Vectorsand
Linear Motion
Vector Quantities:
Have a magnitude And direction
ex: meters, velocity, acceleration
Scalar Quantities:
Have only a magnitude
ex: temperature, speed, time
Distance
• A length between two points
• Scalar quantity
• Unaffected by direction
Displacement
Distance and direction between 2 positions
Vector quantity
Ex: 5m West
Acceleration
Motion of acceleration
Motion of acceleration
Dimensional Analysis
Dimensional Analysis
Step 1: Multiply by 1
Dimensional Analysis
Step 2: Cancel units
Dimensional Analysis
Step 3: Repeat
Dimensional Analysis
Step 3: Repeat
Dimensional Analysis
Step 4: Solve
Unit 2:
Acceleration and Freefall
Gravity
• Pulls on all objects with the same acceleration (neglecting air resistance)
• Earth’s gravitational field decreases as you travel above Earth’s surface
• g = -9.8m/s2
An object is dropped from an airplane and falls freely for 20s before hitting the ground.
A) How far did the object fall?
B) What was it’s velocity after 20s?
Objects Thrown Straight Up
• For objects launched upward, the time to reach the top of their flight is half the total flight time
• Vy @ top is 0m/s
• a=-9.8m/s2 always
• vi = -vf
A physics student throws a tennis ball into the air. It takes 6s for the tennis ball to land.
A) How high did the tennis ball go?
B) What was it’s initial velocity?
Velocity and Acceleration Graphs
Velocity and Distance Graphs
Distance
Velocity
Projectile Motion
Independence of Dimensions
Vertical and Horizontal motions are treated separately
We calculate one at a time
Use the X-Y chart to show your givens
The X-Y Chart
X Y
a
vi
vf
t
d
Horizontal Values
vi = vf in the x direction
a is always 0m/s2 in the X direction
time is the same as the vertical time
Vertical Values
a is always -9.81 m/s2 in the Y direction
Find time or distance using:
d=vit+(1/2)at2
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
Velocity VectorsVelocity vectors
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
Acceleration Vectors
Acceleration vectors (Notice they don’t change)
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
X Y
a
vf
vi
t
d
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
X Y
a
vf
vi 5
t
d 10
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
X Y
a 0 -9.81
vf 5
vi 5 0
t
d ? 10
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
X Y
a 0 -9.81
vf 5
vi 5 0
t 1.43 1.43
d ? 10
A ball is rolling 5m/s and rolls off of a 10m ledge. How far from the ledge does the ball land?
5 m/s
10 m
X Y
a 0 -9.81
vf 5
vi 5 0
t 1.43 1.43
d 7.15 10
Try this one on your own
A careless driver left a car in neutral near the edge of a 15m high cliff. The car rolled at a velocity of 3m/s as it rolled off the cliff.
A) How long did it take the car to reach the bottom?
B) How far from the cliff did it land?
X Y
a
vf
vi 3
t
d 15
Givens:
X Y
a 0 -9.8
vf 3
vi 3 0
t
d 15
We also know:
X Y
a 0 -9.8
vf 3
vi 3 0
t 1.75 1.75
d 5.25 15
Objects Launched at An Angle
Break the velocity down into x and y components
30°
10m/s10sin(30°)
10cos(30°)
SO
HCA
H TOA
Sin(θ) = Opposite Hypotenuse
Cos(θ) = Adjacent
Hypotenuse
Tan(θ) = Opposite Adjacent
θ
Opposite
Adjacent
Objects Launched at An Angle
Break the velocity down into x and y components
30°
10m/s10sin(30°)
10cos(30°)
Objects Launched at An Angle
Break the velocity down into x and y components
30°
10m/svy = 5m/s
Vx = 8.66m/s
Start filling in your X-Y chart
Solve for one dimension at a time
X Y
a
vf
vi
t
d
X Y
a
vf
vi 8.66 5
t
d
X Y
a 0 -9.81
vf 8.66 -5
vi 8.66 5
t
d
X Y
a 0 -9.81
vf 8.66 -5
vi 8.66 5
t 1.01 1.01
d 8.57 10.05
What happens as θ increases?
