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F = maF = ma
““The Force”The Force”
““An energy field created by all living An energy field created by all living things. It surrounds us, penetrates things. It surrounds us, penetrates us, and binds the galaxy together.”us, and binds the galaxy together.” The Force has two components:The Force has two components:
Light sideLight side Dark sideDark side
The Real ForceThe Real Force
Something that causes an object’s Something that causes an object’s motion to change (causes motion to change (causes acceleration)acceleration)..
A “push” or a “pull.”A “push” or a “pull.” Common Examples of forces: Gravity Common Examples of forces: Gravity
fields, pushing on something, fields, pushing on something, compressing a spring, a magnetic field, compressing a spring, a magnetic field, tension, friction, and the “normal” force.tension, friction, and the “normal” force.
Units are Newtons (N)Units are Newtons (N)
Which of the following is an Which of the following is an example of a force?example of a force?
a)a) Your weightYour weight
b)b) A magnet pulling on another magnetA magnet pulling on another magnet
c)c) A bully pushing you down the stairsA bully pushing you down the stairs
d)d) A rope pulling a cartful of turnipsA rope pulling a cartful of turnips
e)e) All of the aboveAll of the above
f)f) None of the aboveNone of the above
Types ofTypes of ForcesForces
•Field•Balloon bending Balloon bending stream of waterstream of water•Projectile Projectile MotionMotion•Magnetic fieldsMagnetic fields
ContactContact Me slapping you upside Me slapping you upside
the headthe head Baseball bat on a Baseball bat on a
baseballbaseball
Easily forgotten Forces!!Easily forgotten Forces!!
Important contact force: Important contact force: FRICTION FRICTION Acts in the opposite direction of motionActs in the opposite direction of motion Produces Produces HEATHEAT AIR RESISTANCE is a form of FRICTION!!AIR RESISTANCE is a form of FRICTION!! SLOWS MOTIONSLOWS MOTION Can be desired (tires on road) or Can be desired (tires on road) or
undesired (skates on ice)undesired (skates on ice)
Easily forgotten forces!!Easily forgotten forces!!
Important Important field forcesfield forces: GRAVITY and : GRAVITY and Magnetic FieldsMagnetic Fields Opperate at a distance (don’t need to “touch”)Opperate at a distance (don’t need to “touch”) Decreases with the distance between objects.Decreases with the distance between objects.
WEIGHT is a FORCE caused by gravityWEIGHT is a FORCE caused by gravity FFweightweight = mass x gravity = mass x gravity
As gravity changes, WEIGHT changes, NOT As gravity changes, WEIGHT changes, NOT MASSMASS
As a meteor passes the earth our As a meteor passes the earth our gravity causes its path to bend. gravity causes its path to bend.
Another meteor passes us and its path Another meteor passes us and its path is not bent nearly as much. Which is not bent nearly as much. Which
meteor is closer to the earth?meteor is closer to the earth?
a)a) The first meteorThe first meteor
b)b) The second meteorThe second meteor
c)c) What meteor?What meteor?
d)d) YesYes
So I’m cruising around Belton in my So I’m cruising around Belton in my awesome car when I see a dog in the awesome car when I see a dog in the middle of the road! What is the main middle of the road! What is the main force that lets me stop my car so the force that lets me stop my car so the
doggy can live?doggy can live?
a)a) Gravitational Gravitational ForceForce
b)b) Electric ForceElectric Force
c)c) Frictional ForceFrictional Force
d)d) Magnetic ForceMagnetic Force
e)e) THE ForceTHE Force
Force is a vectorForce is a vector
Has Has magnitudemagnitude and and directiondirection AmountAmount of force makes a difference of force makes a difference
Little push vs. big shoveLittle push vs. big shove Earth gravity vs. moon gravityEarth gravity vs. moon gravity
Direction makes a differenceDirection makes a difference Push vs. PullPush vs. Pull Thrust vs. DragThrust vs. Drag
Forces “add” to give a net force.Forces “add” to give a net force. NetNet force determines what an object will do. force determines what an object will do.
The law of inertia: An object at rest will stay at rest unless acted upon by an outside force.
An object in motion will stay in motion unless acted upon by an outside force.
