Forces and Motion Chapter 3

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Forces and Motion Chapter 3
By Mr. Leavings

And just what are we going to LEARN?
Explain the meaning of Force Show how force is required to change the motion of an object Explain and discuss Newton’s three laws, the first dealing with inertia, the second with force, third with equal but opposite reactions Describe how changing the mass of a car affects its acceleration Demonstrate how friction can affect motion Identify action-reaction pairs of forces

Force, Mass and Acceleration
Physics Teacher: "Isaac Newton was sitting under a tree when an apple fell on his head and he discovered gravity. Isn't that wonderful?" Student: "Yes sir, if he had been sitting in class looking at books like us, he wouldn't have discovered anything."

THE LAWS Law Statement In your own words: 1st 2nd
An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion will continue with constant speed and direction, unless acted on by an unbalanced force. Objects keep doing what they are doing unless something intervenes. 2nd The acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. If net force, then acceleration. Heavier objects are harder to move. 3rd Whenever one object exerts a force on another, the second object exerts an equal and opposite force on the first. Action, reaction.

Force, Mass and Acceleration
If I asked you to move a cart containing a large, heavy box, would you: Push it Pull it Yell at it till it went where you wanted Every object continues at a state of rest, or of motion, unless a FORCE is applied to change the system.

Force, Mass and Acceleration
Force: an action that has the ability to change motion. Force is described in two units: Pounds and Newtons (there are Newtons in 1 pound) Newton = 1 kg x m sec2

Newton’s 1st Law An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion will continue with constant speed and direction, unless acted on by an unbalanced force.

Newton’s 1st Law Demo: Ring and the Flask
Challenge: get the object into the flask. Rules: Only touch the hoop. Quickest time wins.

Newton’s 1st Law Force Any action that has the ability to change motion. i.e. a push or pull Forces don’t always change motion Units of force: pounds, newtons 1lb = N

Newton’s 1st Law The Difference Between Force and Mass force: newtons
mass: grams, kilograms Force is a push or pull Mass is the amount of “stuff” in an object. Mass is the same everywhere in the universe, force depends on what is acting on the mass.

Newton’s 1st Law Inertia is the tendency of an object to resist changes in its velocity: whether in motion or motionless. These pumpkins will not move unless acted on by an unbalanced force.

Newton’s 2nd Law Newton's second law relates to the applied force on an object. The acceleration of an object is directly proportional force acting upon it and inversely proportional to the mass of the object.

Newton’s 2nd Law

Newton’s 2nd Law It says that: Force causes acceleration
Mass resists acceleration The acceleration you get is equal to the ratio of force over mass

Newton’s 2nd Law Form of Newton’s second law If you want to know…
And you know…. a = F/m the acceleration (a) the mass (m) and force (F) F = ma the force (F) the mass (m) and the acceleration (a) m = F/a the mass (m) the force (F) and the mass (m)

Newton’s 2nd Law An example:
A car rolls down a ramp and you measure a force of 2 Newtons pulling the car. The car has a mass of 500 g (0.5kg). Calculate the acceleration of the car. What do we Know? M = 0.5 kg F = 2 N A = ?

Newton’s 2nd Law Another example:
An airplane with a mass of 5000 kg needs to accelerate at 5 m/s2 to take off before it reaches the end of its runway. How much force is needed from the engine? What do we Know? M = 5000 kg F = ? A = 5 m/s2

Newton’s 2nd Law Even another example:
An snail slimes along with a force of 0.05 Newtons (N). If its acceleration is 0.1 m/s2, what is the mass of the slug? What do we Know? M = ? F = 0.05 N A = 0.1 m/s2

Balanced and Unbalanced Forces
Net Force: The motion of an object depends on the total of all forces acting on it. To figure out Net Force we have to assign directions for forces to be either positive or negative. Positive Negative

Balanced and Unbalanced Forces
Positive 500 N Negative 10 N The above forces are not in equilibrium and the car moves forward. If the forces were equal the car would not move. Positive 490 N

Balanced and Unbalanced Forces
example: An person is pushing on a car to keep it from moving with a force of 3 N. The car has a mass of 500 kg. The driver steps on the gas causing the car to accelerate at 2 m/s2. What happens? What do we Know? Fn = 3 N Fp = ? M = 500 kg A = 2 m/s2 Positive ? Negative 3 N

Balanced and Unbalanced Forces
Newton’s 2nd Law is really describing the NET FORCE. Acceleration can only happen if the net force is not zero.

