___________________ p is a vector. Its magnitude :p = _____ Its direction : same as the direction of ____ The plural of momentum is _________________. units of p = [ ] [ ] =  NOT a newton: (1 N = ) p p m v

Ex: Find the momentum of a 7.0-kg bowling ball that is rolling east at 3.0 m/s. p = = 7.0 kg v = 3.0 m/s =

Ex: Give the direction of p in each case below. 1/ ball moving up during free fall 2/ ball falling down during free fall 3/ ball fired up at an angle at the four points shown below: a b c d At which of the four points shown is the magnitude of the momentum the greatest? All p's are ___________ to the ___________ because the ______ are.

1 st idea: p = mv is similar to____________ more mass  more difficult to _____________ 4.0 kg a/ If v = ___ : p = mv = m( ) =____, but it ____________________. 1.0 kg How is p different from inertia? v = b/ Two objects with _____________ inertias can have ____________ momentum. How? 3 Big ideas in momentum:

Important: Each term will be: positive if the object is moving _________________ negative if the object is moving ________________ 2 nd idea: The total momentum p T for a __________ (group) of objects is found by ____________ the p's for each object as vectors (showing ____________): p T = … = + + +

Ex: Find the total momentum for the system of two objects shown below: 5.0 kg 8.0 kg v = 4.0 m/s v = 2.0 m/s Adding as vectors p T = p 1 + p 2 : p T = =

3 rd idea: Collisions and ___________ in p: ____ A. ____________ (“hit and stick”) Collisions v i = 4.0 m/s wall v f =__  p = p f - p i = - = m = 0.5 kg  p = p f – p i = = = OR Ex: _____________ Inelastic Collision:

B. _______________ (“hit and bounce”) Collisions v i = 4.0 m/s wall m = 0.5 kg Ex: ______________ Elastic Collision:  p = p f - p i = - =  p = p f - p i = = = OR v f =

Momentum changes more during ________ collisions because the object must first be ___________ (one change), and then it must be _________________ (an additional change). 1. The magnitude of  p is _______________ when an object bounces. Why? Inelastic: Stopped only Elastic: Stopped and _____________ The momentum goes from: to this: So  p = The momentum goes from: to this:  So  p =

 Why is  p is ______________ in the above two examples? wall Inelastic: Elastic: vivi v f = 0 vivi v f ≠ 0 In both cases,  p is _________ by the _________ of the ________ acting on the _____. This force is ______________, and this makes  p ____________.

C. Most collisions are ___________ “perfectly” inelastic or elastic. The object bounces back, but with ________________ than it had initially: v i = 4.0 m/s wall v f = -2 m/s  These are called ________________ elastic collisions. In these, the ______________ of  p will be somewhere ______________ the values for inelastic and elastic collisions.

A Realistic Impact: A _________ Impact: F net Think of how a baseball bat _________ (comes into contact with) a ball as a function of _________. bat first _________ ball ball _________ the bat t ___________ force of bat on ball Area = _______ F net t

The ________ of and ____________ (time) of impact determine the future __________ of the ball. The quantity _______ is called the _____________ It is a ______________ quantity. magnitude :J = _______ direction : same as the dir. of ______ units of J: [ ] [ ] = _______ (derived) J J t F net

Ex 1: A net force of 25 N to the right acts on a 40-kg snowman for 3.0 s. Calculate the impulse exerted on Frosty. J = = 40 kg F net = 25 N

Ex 2: Give the direction of the impulse for a: A/ ball moving up during free fall B/ ball falling down during free fall C/ ball fired up at an angle at the four points shown below: All J's are ___________ because that is the direction of ___________

 _____________ changes ________________ Newton's Second Law: F net = Rewrite a as  v/t: F net = Multiply both sides by t: F net = But m  v =  p, so write: F net = Since F net t = ____, the last line can be written: == (Historical note: Newton actually first wrote his second law using _____, and not ____.)