Galileo’s Unique IdeaGalileo’s Unique Idea
Objects don’t need a force to keep Objects don’t need a force to keep moving!moving! Every object naturally wants to Every object naturally wants to
maintain its statemaintain its state of motion or rest of motion or rest INERTIA! INERTIA! (resistance to change in motion)(resistance to change in motion)
Refined by Newton in 1800’s:Refined by Newton in 1800’s:
Basic Info: InertiaBasic Info: Inertia
Inertia depends on:Inertia depends on: MassMass Shape/Mass Distribution of object- rotational Shape/Mass Distribution of object- rotational
inertiainertia Solid Cylinder (like a wheel of cheese,)Solid Cylinder (like a wheel of cheese,) Hoop (like a bicycle tire)Hoop (like a bicycle tire)
Inertia does NOT depend on:Inertia does NOT depend on: Velocity/Speed of objectVelocity/Speed of object
It takes the same amount of force to speed a bus It takes the same amount of force to speed a bus up as to slow it down!up as to slow it down!
Which of these objects has the Which of these objects has the greatest amount of inertia?greatest amount of inertia?
a)a) A 0.5 mg cockroach.A 0.5 mg cockroach.
b)b) A 2.0 g lump of cheese.A 2.0 g lump of cheese.
c)c) A 35 g ball of goo.A 35 g ball of goo.
d)d) A 15 kg baby goatA 15 kg baby goat
e)e) A 300 kg circus freak on roller A 300 kg circus freak on roller skates.skates.
Net ForceNet Force
Net Income: How much money did Net Income: How much money did you make after you counted up all you make after you counted up all profit and expense?profit and expense?
Net Force: How much force is there Net Force: How much force is there after all individual forces are added after all individual forces are added up?up?
What if…What if…The The netnet force acting on an force acting on an
object is zero?object is zero?a)a) The object will slow to a stop.The object will slow to a stop.
b)b) The object will begin to fall.The object will begin to fall.
c)c) The object’s motion will not change.The object’s motion will not change.
d)d) The universe will open up and swallow The universe will open up and swallow the object.the object.
e)e) Time will stop for us but the object will Time will stop for us but the object will grow old and smelly.grow old and smelly.
Fun StuffFun Stuff
Wear your seatbelt! Fun stuffFun stuff Other one
In other words…
You already know this! the important part is the Σ. This means “Sum” or “Net”
Net ForceNet Force
Net Income: How much money did Net Income: How much money did you make after you counted up all you make after you counted up all profit and expense?profit and expense?
Net Force: How much force is there Net Force: How much force is there after all individual forces are added after all individual forces are added up?up?
MassMass AccelerationAccelerationXX
Typical SituationsTypical Situations
Which is easier to accelerate?Which is easier to accelerate? A tiny sports car? Or a ridiculously A tiny sports car? Or a ridiculously
large and completely unnecessary SUV?large and completely unnecessary SUV?
Your car has stalled in the middle of Your car has stalled in the middle of the road!the road! Easier to push it to the side by yourself? Easier to push it to the side by yourself?
Or with friends? Or with friends?More mass requires more Force!
Don’t Don’t forget the forget the
ForceForce
Causes accelerationsCauses accelerations Gravity leads to: Projectile Motion, and more Gravity leads to: Projectile Motion, and more
projectile motionprojectile motion ““Pushes and Pulls” can also cause Pushes and Pulls” can also cause
accelerations (like this).accelerations (like this). Measured in Measured in NewtonsNewtons (N) (N)
The amount of force that causes a 1 kg mass The amount of force that causes a 1 kg mass to accelerate at 1 m/sto accelerate at 1 m/s22
Always make sure your mass is in Always make sure your mass is in kilograms (kg)!kilograms (kg)!
Force (N) = mass (kg) x acceleration Force (N) = mass (kg) x acceleration (m/s(m/s22))
Calculate the followingCalculate the following
1. What force is required to push your 1,100 kg car with an acceleration of 0.5 m/s2?
Calculate the followingCalculate the following
2. If a 10 N force is applied to an object that causes it to accelerate at 22 m/s2, what is the mass of the object?
Calculate the followingCalculate the following
3. The net force on the propeller of a 3.2 kg model airplane is 7.0 N forward. What is the acceleration of the airplane?
Calculate the followingCalculate the following
4. A force is applied to a 1.5 kg ball that causes it to accelerate from rest to a velocity of 4.5 m/s in 0.5 seconds. What is the magnitude of the force?Remember: Fnet = maand a = (Vf-Vi)/t
Calculate the followingCalculate the following
5. A 12 kg box starts from rest and slides down a frictionless ramp. If the gravitational force pulling it down the ramp is 35 N, what is the final velocity of the box after 3.4 seconds?