Balanced and Unbalanced Forces
Force Diagrams show all the different forces acting on an object. They can also show magnitudes by changing the arrow size, or by including numbers. FN FG

Balanced and Unbalanced Forces
Force of Gravity (FG): Pulls an object straight down Normal Force (FN): Force on an object from support (like a table) that is perpendicular to the support FN FG

Balanced and Unbalanced Forces
Force of Friction (Ff): Force that acts against another force if there is motion. Tension Force (FT): Force acting on an object if it is suspended from something. Applied Force (Fapp): Any force acting on an object other than those already mentioned.

Balanced and Unbalanced Forces
This diagram shows four forces acting upon an object. There aren’t always four forces, For example, there could be one, two, or three forces. FN Ff Fapp FG

Balanced and Unbalanced Forces
A man drags with his daughter inside with a rightward acceleration. Draw a force diagram of the sled. FN Ff Fapp FG

Balanced and Unbalanced Forces
A spider is hanging from its thread in a tree. Draw the force diagram for the spider. The tensile force (FT) of the thread is exerting a force on the spider upwards – this keeps it in place. FT FG

Balanced and Unbalanced Forces
On a flat, horizontal plane, the force of gravity always equals the normal force. FN = 50 N FNet = 0 N FG = 50 N

Balanced and Unbalanced Forces
A cupcake is being pulled along a table with a force of 25 N, and a frictional force of 10 N. What is the overall motion? FN = 50 N Fapp = 25 N Ff = 10 N FG = 50 N No motion up or down. Motion to left.

Weight and Gravity Gravity: a force that pulls every mass toward every other mass. Since Earth is the biggest mass around, gravity pulls everything toward the center of the earth.

Weight and Gravity Gravity depends on mass! Fw < Fw
The force of gravity depends on how much mass you have. If you have more mass, gravity pulls on you with more force. Fw < Fw

Weight and Gravity On earth the force due to gravity is 9.8 Newtons. Notice this number is the same as accel due to gravity fro 1 kg! On Mars that force is adjusted lower since that planet is smaller and the force due to gravity is only 3.8 Newtons. BUT YOUR MASS REMAINS THE SAME!

Weight and Gravity Fw = mg
Weight: force created by gravity on objects. Mass (kg) Fw = mg Weight Force (N) Acceleration due to gravity (9.8 m/s2)

Weight and Gravity Form of Weight equation to use If you want to know…
And you know…. Fw = mg the weight (Fw) the mass (m) and gravity (g) m = Fw/g the mass (m) the weight (Fw) and the gravity (g) g = Fw/m the gravity (g) the weight (Fw) and the mass (m)

Weight and Gravity Lets do an example: around 1587 Galileo dropped two balls from the leaning tower of Pisa to see which would fall faster. Calculate the weight of each ball Calculate the acceleration of each ball’s fall Ball 1: 1kg Ball 2: 5kg Part a) Fw1 = mg = (1kg)(9.8m/s2) Fw1 = 9.8 N Fw2 = mg = (5kg)(9.8m/s2) Fw2 = 49 N Part b) A1 = Fw1/m = (9.8N)/1kg A1 = 9.8 m/s2 A2 = Fw2/m = (49N)/5kg

Weight and Gravity Lets do another example: FN FG
An elephant is sitting in a Zoo (on earth), it has a mass of 5400 kg. What is the Normal force that is acting upon the elephant? FN What do we know? M = 5400kg G = 9.8 m/s2 Fw = ? Fw = (5400kg)x(9.8 m/s2) Fw = 52,920 N FG Fw = Fg = Fn

Law of Universal Gravitation
Why does the Moon orbit the earth? The same gravity that gives you weight is what holds Earth and the Moon together. If you could simply drop the Moon it would fall to earth, this does not happen because the Moon is moving fast in a direction perpendicular to Earth’s gravity. The force of gravity bends the Moons path toward the Earth giving it a nearly circular orbit.

