Chapter 4

Forces in one Dimension

Force

is a push or pull exerted on an object • Can cause objects to speed up • Can cause objects to slow down • Can cause objects to change direction FORCE is a vector quantity; It has both magnitude and direction

A force can change the speed and direction of an object, therefore a force changes an object’s ……..

VELOCITY A change in an object’s velocity is ……..

ACCELERATION Therefore a force causes an acceleration

Force is measured in Newtons N it is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one meter per second squared; kg m/s

2

Types of forces •

Contact Force-

an object from the external world touches the other object (SYSTEM) being studied •

Field Forces-

forces exerted without contact to the system; gravity and magnetism •

Agents

- the cause of the force

When analyzing how a force affects motion of an object it is Important to identify the object (the system) and all the forces acting on it. Book sitting on a table System= Book F table on the book Physics Forces acting on the book external world F earth on book F earth on book F table on the book

Physics Motion diagram Book sitting on a table 1. Draw a diagram of the situation.

2. Circle the system 3. Identify all areas where the system touches the external world- These are the contact forces 4. Identify all the field forces acting on the system

Free Body Diagram similar to the particle model for motion.

1. Represent the object (system) with a dot 2. Represent each force with an arrow that points in the direction the force is applied 3. Try to make each arrow proportional to the magnitude of the force. If unsure of the magnitude make your best estimate 4. All force arrows should point away from the dot even if they are a push Book on table F table on the book F earth on book

Physics How would you describe this motion diagram?

Book is moving to the right Identify the system The book Identify the forces.

Force of table Force of gravity Push or pull on the book Friction

Combining Forces

Suppose you push on a table and exert 100 N of force; you would create an acceleration. If someone else joined you and exerted the same force the acceleration would be twice as much and the resultant force vector would be 200 N

Suppose the other person would push from the other side with a force of 100 N?

The resultant force would be zero, and therefore no acceleration would be created and the table would not move

Suppose one person pushed with a force of 100 N and the other pushed with a force of 50 N in the opposite direction This would result in a net force of 50 N in the direction of the greater force.

Sir Isaac Newton (1642-1727), mathematician and physicist, one of the foremost scientific intellects of all time. Developed Laws explaining motion, force and gravity. Also is credited with the development of Calculus. Actually wrote more on religion and philosophy than science and math.

Newton’s First Law of Motion-

An object at rest tends to remain at rest an object in motion tends to remain in motion in a straight line at a constant speed, if the net force on an the object is zero.

Inertia

tendency of an object to resist change; Newton’s first law is sometimes referred to as the Law of Intertia

Force

Friction Normal Spring Tension Thrust Weight

Common Forces

Symbol Definition

F f F F F F F N sp T thrust g Contact force that opposes sliding between 2 surfaces

Direction

Parallel to surface and opposite the direction of sliding Contact force exerted by a surface on an object Perpendicular to and away from the surface Push or pull a spring exerts on an object The force exerted by a taut rope or cable attached to an object General term used to describe forces that move objects such as rockets, planes, cars etc.

A field force caused by the pull of gravity Opposite the displacement of object at end of spring Away from object and parallel to rope In the same direction as the acceleration Down toward center of Earth

Newton’s 2

nd

Law of Motion 𝐹𝑛𝑒𝑡 = 𝑚𝑎

What net force is required to accelerate a car at a rate of 2 m/s 2 if the car has a mass of 3,000 kg? Fnet=(3000kg)(2 m/s 2 ) = 6000 N

𝑎 = 𝐹𝑛𝑒𝑡 𝑚

What is the acceleration of softball if it has a mass of 0.5 kg and hits the catcher's glove with a force of 25 N? a= 25 N/ .5 kg = 50 m/s 2

𝑚 = 𝐹𝑛𝑒𝑡 𝑎

What is the mass of a falling rock if it produces a force of 147 N? m= 147 N/ 9.8m/s 2 = 15 kg

Weight and Apparent Weight Weight- a measure of the force of gravity on an object; we measure weight in pounds or kilograms, but really it is a force

F

g

=ma F

g

= m(9.8 m/s

2

)

Weight changes when g varies, on or near the surface of the earth g is constant. Therefore if you step on a bathroom scale the scale provides the only upward force and therefore records you weight. F scale

F

g

Apparent weight- is the force an object exerts as a result of all the forces acting on it, giving the object an acceleration Suppose you are standing on a scale in an elevator and the elevator accelerates upward. Would the scale read more , less or equal to when the elevator is standing still?

The scale will read more because the upward force is added to the upward force of the scale

F scale F elevator F gravity

Suppose the elevator cable broke. What would the scale read? The scale would read less and if the person was in free fall it would read zero because both you and the scale would be acceleration at the same rate (-9.8 m/s 2 ) Weightlessness- there is no contact force pushing up on the object and would have an apparent weight of zero.

Drag Force and Terminal Velocity Drag Force force exerted by a fluid (liquid or gas) on the object on the object moving through the fluid; drag force is opposite the motion of the object • Properties of the fluid  Viscosity, temperature • Properties of the object moving through the fluid  Size, shape and mass • Motion of the object- as speed increases so does the magnitude of the drag force. Because the faster it moves the more molecules it is coming into contact with.

If a tennis ball is dropped it starts with an initial velocity of 0 m/s and therefore the drag force is also zero. As the ball falls the velocity increases as does the drag force. Eventually the drag force upwards is going to equal the force of gravity downward and the ball will stop accelerating and will continue to fall at a constant velocity.

Terminal velocity the constant velocity that is reached when the drag force is equal to the force of gravity.

Newton's Third Law

Newton's Third Law is often stated: For every action there is an equal and opposite reaction.

•

For every action there is an equal and opposite reaction.