GravityGravity“Gravitational Force”“Gravitational Force”
Force which is exerted by any object Force which is exerted by any object with mass.with mass.
Earth’s gravitational force is Earth’s gravitational force is measured as Fmeasured as Fgg = mg, g = = mg, g = 9.8m/s9.8m/s22
Direction is always downDirection is always down Designated FDesignated Fgg
sometimes called weightsometimes called weight
Gravitational ForceGravitational Force
Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation The amount of force is directly The amount of force is directly
proportional to the mass of each of the proportional to the mass of each of the objects.objects.
The gravitational force between two The gravitational force between two objects objects decreasesdecreases as the distance as the distance between them (r) increases! This is an between them (r) increases! This is an inversely proportional relationship!inversely proportional relationship!
Don’t worry, we wont be Don’t worry, we wont be using this equation yet!using this equation yet!
The The amountamount of gravitational force exerted on of gravitational force exerted on an objectan object
1 lb = 4.448 N1 lb = 4.448 N 1 N = 0.225 1 N = 0.225 lb lb
MASSalways the same
(kg)
WEIGHTdepends on gravity
(N)
FW = mgFW (also W or Fg): weight
(N)m: mass (kg)g: acceleration due to
gravity (m/s2)
Weight and mass are two completely different
things!!!
Would you weigh more on Earth Would you weigh more on Earth or Jupiter?or Jupiter?
greater gravitygreater gravity
greater weightgreater weight
greater massgreater mass
Jupiter because...Jupiter because...
WeightWeight Find your weight on different Find your weight on different
planets!planets! First, find your mass in kilograms: take First, find your mass in kilograms: take
your weight and divide it by 2.2 your weight and divide it by 2.2 (because 1 kg weighs 2.2 lbs)(because 1 kg weighs 2.2 lbs)
Now, to find how many Newtons you Now, to find how many Newtons you weigh, take your mass (m) and multiply weigh, take your mass (m) and multiply it by the gravitational acceleration (g). it by the gravitational acceleration (g). Remember: F=ma, or Remember: F=ma, or FFWW = mg = mg
ggearthearth: 9.8 m/s: 9.8 m/s22
ggmoonmoon: 1.67 m/s: 1.67 m/s22
ggmarsmars: 3.7 m/s: 3.7 m/s22
ggsunsun: 274.13 m/s: 274.13 m/s22
ggplutopluto: 0.42m/s: 0.42m/s22
To convert Newtons to Pounds, To convert Newtons to Pounds, remember: remember: 1 lb = 4.448 N1 lb = 4.448 N
What is the weight of a 60 What is the weight of a 60 kg person on earth?kg person on earth?
a)a) 5.8 N5.8 N
b)b) 58 N58 N
c)c) 588 N588 N
d)d) 5880 N5880 N
e)e) 60 kg60 kg
f)f) None of the aboveNone of the above
What is the weight of a 60 kg What is the weight of a 60 kg person on the moon? person on the moon?
(g(gmm= 1.67 m/s= 1.67 m/s22))
a)a) 1 N1 Nb)b) 10 N10 Nc)c) 100 N100 Nd)d) 1000 N1000 Ne)e) 1.67 N1.67 N
Force of NormalForce of Normal The force that a surface exerts on an The force that a surface exerts on an
object.object. Force is always in a direction Force is always in a direction
perpendicular to the surface the object or perpendicular to the surface the object or system is in contact withsystem is in contact with
Usually a balancing force when an object Usually a balancing force when an object is in contact with another objectis in contact with another object
Designated FDesignated FNN or N or N
Force of Normal - Force of Normal - ExampleExample
Let’s say the box in this diagram has Let’s say the box in this diagram has a mass of 25 kg. a mass of 25 kg.