[J] = [ ][ ] = [ ] [ ] J = F net t = From this last equation, the _______ of impulse J can be written two ways: This is true because: 1 N·s = 1 ( ) s = 1 If you re-write  p = p f - p i and substitute in, you get: J = F net t = or: [J] = ( ) ( ) = ( ) ( ) = __________   ____________

Ex: An impulse of 24 N·s north is applied to a 0.15-kg baseball initially moving at an initial speed of 40 m/s south. What is the change in momentum of the baseball? Equation: Given: J = m = v = Unknown: Answer:  p = =

Ex: A 0.5-kg ball is moving at 4.0 m/s to the right when it hits a wall. Afterwards, it moves 2.0 m/s to the left. Determine the impulse exerted on the ball by the wall. v i = 4.0 m/s wall v f = -2 m/s m = 0.5 kg

This can be written: J = And can be rearranged to: p f = This says, "J is what you add to ___ to get ___." p i = mv i = (0.5)(4) = 2 kgm/s Before the impulse: Ex. The last example found  p = J = -3 Ns = ___ kgm/s pp ==F net tJ p i = 2 Adding the impulse of -3 Ns Ns from the wall to p i :

The impulse J is ______________ (to the left) in the previous example because _____ from the wall is. The wall in the previous example exerts its force for a time of 0.12 seconds. Calculate the net force that acts on the ball during that time.

The equation: Ft =  p has many applications in sports and collisions…. 1. To ______________ (make the most of)  p, you can:  apply a ____________ F ___t (hit harder)  ____________ the impact time: F___ (follow through)   Both of these help you to take a ball moving in one direction and allow you to send it in another direction with a _____________________ velocity.

2. Suppose 2 identical cars (m=1000 kg), traveling at the same initial v i (30 m/s) both come to rest: a/ Car A hits a _________ wall and stops in 1 s. b/ Car B hits _________ barrels and stops in 4 s.  For both cars:  p = m f v f – m i v i = = A : F t =  p F ____ = -30,000 F = ________ __________ time to stop _________ force of impact Apply Ft =  p to each car to find force on car: B : F t =  p F ____ = -30,000 F = ________ __________ time to stop _________ force of impact

_________________ are a fact of life: 1. In _________ : Hands, feet, heads, bats, rackets, clubs, collide with balls, nets, goals, posts, people, diving boards, etc. _________collide with each other. 2. __________ collide with other cars, buildings, people, bicycles, etc. 3. __________ or parts of atoms collide with other atoms. Light collides with ____________. 4. Planets, stars, and galaxies collide with __________________. Physics uses _____________________ to study collisions because it allows us to ignore the ____________ between the objects, which can be very __________________ during a collision.

 The total ______________ of a system of objects will change if a net ____________ is applied to it: impulse = change in momentum = A collection of objects that _____________ with each other is called a ____________ of objects: _________ forces: SYSTEM

1 2 3 Any ___________ (outside) force exerts _________ force on the system The “system” exerts no force, such as__________ on the “outside” No F net  no ____  no _____  p total _____________________ But what if there is ________ impulse acting on the system? This can only happen if the system is ________________, which means there is no net ____________ acting on it. SYSTEM

= (In ___________) If the “system” consists of 2 objects, this is written: = The Law of Conservation of Linear Momentum : The __________ momentum of an isolated system of objects ____________________. This means that the total p _________ a collision (or an explosion) equals the total p ________ the collision:  the prime symbol: ' represents “_______”

Ex 1: ___________ Collision. A 1.0-kg block and a 2.0-kg block slide on a horizontal frictionless table as shown. 1.0 kg 2.0 kg The "system" consists of _____ blocks. The system is "isolated," b/c there is no ___________. The two blocks collide and ____________ (exert forces on each other). After the collision, they move apart with the velocities shown below: 1.0 kg 2.0 kg

Conservation of momentum says: (Velocities have direction: left is_____________ ) ================== w/units:

Ex 2: ______________ Collision. A 4.0-kg block and a 2.0-kg block slide on a horizontal frictionless table as shown below. 2.0 kg 4.0 kg After they collide, they ________________ and move ________. What is the velocity of the "stuck together" mass? 2.0 kg 4.0 kg  Notice that the final v does not have _______________ 1 or 2, because both masses ________________________ ____________________.

