight We use Elevator Problems to discuss Apparent Weight, the concept of weightlessness, and Free Fall © 2014 Pearson Education, Inc.

Apparent Weight The weight of an object is the force of gravity on that object. Your sensation of weight is due to contact forces supporting you. Let’s define your apparent weight wapp in terms of the force you feel: Apparent Weight is defined as Fn © 2015 Pearson Education, Inc.

Apparent Weight The only forces acting on the man are the upward normal force of the floor and the downward weight force: n = w + ma wapp = w + ma Thus wapp > w and the man feels heavier than normal. © 2015 Pearson Education, Inc.

Weightlessness: is simply a sensation experienced by an individual when there are no external objects touching one's body and exerting a push or pull upon it. Weightless sensations exist when all contact forces are removed. These sensations are common to any situation in which you are momentarily (or perpetually) in a state of free fall Weightlessness is only a sensation; it is not a reality corresponding to an individual who has lost weight. As you are free falling on a roller coaster ride (or other amusement park ride), you have not momentarily lost your weight. Weightlessness has very little to do with weight and mostly to do with the presence or absence of contact forces. © 2014 Pearson Education, Inc.

Freefall when your acceleration (a = -g) When in free fall, the only force acting upon your body is the force of gravity - a non-contact force. Since the force of gravity cannot be felt without any other opposing forces, you would have no sensation of it. You would feel weightless when in a state of free fall. © 2014 Pearson Education, Inc.

Weightlessness A person in free fall has zero apparent weight.
“Weightless” does not mean “no weight.” An object that is weightless has no apparent weight. © 2015 Pearson Education, Inc.

Equation Jeopardy Problems

2.9 Forces Come In Pairs Newtons 3rd Law

Forces come in pairs Suppose you wear rollerblades and push abruptly on a wheeled cart loaded with a heavy box. If you and the cart are on a hard smooth floor, the cart starts moving away (it accelerates), and you also start to move and accelerate in the opposite direction. You exerted a force on the cart and the cart exerted a force on you. Because the accelerations were in opposite directions, the forces must point in opposite directions. © 2014 Pearson Education, Inc.

Testing experiment: Newton's third law of motion
Attach one spring scale to a hook on the wall and pull on its other end with a second spring scale. If the hypothesis is correct, then the scale you pull should have the same reading as the scale fixed to the wall. You find that the scales have the same readings. If you reverse the scales and repeat the experiment, you find they always have the same readings. © 2014 Pearson Education, Inc.

Newton's third law of motion
When two objects interact, object 1 exerts a force on object 2. Object 2 in turn exerts an equal-magnitude, oppositely directed force on object 1. These forces are exerted on different objects and cannot be added to find the sum of the forces exerted on one object. © 2014 Pearson Education, Inc.

Tips for Newton's third law of motion
The forces in Newton's third law are exerted on two different objects. This means that the two forces will never appear on the same force diagram. Also, they should not be added together to find the sum of the forces. You have to choose the system object and consider only the forces exerted on it! © 2014 Pearson Education, Inc.

3rd Law Conceptual Questions

Push me and I push back! For example, with the palm of your hand, push on a book, desk or table. You are exerting a force on the object you are pushing. At the same time, you can feel a force on your hand. There seems to be two forces: the one your hand exerted on the object, and another force on your hand. What is the relationship between these forces? ANSWER: THEY ARE EQUAL IN MAGNETUDE AND OPPOSITEDLY DIRECTED! This is true whether or not a big object is pushing a smaller object or whether the objects are stationary or moving. WHEN EVER TWO OBJECTS TOUCH THEY HAVE TO FOLLOW THIS SIMPLE RULE!