That means it has a weight of 245 N.That means it has a weight of 245 N. Since the ground is level, the Since the ground is level, the
Normal Force is going to be equal to Normal Force is going to be equal to the box’s weight, but the force is the box’s weight, but the force is exerted in a different direction (up).exerted in a different direction (up).
Force of Normal - Force of Normal - Example 2Example 2
That last one was easy! Let’s say this box That last one was easy! Let’s say this box is seated on an incline and still has a mass is seated on an incline and still has a mass of 25 kg.of 25 kg.
The weight of the box (mg) is still directed The weight of the box (mg) is still directed straight down, but the Normal Force is at straight down, but the Normal Force is at an angle, which makes it a little harder to an angle, which makes it a little harder to find…find…
FFNN = wcos = wcosθθ
TensionTension
Force applied by a Force applied by a string or cable string or cable when the object or when the object or system is hangingsystem is hanging
Direction can be Direction can be variablevariable
A force of tension A force of tension is described as Fis described as FTT or T or T
Basic Info: Basic Info: Force Force DiagramsDiagrams
Definition: A Diagram that shows all Definition: A Diagram that shows all the forces acting the forces acting onon a body a body
Does Does NOTNOT include forces exerted include forces exerted byby the body!the body!
Forces are drawn as vectors.Forces are drawn as vectors.
Free Body DiagramFree Body Diagram Simple drawing of all Simple drawing of all
forces working on an forces working on an object or systemobject or system
Use a box to Use a box to represent the object represent the object or systemor system
All forces move away All forces move away from the box.from the box.
Remember: gravity Remember: gravity will always affect an will always affect an object and so Fg will object and so Fg will always be in a F.B.D!always be in a F.B.D!
Diagram the Diagram the forces acting on a forces acting on a car stuck in a car stuck in a traffic jam.traffic jam.
Diagram the Diagram the forces acting on a forces acting on a car driving on IH-car driving on IH-35.35.
Basic Info: Unbalanced Basic Info: Unbalanced ForcesForces
Objects that are NOT in equilibriumObjects that are NOT in equilibrium Will accelerate!Will accelerate!
Objects in equilibrium will not accelerate Objects in equilibrium will not accelerate (inertia)(inertia) Net force required to speed up, slow down, turn, Net force required to speed up, slow down, turn,
etc.etc.
Demos:Demos: Frictionless Track at an angle- Remember Frictionless Track at an angle- Remember
Forces are Vectors and can have 2 Forces are Vectors and can have 2 components!!components!!
Which of these situations shows balanced forces?
Which will accelerate?
A B
C
D: all of them
E: none of them
1.1. As a 1150 kg car is driving on the highway the As a 1150 kg car is driving on the highway the engine is supplying a force of 900 N. The total engine is supplying a force of 900 N. The total force of friction (including air resistance and force of friction (including air resistance and the internal friction of the engine) is 460 N. the internal friction of the engine) is 460 N. What is the net force on the car in the What is the net force on the car in the direction of motion? direction of motion?
3.3. A force of 150 N is applied to a 15 kg wood A force of 150 N is applied to a 15 kg wood block to make it slide across a piece of block to make it slide across a piece of sandpaper.sandpaper.
a)a) What is the force of normal acting on the wood What is the force of normal acting on the wood block?block?
b)b) What is the force of friction acting on the wood What is the force of friction acting on the wood block if the block if the μμ of the sandpaper is 0.995? of the sandpaper is 0.995?
c)c) What is the net force acting on the wood block?What is the net force acting on the wood block?
d)d) What is the acceleration of the block?What is the acceleration of the block?
4.4. A 8 kg block of cheese is sitting on a ramp A 8 kg block of cheese is sitting on a ramp with a 30with a 30oo incline and a µ of 0.745. Draw a incline and a µ of 0.745. Draw a force diagram showing all the forces force diagram showing all the forces acting on the cheese.acting on the cheese.
Formulas!Formulas!
Fnet = maFnet = ma W = mgW = mg FFff = = μμFFNN
FFnetnet = F = FAA – F – Fff
Object on a flat surface:Object on a flat surface: FFNN = Weight = Weight
Object on an incline:Object on an incline: FFNN = Wcos = Wcosθθ
FFAA = Wsin = Wsinθθ