Conservation of momentum says: (The ______________ on _____ are dropped.) The combined mass moves to the ________. ================ w/units:

Ex 3: ___________ /Spring Release. A 3.6-kg mass and a 1.2-kg mass are connected by a spring and __________ on a horizontal frictionless table: When the spring _______________, the 3.6-kg mass moves off to the left at the speed given. Determine the speed of the 1.2-kg mass. 1.2 kg 3.6 kg 1.2 kg 3.6 kg

Conservation of momentum says: Both masses begin at rest  ________ for both. ================== w/units:

In this example: 1. The total momentum of the system _________ the spring is released equals ______ because both masses begin _____________. 2. The total momentum of the system ________ the spring is released equals ______ because of the Law of ___________________ of Linear Momentum. 3. __________ mass receives a greater force b/c of Newton's 3 rd Law: ________ but ____________ forces. 4. The smaller mass moves ___________ because acceleration a = F/m is _____________ proportional to mass, and its mass is _____________.  It has ____ less mass, so it gains ____ more speed.

In sum: ________________, is used in 3 cases: 1. _____________ (bouncing): 2. _______________ (sticking): 3. ____________ /__________ release: total p = ____total p = ___________ v ____________ _______________ mass

Newton’s Law of Universal Gravitation: Two objects of mass m 1 and m 2 separated by a center-to-center distance r ___________ each other with a gravitational force: …where G = ____________________________ is called the _______________ gravitational constant. F g =

Notes: 1. F g is an _________ range, _______________ force. 2. F g is stronger when the objects are__________. 3. The constant G is very __________  F g is the ________________ of the fundamental forces. 4. F g is always ___________________. 5. Both masses pull each other with ____________ magnitude forces, but in _____________ directions. 6. Equation is only true for ____________ masses.  for spheres, you must assume mass is concentrated at __________________  for complicated shapes, _____________ is needed, but equation works ________________ anyway.

Ex. A mass of 1.8 x 10 3 kg (F-150) is 0.50 meter from a mass of 6.0 x 10 1 kg (student). Find the magnitude of the force of gravitational attraction between the two masses. Show all work. F g = Which mass pulls with a greater force? F g =

FgFg m1m1 FgFg m2m2 FgFg r Double m 1  F g ________________ Triple m 2  F g ________________ Double both m 1 and m 2  F g ________________ Triple m 1 and double m 2  F g ________________ Double r  F g ________________ Halve r  F g ________________ Triple r  F g ________________ Double m 1 and r  F g ________________ Double m 1, m 2 and r  F g ________________

Ex: If the F g is between an object of mass m and a planet, then F g is called the _________: F g = ___ F g = Gm 1 m 2 r 2 r = R e = ________________ M e = ________________ F g = m Ex: Earth F g = w = g = = MeMe

The space shuttle orbits at ≈ _______ = __________ above Earth's surface. Its __________ distance from Earth's center is r = _____ + _____ Mm = _______ Mm. = ________ Re So the ___________ (F g ) of the shuttle and all its contents in orbit, compared to its weight on land, is: Ex: Are you weightless in the space shuttle (mass = m s )? R e = ___________ ≈ ___________ Earth F g = GM e m s = =  msms

Ex: r is the ____________________ distance Earth r = 1 R e r = __ R e __ R e above surface __ R e above surface A B C If F g at surface = 200 N, what is the weight (F g ) at A? At B? At C? __ R e above surface r = __ R e

Ex: A 20-N box on a table is lifted from 1 m to 2 m above the floor. Since the height was doubled, the new weight should be w = 20/2 2 = 5 N ?????? 20 N table 1 m 5 N ? 2 m This _________ ______________ because these heights are ______________ from ________ _____________.