The man weighs 700 N. The force exerted by the table on the man is:
a) Larger than 700 N b) Equal to 700 N c) Smaller than 700 N d) There is no force. ANSWER: EXACTLY 700 N

A hand pushes on a balloon against a wall with a force of 10 N
A hand pushes on a balloon against a wall with a force of 10 N. The force exerted by the balloon on the hand is: a) Larger than 10 N b) Equal to 10 N c) Smaller than 10 N d) There is no force. ANSWER Exactly 10 Newton’s

A building is being torn down. The wrecking ball smashes through a wall. Does the ball put a larger force on the wall than the wall puts on the wrecking ball? Explain your answer. THE BALL AND THE WALL EXPERIENCE THE SAME EXACT FORCE… HOWEVER the EFFECT OF THE FORCE ON EACH OBJECT RESULTS IN A DIFFERENCE IN ACCELERATION. WHY? THE INDIVIDUAL BRICKS IN THE WALL HAVE A MUCH SMALLER MASS so the ACCELERATION (Resulting effect) is greater than the resulting ACCELERATION (Change in motion) of the Ball which has a much GREATER MASS (or Inertia). THE FORCES ARE EQUAL but the EFFECT of the FORCES on specific object can BE (Often times are) Different!

Imagine that you hold the two force probes, one probe in each hand
Imagine that you hold the two force probes, one probe in each hand. You will notice that each force probe has a hook on it. Connect the two force probes together and pull as seen in the following figure. You can experimentally do this by connecting your fingers together with somebody else. Try having them pull on you with out pulling back. What happens if somebody doesn’t resist the effort force of pulling?

Runners and Rockets In order for you to walk, the floor needs to have friction so that your foot sticks to the floor as you straighten your leg, moving your body forward. The friction that prevents slipping is static friction. The static friction has to point in the forward direction to prevent your foot from slipping. © 2015 Pearson Education, Inc.

Exercise Newton’s Third Law
A fly is deformed by hitting the windshield of a speeding bus.  v The force exerted by the bus on the fly is, B. equal to that exerted by the fly on the bus.

Exercise 2 Newton’s Third Law
Same scenario but now we examine the accelerations A fly is deformed by hitting the windshield of a speeding bus.  v The magnitude of the acceleration, due to this collision, of the bus is greater than equal to less than that of the fly.

Exercise 3 Newton’s 3rd Law
Two blocks are being pushed by a finger on a horizontal frictionless floor. How many action-reaction force pairs are present in this exercise? a b 2 4 6 Something else

a b 6 Exercise 3 Solution: Fa,f Ff,a Fb,a Fa,b FE,a Fa,E FE,b Fb,E
Fg,a Fa,g Fg,b Fb,g 6

Normal Force and Weight
FN mg The Normal Force, FN, is always perpendicular to the surface that is creating it. Weight, mg, is always directed downward. We know where the weight force comes from - but what is the origin of the Normal Force?

The Normal Force is a consequence of Newton's Third Law and is due to the electrons in the table repelling the electrons in the box - which results in an upward, Normal Force. We discuss electron interactions in more detail in AP 2 course FN mg The box is being pulled down by gravity (mg), and the Normal Force is pushing up on the box. Is this a Newton's Third Law action-reaction pair of forces?

FN mg FN Fbox on table Fbox on earth mg No! The Normal force and the gravitational force, mg, both act on the box. Action reaction force pairs act on different objects. The Normal force and the force that the box exerts on the table is an action reaction pair. The force that the earths' gravity (mg) exerts on the box is an action reaction pair with the gravitational force that the box exerts on the earth.

FN mg If the table is not accelerating in the y direction and the box is not moving up and down on the table, then FN = mg.

But, if the table is in an elevator and is accelerating upwards, then we have: The Normal Force is greater than the weight. If the box was replaced with a person, the person would feel heavier than their typical weight. FN mg a Thus we have another name for the Normal Force - it is also called the Apparent Weight.

Extra Stuff Friction Apparent Weight Elevator Problems

15 A 42.3 kg object rests on a table. What is the Normal force exerted by the table on the object? Use g = 10.0 m/s2. [This object is a pull tab] Answer

16 A 42.3 kg object rests on a table. The table is placed in an elevator and accelerates upwards at 1.55 m/s2. What is the Normal force (Apparent Weight) exerted by the table on the object? Use g = 10.0 m/s2.

