What is gravity? Where does it come from? What kinds of things
have gravity? I have two masses. One is a basketball. The other is
a 5lb bag of potatoes. If I hold them at the same height and drop
them at the same time, which one hits the ground first? Do they
have a constant velocity? Do they have the same gravitational force
acting on them?
Slide 3
What if I use a piece of paper and a book? What happens now?
Why? First http://www.youtube.com/watch?v=oBdalzRJR5g Second
http://www.youtube.com/watch?v=_mCC-68LyZM
Slide 4
Equations!!! Equations in IB look different. Fill in the
following chart based on the given equations.
ConceptVariableUnit
Slide 5
2.1.1 Define displacement, velocity, speed and acceleration.
Distance a scalar quantity of position changed Displacement - a
vector quantity of a change in the position of an object. Speed is
the rate of change of distance with respect to time. (scalar)
Velocity is the rate of change of displacement with respect to
time. (vector quantity) Acceleration is the rate of change of
velocity with respect to time. (vector quantity)
Slide 6
2.1.1 Define displacement, velocity, speed and acceleration. A
mass initially at 0m moves 10m to the right and then 2m to the
left. What is the final displacement? What is the final distance
traveled? A mass initially at 0m, first moves 5m to the right and
then 12m to the left. What is the total distance covered by the
mass and what is the change in displacement?
2.1.1 Define displacement, velocity, speed and acceleration.
Speed is normally given in m/s or km/h. OR ms -1 or kmh -1 What the
difference between speed and Velocity Speed is a scalar, velocity
is a vector.
Slide 9
2.1.1 Define displacement, velocity, speed and acceleration. A
car of length 4.2m travelling in a straight line takes 0.56s to go
past a mark on the road. What is the speed of the car? A car starts
out from the 100km mark in a straight line and moves a distance of
20km towards the right, and then returns to its starting position
1h later. What is the average speed and the average velocity for
this trip?
Slide 10
V = 7.5 m/s Avg speed = 40km/h, avg velocity = 0km/h Starting
point is irrelevant.
Slide 11
2.1.2 Explain the difference between instantaneous and average
values of speed, velocity and acceleration. A car travels 16 km and
takes about 4 hours. What is the cars velocity? Really? Are you
sure? Are you saying that the car traveled at a speed of 4km/h the
entire time?
Slide 12
2.1.2 Explain the difference between instantaneous and average
values of speed, velocity and acceleration. 4km/h is the average
velocity. At any given moment that car could have been moving at
0km/h or even 100km/h. If we look at the velocity at any given
moment in time we would be looking at the INSTANTANEOUS VELOCITY.
Double check your equations. Avg Velocity = Displacement / time
Instantaneous velocity = velocity at given moment. ex. Initial
velocity, final velocity.
Slide 13
Equations
Slide 14
2.1.1 Define displacement, velocity, speed and acceleration. We
mostly look at constant acceleration situations. In this case the
instantaneous acceleration and average acceleration are the same
thing. Acceleration due to gravity is 9.8m/s 2 or 10m/s 2 or
9.81m/s 2. Dont forget about the ball thrown upward. Dont forget
about the variable table!
Slide 15
Acceleration An object starting with an initial velocity of 2
m/s undergoes constant acceleration. After 5s its velocity is found
to be 12m/s. What is the acceleration? A ball is thrown downward
from a 70m tower with an initial velocity of 3m/s. How fast would
it be going after 2 seconds? What would its position be after
2seconds?
Slide 16
Acceleration 2m/s 2 22.6m/s, 44.4m high
Slide 17
2.1.1 Define displacement, velocity, speed and acceleration. A
mass has an initial velocity of 10m/s. It moves with acceleration
-2m/s 2. When will it have a zero velocity? What is the
displacement after 10s of a mass whose initial velocity is 2m/s and
moves with acceleration of 4m/s 2 ? A car has an initial velocity
of 5m/s. When its displacement increases by 20m, its velocity
becomes 7m/s. What is the acceleration? A body has initial velocity
of 4m/s and a velocity of 12m/s after 6s. What is the
displacement?
Slide 18
t = 5s s = 220m a =.6m/s 2 s = 48m
Slide 19
Ready for a challenge! Two balls start out moving to the right
with constant velocities of 5m/s and 4m/s. The slow ball stars
first and the other 4s later. How far from the starting position
are they when they meet? A mass is thrown upwards with an initial
velocity of 30m/s. A second mass is dropped from directly above, a
height of 60m from the first mass, 0.5s later. When do the masses
meet and how high is the point where they meet?