Ex: A 600-N volleyball player jumps in the air. What is the force of gravity acting on her… 1/ …while in the air? 2/ …as she is landing? 3/ …when she is again at rest on the ground? 4/ What is her weight in all three cases above?

Ex: d/ What is the reaction force to the weight of the rock in each case? A rock in freefall: Same rock at rest on a table: b/ What is the net force acting on the rock in each case? F g = 1.33 N free fall: F net = ______ on table: F net = ______ c/ What is the acceleration of the rock in each case? free fall: a = ______ on table: a = ______ a/ What is the weight of the rock in each case? F g = 1.33 N

Ex: Cavendish "Weighing the Earth" Experiment: m1m1 thin wire Pb barbells When a ____ sphere (m 2 ) was brought close to the barbells, the _______________ attraction caused the thin wire to _________. Then F g, r, m 2 and m 1 were substituted into: F g = and this was solved to find ______. Once _____ was known, an object of known mass m and weight w were used to find ___________ unknown mass M e using r From the wire's properties, the ______________ needed to make the wire twist that much could be _____________ G m R e 2 w =

One last note: g = F g = Even though g appears in the equation for w, an object does NOT have to be ________________ to use this equation. Think of g as simply a ________________________ between ____ and ____. In fact, g can have ___________________ in different locations, which is why ____________ may change even though _________ remains the same. ________ equation acceleration ____________ = In PhysRT: Not in PhysRT: Solve this for:

A __________ is an idea used to explain how objects can ________________ on each another without touching ("at a _____________" forces) even if separated by a ____________: Examples of fields: 1.__________________ 2. _________________ 3. _________________ object 1 object 2 All fields are _________ because they represent ____________. field of 1 field of 2 the 2 fields ____________ with each other

The force of ______________ is explained by saying that a gravitational ___________ exists around every______________. Here is how it works: 2. To study that field, put a ______ mass m in it, and measure the gravitational ________ F g pulling on it: 1. Suppose there is a _______ somewhere near here (not shown). Because of that mass, there must be a _________________ field all around it.

Then the ____________ (magnitude) of the field g is given by the force _______ mass: units of g: [g] = [ ] / [ ] [g] = And since 1 N = __________, these units can be written: = derived  _________ = __________  fundamental direction of g : ____________________

Ex: A 5.0 kg mass experiences a gravitational force of 30.0 N when placed at the position shown here. Determine the strength (magnitude) and direction of the gravitational field at the point shown. strength: g= = 30 N 5.0 kg direction: Same direction as_____

Ex: What will a 0.10 kg stick of butter weigh when placed in the gravitational field shown? g = = g = 8.2 N/kg g =  same as  g = When F g is due to a planet, we call it _________. So you can write: planet Butterway What is the force of gravity acting on the butter?

> > > > > > > > Ex: To find the shape of the g field around a "point" mass m, use a “test” mass m t. _____ field line in the circle out here _____ field lines in the circle in here m The force arrows are connected into ____________.

Notes: The lines are __________ to the forces. They are “__________________ " that act on a test mass m. 2. Closer lines  _____________ field ________ the mass. Also, the lines ________________ because then one point would have _______________ 3. The arrows show______________ by pointing in towards the mass. We say g is directed _______________________.