Tension Force FT a mg When a cord or rope pulls on an object, it is said to be under tension, and the force it exerts on the object is called a tension force, T or FT. Are the forces shown on the diagram to the right an action reaction pair?

Tension Force FT a mg No, they are not an action reaction pair. The Tension force and mg are both operating on the pail. Action reaction pairs operate on different objects. If the hand is pulling the pail up with a constant velocity, what is the relationship between FT and mg?

Tension Force FT a mg They are equal. If the pail is moving  with a constant velocity, then ay = 0.

It's now time to do that. Look at the box
Friction When we first discussed Newton's First Law, the concept of friction as a force that opposes motion was introduced without any mathematical details, or even qualitative discussion. It's now time to do that. Look at the box to the right. You're pulling the box with an applied Force, Fapp. Is it harder to get the box moving or keep it moving? What happens if you increase the mass of the box? Fapp v What happens if you pull the box over a surface of ice, compared to a surface of sandpaper?

The more massive the box - the more Fapp
Friction You probably found it harder to get the box moving - once moving, it needed less Fapp to keep it moving. The more massive the box - the more Fapp was required to start it moving and to keep it moving. And, it is much easier to pull a box over an icy surface versus over sandpaper - a smaller Fapp is needed. So, the friction force appears to depend on whether the object was at rest or moving, its mass and the surface it was moving on. Fapp v

Friction We'll first address the issue of the difference in Fapp required to overcome the friction of a stationary object and a moving object by distinguishing between two types of friction - static and kinetic. Static friction force is the force that works to prevent the motion of  a stationary object. Kinetic friction force is the force that acts opposite to the motion of a moving object.

In both Static and Kinetic friction, it is harder to move a more massive object - so there is a dependence on the Normal force - the force that the surface is exerting on the stationary or moving object. Also - both types of friction depend on the type of material that the object and the surface are made of. This is represented by the coefficient of static friction (μs) and the coefficient of kinetic friction (μk). These coefficients have been measured for many material interfaces. Friction It is interesting to note that the contact area between the object and surface does not affect the friction force.

Mass and Weight One More Time

Mass and Weight Mass and weight are not the same thing.
Mass is a quantity that describes an object’s inertia, its tendency to resist being accelerated. Weight is the gravitational force exerted on an object by a planet: w = –mg © 2015 Pearson Education, Inc.

Example: Apparent weight in an elevator
Anjay’s mass is 70 kg. He is standing on a scale in an elevator that is moving at 5.0 m/s. As the elevator stops, the scale reads 750 N. Before it stopped, was the elevator moving up or down? How long did the elevator take to come to rest? The scale reading as the elevator comes to rest, 750 N, is Anjay’s apparent weight. Anjay’s actual weight is w = mg = (70 kg)(9.80 m/s2) = 686 N © 2015 Pearson Education, Inc.

Example: Apparent weight in an elevator (cont.)
The vertical component of Newton’s second law for Anjay’s motion is Fy = n  w = may n is the normal force, which is the scale force on Anjay, 750 N. w is his weight, 686 N. We can thus solve for ay: © 2015 Pearson Education, Inc.

The acceleration is positive and so is directed upward, exactly as we assumed—a good check on our work. The elevator is slowing down, but the acceleration is directed upward. This means that the elevator was moving downward, with a negative velocity, before it stopped. © 2015 Pearson Education, Inc.

To find the stopping time, we can use the kinematic equation (vy)f = (vy)i + ay Δt The elevator is initially moving downward, so (vy)i =  5.0 m/s, and it then comes to a halt, so (vy)f = 0. We know the acceleration, so the time interval is © 2015 Pearson Education, Inc.

Couple of Thoughtful Force Questions!!!!

Question 1 An object, when pushed with a net force F, has an acceleration of 2 m/s2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be ½ m/s2 1 m/s2 2 m/s2 4 m/s2 Answer: B © 2015 Pearson Education, Inc.