People associate "action" and "reaction" with "first an action, then a reaction" - as in, first Suzie smacks Johnnie (action) then Johnny says "Mommy! Suzie hit me!" (reaction). That is NOT what is going on here! The action and reaction forces exist at the same time.

• "action...reaction" means that forces always occur in pairs. (Forces are interactions between objects, like conversations are interactions between people.) • The two forces involved are called the "action force" and the "reaction force."

If A pushes B, then B pushes A A pushes B action force B pushes A reaction force Both of these forces are occurring at the same time, They are interacting

http://www.batesville.k12.in.us/physics/phyne t/mechanics/newton3/ActionReaction.html

“For every action there is an equal and opposite reaction.”

“equal" means two things:

• Both forces are exactly the same size. They are equal in magnitude.

• Both forces exist at exactly the same time. They both start at exactly the same instant, and they both stop at exactly the same instant. They are equal in time.

“For every action there is an equal and opposite reaction.” "opposite" means • that the two forces always act in opposite directions - exactly 180 o apart.

Why Don't Action & Reaction Forces Cancel?

"If A pushes B, then B pushes A with an equal and opposite force. If these forces are equal and opposite, they cancel, producing a net force of zero. This means that neither object can accelerate, which means that Newton's Laws predict that nothing can ever move.“`

We know this statement has to be untrue because we know that things do move? WHY IS IT UNTRUE?

Farmer Brown hitches Old Dobbin to his wagon one day, then says, "OK, Old Dobbin, let's go!" Old Dobbin turns to Farmer Brown and says, "Do you remember back in high school, when we took Physics together?

"Yes, I do. We were lab partners in that class, and we had a lot of fun." says Farmer Brown.

"Ah, yes! Those were the good old days, all right!", says Old Dobbin, "You do remember Newton's Three Laws, of course, which tell how all objects move?“ "Yes, I do! I remember that Newton's Laws of Motion are the cornerstone of mechanics. Now, let's get this wagon moving!" "Do you remember how Newton's Third Law says that every action force has an equal and opposite reaction force?", says Old Dobbin, ignoring Farmer Brown's impatience.

"Yes, I do." says Farmer Brown, sensing trouble.

"Newton's Third Law says that if I pull on the wagon, the wagon exerts an equal and opposite force on me. Don't you agree?", asks Old Dobbin.

"Yes... but..." "If these two forces are equal and opposite, they will cancel, so that the net force is zero, right?", argues Dobbin.

"Well, I suppose so," stammers Farmer Brown.

"The net force is always the important thing. If the net force is zero, then Newton's Second Law (and Newton's First Law, too) says that the acceleration of the wagon must be zero."

"Yes, I remember Newton's Second Law very well, Old Dobbin.", says Farmer Brown, hopefully. "This physics discussion is certainly interesting, but let's get going!" "But that's the point!", objects Old Dobbin, "If the wagon's pull is always equal and opposite of my pull, then the net force will always be zero, so the wagon can never move! Since it is at rest, it must always remain at rest! Get over here and unhitch me, since I have just proven that Newton's Laws say that it is impossible for a horse to pull a wagon!" At this point, Farmer Brown throws up his hands in dismay and turns to you. "Please help me!" he says, "I really should have paid more attention in physics class! I know that Newton's Laws are correct, and I know that horses really can pull wagons. There has to be an error in Old Dobbin's argument, but what is it? How can I convince Old Dobbin that if he pulls on the wagon, it will move?"

F old dobbin F wagon F net =0 if net force is zero there is no acceleration and therefore no movement

Only the forces that act on an object can cancel. Forces that act on different objects don't cancel The yellow arrow labeled "wagon" is a force exerted by the wagon on the horse. The blue arrow labeled "horse" is a force exerted by the horse on the ground.

The two forces colored yellow in the diagram are a Newton's Third Law force pair - "horse pulls wagon" and "wagon pulls horse". They are equal in magnitude and opposite in direction.

The two forces colored blue in the diagram are a Newton's Third Law force pair - "horse pushes ground" and "ground pushes horse". They are also equal in magnitude and opposite in direction.

Why does the wagon accelerate?

Newton's 2nd Law says that an object accelerates if there is a net (unbalanced) force on it. Looking at the wagon in the diagram above, you can see that there is just one force exerted on the wagon - the force that the horse exerts on it. The wagon accelerates because the horse pulls on it! If the ground pushes harder on the horse than the wagon pulls, there is a net force in the forward direction, and the horse accelerates forward.

If the wagon pulls harder on the horse than the ground pushes, there is a net force in the backward direction, and the horse accelerates backward. (This wouldn't happen on level ground, but it could happen on a hill...)

HOMEWORK

The Question: "When a rifle shoots a bullet, Newton's Third Law says that the force that the rifle exerts on the bullet is exactly the same size as the force that the bullet exerts on the rifle - yet the bullet gets a much greater acceleration than the rifle. How can this be?"

Tension - the force exerted by a string, rope, chain etc.

F T F g If the bucket is hanging, the bucket is in equilibrium and therefore the tension on the rope is equal to the weight (gravitational pull downward) of the bucket.

When talking about tension we will always assume that the rope is massless.

Therefore the tension on a rope is equal to the weight of all objects hanging below it

Tug-of-war Suppose each side of this tug of war are exerting 500 N of force. What is the tension on the rope?

F right on left = 500 N= F A on rope F left on right = 500 N= F B on rope

A 50.0 kg bucket is being lifted by a rope. The rope will not break if the tension is 525 N or less. The bucket started at rest and after being lifted for 3.0 m it is moving at 3.0 m/s. If the acceleration is constant is the rope in danger of breaking?

F net =F T + (-F g ) F T =F net + F g = ma + mg = m(a + g)

𝑣

𝑓 2

= 𝑣

𝑖 2

+ 2ad