As seen from far away, Earth's field is very similar to a __________ mass. The g field lines are ______________ to the surface. ____________ to Earth, the lines don’t spread out as much: surface > > > > > > > > E Coming even closer, ________ spreading surface

g at Earth's surface is ___________ because on the surface you remain the same ___________ from Earth's center (one Earth _____________ ). In fact, g is simply the _________________ due to gravity. Its value is ____________ near Earth's surface. This means that an easy way to find g would be to __________ an object and measure its ____________________ in free fall. Close to the surface, the lines appear __________ spaced and ___________. >> > surface

> > > > > > > > E The field g around Earth (or a point mass) is proportional to ________ because _______ is. g = ( )/m g = ~ At the surface, r = ___, so g = = But at greater r's, g will be _________. ( Note: For any planet, use: g p = ) /m

> > > > > > > > E Ex. g as a function of distance from Earth's center: g = ____ g = ____ /2 2 = _____ g = ____ /3 2 = _____ g = ____ /4 2 = _____ Compare: Big G = ________________________ never changes! g r 1R e 2R e 3R e 4R e R e 2R e 3R e 4R e

In sum: g = the gravitational ____________ = the ________________ due to gravity direction: _____________________________ units of g:derived: ______________ fundamental: ______________ How to find g: 1. Take a mass and weigh it (find F g ):  Calculate: g = = 2. Drop an object and find its _________________. 3. For a planet of mass M p and radius R p :  Calculate: g =

___________ Circular Motion (UCM) occurs when an object moves in a circle at __________________ ____________: circular motion around an axis that is ______________________ ____________ axis _____________ axis ____________: circular motion around an axis that is ______________________ A. The 2 types of "Turning Around:"

B. Two types of Rotational/Revolutionary Speeds: 1. ____________ speed  ("omega")  _________ for all points on a solid object  units: _____________, rpm’s, etc 2.___________ speed v  depends on ______________________ of rotation or revolution  units: _______, mph, etc  v = ______ =_________  In Regents physics, ______________ is the only type of speed we deal with

Ex: Earth rotation axis equator  = _____________ Everywhere on Earth, the __________speed is the same: But _________ speed v = __________ is greatest at the ______________ and zero at the _________. r r NYS latitude Rockets are launched from ____________ because its _________________________________

C. Linear velocity is always ___________ to the circle in the _____________ of motion. Ex: _____________ (CW) uniform circular motion:

Ex: __________________ (CCW) uniform circular motion: In _________ CW and CCW motion: 1. The __________ (_____________ of v) remains constant. 2. The ___________ of v is changing. Because of this, the object must be __________________ NOTICE:

D. The direction of _________________ during UCM From a = _______  a has the same  direction as ____. where Δv = = a is directed towards the circle’s _____________. It is called ___________________ acceleration: a c. It occurs b/c the velocity _______________________.

Ex: Direction of ____ for ____ and ______motion v v v 7 v Notice: Even though a is always ____________________, it is always _____________________ in both cases. The angle between v and a c is always _______ v v v 7 v

E. The _______________ of a c is given by: a c = units of a c = [ ] 2 / [ ] = acac acac v r acac m

F. What causes a ? What causes a c ? The magnitude of F c is given by: F c = = units of F c = = FcFc FcFc v r FcFc m [ ] [ ] 2 / [ ]

1. Although F c is always ______________ _____, it is always towards the __________. This was also true for a c, because force F and the a that it __________ are always ____________________________. G. Direction of ____ for ____ and ______ motion 3 5 v v v 7 v 3 5 v v v 7 v 1 1

2. During UCM, the F c is an _____________ force and F net ___ 0. Remember: _____________ is changing direction (even though __________ is constant), and this is an __________________. 3. Without F c, the object would move off on a ____________ (in the direction of its ___.) 4. F c can be provided by many different forces: ____________ holds planets in elliptical orbits. ____________ keeps cars on road during turns __________________ allows birds to turn in air _________ keeps rock turning in a circle ________________ keeps rider on loop-d-loop ride

Ex: A 1500-kg car moves clockwise in a circle of radius 25 m at a speed of 12 m/s. Calculate a/ the centripetal acceleration of the car; b/ the centripetal force acting on the car. c/ What direction are v, a c and F c when the car is at the point shown? d/ What provides the F c that allows the car to turn? e/ In which direction would the car move if F c became 0? a c = = F c = =