Question 1 An object, when pushed with a net force F, has an acceleration of 2 m/s2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be ½ m/s2 1 m/s2 2 m/s2 4 m/s2 © 2015 Pearson Education, Inc.

Question 2 A 40-car train travels along a straight track at 40 mph. A skier speeds up as she skis downhill. On which is the net force greater? The train The skier The net force is the same on both. There’s not enough information to tell. Answer: B © 2015 Pearson Education, Inc.

Question 2 A 40-car train travels along a straight track at 40 mph. A skier speeds up as she skis downhill. On which is the net force greater? The train The skier The net force is the same on both. There’s not enough information to tell. © 2015 Pearson Education, Inc.

Question 3 An object on a rope is lowered at constant speed. Which is true? The rope tension is greater than the object’s weight. The rope tension equals the object’s weight. The rope tension is less than the object’s weight. The rope tension can’t be compared to the object’s weight. Answer: B © 2015 Pearson Education, Inc.

Question 3 An object on a rope is lowered at constant speed. Which is true? The rope tension is greater than the object’s weight. The rope tension equals the object’s weight. The rope tension is less than the object’s weight. The rope tension can’t be compared to the object’s weight. Constant velocity Zero acceleration © 2015 Pearson Education, Inc.

Question 4 An object on a rope is lowered at a steadily decreasing speed. Which is true? The rope tension is greater than the object’s weight. The rope tension equals the object’s weight. The rope tension is less than the object’s weight. The rope tension can’t be compared to the object’s weight. Answer: A © 2015 Pearson Education, Inc.

Question 4 An object on a rope is lowered at a steadily decreasing speed. Which is true? The rope tension is greater than the object’s weight. The rope tension equals the object’s weight. The rope tension is less than the object’s weight. The rope tension can’t be compared to the object’s weight. Decreasing downward velocity Acceleration vector points up points up © 2015 Pearson Education, Inc.

Question 5 A 4.0 kg object is pulled along a frictionless surface to the right by a 6.0 N force. How long does it take the object to travel a distance of 25.0 m assuming the object starts at rest? Draw the illustration and include the arrows. The top arrow is showing the boxes acceleration direction. You can use kinematics or dynamics equations to solve this example.

Solution To Question 5 Use F=ma to find acceleration.
6 Newtons = a*4kg or 1.5 m/s2 then use the acceleration in the equation x= 1 2 𝑎 𝑡 2 and solve for time. 25 = 1 2 (1.5 𝑥 𝑡 2 )

Question 7 An 85.0 kg person stands on a scale that reads weight in Newtons while standing in an elevator. What is the reading on the scale when (a) The elevator is stopped? (b) The elevator is accelerating upward at 3.5 m/s2? Elevator Stopped…. Forces are balanced Therefore weight would be 85 kg x 9.8 m/s or approximately 850 Newton's Note the Weight down would equal the normal force supplied by the spring scale. Hence if the elevator is stopped the reading would be exactly equal to the persons weight. See part B on next slide

Question 7 Normal Up is larger than the weight down. Hence the scale reading would be Greater than if it was not accelerating at all. Answer for part b is newton's With the elevator accelerating upward the force supplied as the Normal which would be the reading that the scale would show would be a combination of the acceleration due to gravity and the acceleration of the elevator upward m/s2 and 3.5 m/s2… this is 13.3 m/s2 and you would have to multiple this time the mass of the person riding the elevator. The Scale would read Newtons

Question 9 An 85.0 kg person stands on a scale that reads weight in Newtons while standing in an elevator. What is the reading on the scale when the elevator is moving upward at a constant speed of 5.0 m/s? Add Color to the question words Constant speed… then re-ask the question again by saying “WHAT DOES A CONSTANT SPEED IMPLY?” The answer is balanced force… Therefore the weight would be the same as if the object was stationary. The weight would be approximately 850 Newtons

Prepared by Dedra Demaree, Georgetown University

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Prepared by Dedra Demaree, Georgetown University

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