Slide 20
t=20s so s = 80m t=2.35s so s is 42.9m
Slide 21
Exercises (Hamper, Ch2) 1)Convert the following speeds into
m/s. a) A car travelling at 100 km/h b) A runner running at 20 km/h
3)Calculate the final velocity of a body that starts from rest and
accelerates at 5m/s for a distance of 100m. 4)A body starts with a
velocity of 20m/s and accelerates for 200m with an acceleration of
5m/s. What is the final velocity of the body? 5)A body accelerates
at 10m s -2 reaching a final velocity of 20m s -1 in 5s. What was
the initial velocity of the body? 6) A ball is thrown upwards with
a velocity of 30m/s. What is the displacement of the ball after 2s?
7) A ball is dropped. What will its velocity be after falling 65cm?
8) A ball is thrown upwards with a velocity of 20m/s. After how
many seconds will the ball return to its starting point?
Slide 22
Graphing
Slide 23
Cheat Sheet
Slide 24
The slope of d-t graph gives the value of the v-t graph The
slope of v-t graph gives the value of the a-t graph Area under a-t
graph gives the change in velocity Area under v-t graph gives the
change in displacement.
Slide 25
Example
Slide 26
Bell Ringer Sept 4/5 Consider the following graph
Slide 27
Bell Ringer Sept 4/5 What is the initial displacement? What is
the velocity for the first 10s? Second 5s? When is the object at
the origin? What is s? What is the total distance traveled? What is
the avg velocity?
Slide 28
Initial displacement is -10m 2m/s, -2m/s 5s and 15s s = 10m,
total distance = 30m Avg speed = 2m/s, avg velocity =.66m/s
Slide 29
Interpreting graphs A mass starts out from zero with velocity
10m/s and continues moving at this velocity for 5s. The velocity is
then abruptly reversed to -5m/s and the object moves at this
velocity for 10s. For this event find: a) The graph b) The change
in displacement c) The total distance travelled d) The average
speed e) The average velocity
Slide 30
Slide 31
a) See previous slide b) 10 x 5m = 50m, -5 x 10 = -50m, s = 0
The object moved toward the right, stopped and returned to its
starting position. c) 50m to the right, 50m to the left, 100m total
d) Avg velocity =0 e) Avg speed= 100m/15s = 6.7m/s
Slide 32
Use the graph and your understanding of slope calculations to
determine the acceleration of the rocket during the listed time
intervals. t = 0 - 1 s, t = 1 - 4 s, t = 4 - 12 s
Slide 33
a = 40 m s -2 b = 20 m s -2 c = - 20 m s -2
Slide 34
Describe the motion depicted by the following velocity-time
graphs. In your descriptions, make reference to the direction of
motion (+ or - direction), the velocity and acceleration and any
changes in speed (speeding up or slowing down) during the various
time intervals (e.g., intervals A, B, and C).
Slide 35
The object moves in the + direction at a constant speed - zero
acceleration (interval A). The object then continues in the +
direction while slowing down with a negative acceleration (interval
B). Finally, the object moves at a constant speed in the +
direction, slower than before (interval C). The object moves in the
+ direction while slowing down; this involves a negative
acceleration (interval A). It then remains at rest (interval B).
The object then moves in the - direction while speeding up; this
also involves a negative acceleration (interval C). The object
moves in the + direction with a constant velocity and zero
acceleration (interval A). The object then slows down while moving
in the + direction (i.e., it has a negative acceleration) until it
finally reaches a 0 velocity (stops) (interval B). Then the object
moves in the - direction while speeding up; this corresponds to a -
acceleration (interval C)
Slide 36
Consider the velocity-time graph below. Determine the
acceleration (i.e., slope) of the object as portrayed by the
graph.
Slide 37
The acceleration (i.e., slope) is 4 m/s/s. If you think the
slope is 5 m/s/s, then you're making a common mistake. You are
picking one point (probably 5 s, 25 m/s) and dividing y/x. Instead
you must pick two points (as in the discussed in this part of the
lesson) and divide the change in y by the change in x.
Slide 38
Determine the displacement of the object during the time
interval denoted by the shaded area.
A car (A) moves to the left with speed 40km/h (with respect to
the road). Another car (B) moves to the right with speed
60km/h(also with respect to the road). Find the relative velocity
of B with respect to A.
Slide 43
Do pg 46 #4,5, 6, 8, 9, 11, 12
Slide 44
FORCES!!!
Slide 45
Types of forces Gravitational between objects as a result of
their masses. (also called weight) Normal reaction between two
surfaces that are touching Frictional- force that opposes the
relative motion of two surfaces. (Includes Air resistance/drag)
Applied force of an outside object pushing or pulling Tension- when
a string/spring is stretched, it is equal and opposite the force
acting on it. Compression opposite of tension (applies to solid
objects) Upthrust the upward force that acts on objects when it is
submerged in a fluid. Causes objects to float. Lift caused when air
flows over an aircrafts wing. Causes an upward force.