Law of Universal Gravitation
Law of Universal Gravitation: a force of attraction that exists between any two objects that have mass. Mass 2 Mass 1 m1 m2 _________ F = G Force of Gravity d2 Distance between mass 1 and mass 2 Gravitation constant: 6.67 x Nm2/kg2

Law of Universal Gravitation
Example: The mass of Jupiter's third largest moon, Io, is 8.9 x 1022 kg. The radius of Io is 1,815 km. Use the equation for universal gravitation to calculate your weight if you were on the surface of Io and had a mass of 50 kg.

Law of Universal Gravitation
m1 m2 _________ F = G d2 F = (6.67x 10-11Nm2/kg2)(8.9x1022kg)(50kg) ____________________________ (1,815,000m)2 F = 90.1N

Friction What is friction?
Term used to describe forces that result from relative motion between objects (like the wheel and axel of a car) Frictional forces ALWAYS work against the motion that produces them.

Friction Kinds of Friction
Air Friction: The air moving around moving objects creates an opposing force. Sliding Friction: When two surfaces rub against each other, caused by irregularities in the surfaces Viscous Friction: Objects that move in water or other fluids. Rolling Friction: Caused by one object rolling over another, like car tires on a road.

Friction Remember our Net Force diagrams? We have already seen friction in action. Fapp = 25 N Ff = 10 N Fnet = 15 N to the left Sliding Friction!

Momentum Defined p = m v p = momentum m = mass v = velocity

Momentum of a Bus Bus: m = 9000 kg; v = 100 m /s
Calculate the momentum of the bus. What is known? m = 9000 kg v = 100 m/s What is missing? momentum  p = ? Equation p = m·v Solve p = (9000 kg)(100 m/s) = 900,000 kg·m/s

Conservation of Momentum
Momentum in a system is ALWAYS conserved. The total momentum two or more objects have prior to a collision is equal to the total momentum after the collision.

Conservation of Momentum
The total momentum of the objects is the same before and after the collision. Positive is defined as the right direction. before: pT = m1 v1 - m2 v2 v1 v2 m1 m2 m1 v1 - m2 v2 = - m1 va + m2 vb after: pT = - m1 va + m2 vb va vb m1 m2

Directions after a collision
Some collisions cause the objects to go in opposite directions. Other collisions cause the objects to go in similar directions. m1 v1 v2 m2 m1 va vb m2

Elastic vs. Inelastic Elastic collisions occur when the object “bounce” off each other and no energy is lost to changes in shape. Inelastic collision occur when the objects get “stuck” to each other, or energy is lost to changes in shape. m1 v1 v2 m2 m1 vb m2

Sample Problem continued on next slide 35 g 7 kg 700 m/s v = 0
A rifle fires a bullet into a giant slab of butter on a frictionless surface. The bullet penetrates the butter, but while passing through it, the bullet pushes the butter to the left, and the butter pushes the bullet just as hard to the right, slowing the bullet down. If the butter skids off at 4 cm/s after the bullet passes through it, what is the final speed of the bullet? (The mass of the rifle matters not.) 35 g 7 kg 4 cm/s v = ? continued on next slide

Sample Problem (cont.) Let’s choose left to be the + direction & use conservation of momentum, converting all units to meters and kilograms. 35 g 7 kg p before = 7 (0) + (0.035) (700) = 24.5 kg · m /s 700 m/s v = 0 35 g 7 kg p after = 7 (0.04) v = v v = ? 4 cm/s p before = p after = v v = 692 m/s v came out positive. This means we chose the correct direction of the bullet in the “after” picture.

Sample Problem (0.035) (700) = 7.035 v v = 3.48 m/s 35 g 7 kg 700 m/s
Same as the last problem except this time it’s a block of wood rather than butter, and the bullet does not pass all the way through it. How fast do they move together after impact? v kg (0.035) (700) = v v = 3.48 m/s Note: Once again we’re assuming a frictionless surface, otherwise there would be a frictional force on the wood in addition to that of the bullet, and the “system” would have to include the table as well.

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