Slide 46
Free Body Diagram Five Steps. 1) Is there gravitational force?
(F g ) 2) Is it sitting on a surface? (F n ) 3) Is there some thing
pushing or pulling? (F app ) 4) Is there friction? (F f ) 5) Is it
accelerating? a = ? http://www.youtube.com/watch?v=BuPfDI7TyL0
Slide 47
Forces are vectors Magnitude and direction Many times the
direction is the x or y This means they can be resolved into
components. This also means they can be added and subtracted.
http://www.youtube.com/watch?v=IrY-FlJ0c7Y
Slide 48
Practice/Application 1. A person is trying to lift a heavy
concrete block without success. The upward force exerted on the
block by the person is P, the contact force on the block by the
floor is C, the weight of the block is W. Which one of the
following is true about the magnitudes of the forces on the block
while the person is trying to lift it? a) P + C =W b) P + C < W
c) P+ C > W d) P = C = W
Slide 49
Practice/Application 2. Consider the vector with a magnitude of
7N acting at an angle of 140 to the horizontal. What will the
horizontal and vertical components of this vector be? 3. An object
O is acted upon by three forces as shown in the diagram. What is
the magnitude of the resultant force acting on O?
Slide 50
Answers 1) Since the person is not succeeding to lift the box,
the weight of the box must be equal to the sum of the upward force
and the floor contact force. Answer: A 2) y= 5.4 x = -4.5 3) The 6N
and 3N forces are acting against each other. This results in a 3N
force to the left. This resulting 3N force left and the 4N upward
force can be resolved using Pythagoras. Answer = 5N
Slide 51
Practice/Application 4) A block of wood of mass 4kg rests on a
slope, inclined at an angle of 25 to the horizontal as shown.
Calculate: a) The weight of the block b) The normal reaction force
of the plane acting on the block. c) The resultant accelerating
force down the slope d) The acceleration of the block down the
slope
Slide 52
Answers 4) There are several a) F g = mg => F g = 40N b) F N
= F g cos => F N = 36.6N c) F R = F g sin => F R = 16.9N d) F
g = mg => a = 4.2m/s 2 5) d
Slide 53
Pg 73 # 1, 2, 4, 6, 7
Slide 54
Equilibrium Occurs when the net force on an object is zero. An
object can move and still be at equilibrium. Neutral
equilibrium(translational) an object is at equilibrium, it is then
moved and then it is still at equilibrium. A displacement results
in another equilibrium position. The net force acting on an object
is zero.
Slide 55
Newtons Three Laws First Law - Inertia An object will remain at
its state of rest or of constant velocity unless acted upon by a
force
Slide 56
Practice 1) For an object to be in translational equilibrium a)
It must be at rest b) it must be moving with constant acceleration
c) No external force must be acting on it d) The net force acting
on it must be zero
Slide 57
2) A rain drop falling through air reaches a terminal velocity
before hitting the ground. At terminal velocity, the frictional
force on the raindrop is a) Zero b) Less than the weight of the
raindrop c) Greater than the weight of the rain drop d) Equal to
the weight of the raindrop
Slide 58
A car is travelling along a level highway at a constant
velocity in a straight line. Air resistance is not negligible. Draw
the free-body diagram for this car.
Slide 59
Newtons Second Law The rate of acceleration of an object is
directly proportional to the applied force and inversely
proportional to its mass. OR. F=ma
Slide 60
Practice 4) A car mass 1100kg accelerates from 10m/s to 30m/s
in 5.5s calculate the cars engine force. 5) A boy on a bicycle,
travelling at 12m/s applies the brakes and comes to rest in a
distance of 16m. If the combined mass of the boy and bicycle is
70kg, calculate the braking force.
Slide 61
6) An elevator of mass 800kg is supported by a thick metal rope
capable of withstanding a tension of 1200N. Calculate the tension
in the rope when the elevator is: a) Not moving, between floors b)
Moving at constant velocity, of 2m/s upward c) Moving at constant
velocity, of 2m/s downwards d) Accelerating upwards at a rate of
3m/s e) Accelerating downwards at a rate of 3m/s
Slide 62
Newtons Third Law
http://www.youtube.com/watch?v=8bTdMmNZm2M&f
eature=edu&list=PL772556F1EFC4D01C When two bodies A and B
interact, the force that A exerts on B is equal to the force that B
exerts on A but acts in the opposite direction.
Slide 63
7) A man pushes a car along a road. He exerts a force F on the
car. In this situation, what is the equal and opposite force to F
as referred to in Newtons third law? 8) Newtons third law
identifies pairs of forces that are equal in magnitude. One of the
forces acting on a bird in flight is the gravitational force W
downward. What is the re-action force?