10m/s
10°
What happens as θ increases?
10m/s
10°
10m/s sin(10°)
10m/s cos(10°)
What happens as θ increases?
10m/s
10°
1.74 m/s
9.84 m/s
What happens as θ increases?
10m/s
55°
10m/s sin(55°)
10m/s cos(55°)
What happens as θ increases?
10m/s
55°
8.19 m/s
5.74 m/s
Range
Horizontal Distance a projectile travels before landing
For a given velocity, 45° produces the greatest range
Range
Air Resistance
No Air Resistance
Air Resistance
With Air Resistance
No Air Resistance
Forces And Newton’s Laws
A Force is a push or a pull on an object
Units- Newtons (N)
Forces only exist as a result of an interaction
Contact Force- Results from 2 objects touching each other
Field Force- A push or a pull between 2 bodies that aren’t touching.
What field force have we discussed so far in class? Can you think of any others?
FN
Fg
For an object resting on a level surface FN = -Fg
Concurrent Forces
Two or more forces acting on the same object at the same time are considered to be concurrent with each other.
They are sometimes said to be acting concurrently
When you will see the term “Concurrent”:
The magnitude of the resultant of two concurrent forces is a minimum when the angle between them is:
A) 0° B) 45° C) 90° D) 180°
When you will see the term “Concurrent”:
The magnitude of the resultant of two concurrent forces is a minimum when the angle between them is:
A) 0° B) 45° C) 90° D) 180°
Resultant
Forces are vector quantities. They can be expressed and added using arrows just like distance and velocity vectors. We call this sum the resultant
2N + 2N = 4N
Net Force
FNet
Sum or “Net” of all forces acting on an object
FNet = F1 + F2 + F3…Not in reference table
Equilibrium
A state where FNet is 0N
A force that causes equilibrium is called an equilibrant
An equilibrant is equal in magnitude to, but opposite in direction of a resultant (or FNet)
In other words:
What force would we need to cancel out or neutralize the forces we have now?
Components
• We can find the components of forces the same way we found components of velocities and distances
FFy
Fx
Fx = F cos(θ)
Fy = F sin(θ)θ
Free Body Diagrams (FBD’s)
• FBD’s are used to show the forces acting on an object.
• Start with a square and draw all forces originating from the center of the square pointing outward
**Ignore MC questions that show it differently**
What does the FBD look like for an object that weighs 1 N and is being pulled on to the right with a force of 1N, but being held still by a force of friction of 1N?
2 N
1 N 2 N
1 N
Find FNet:
2 N
1 N 2 N
1 N
Step 1:Find Fy and Fx:
1 N
1 N
1 N
1 N
FNet
Step 2: Add your vertical and horizontal vectors
1 N
1 N
1 N
1 N
1.4N
Step 3: Solve
1 N
1 N
1 N
1 N1.4N
Newton’s First Law
“An object at rest will stay at rest and an object in motion will stay in motion unless acted on by an unbalanced force.”
Inertia- The resistance of an object to a change in motion
Inertia is directly proportional to mass
Which Object Has More Inertia?
Which Object Has More Inertia?
A B
20 m/s Right10 m/s Right
Newton’s Second Law
• The acceleration of an object is directly proportional to the net force acting on it and indirectly proportional to it’s mass.
Think of it this way:• Bigger forces cause bigger accelerations
• Bigger masses cause smaller accelerations
Newton’s Second Law
• You can express Newton’s 2nd Law as an equation:
Mass vs Weight
• Mass- Amount of matter in an object– Units- kg– Unchanged by gravitational field
• Weight- Force of pull on an object caused by gravity– Units- N– Depends on gravitational field strength
Weight (Fg)
• Always directed towards Earth (down)
• Force of Gravity
• Fg = mg g=Fg/m Units: m/s2 = N / Kg
• g = 9.8m/s2
Newton’s Third Law
“For every action there is an equal and opposite reaction”
If a person weighing 700N is standing in an elevator that’s accelerating up, what force does the elevator apply on the person?
Fg
FNet =
a = + 2 m/s2
m = 70kg
FN=
Ff = µFN
Solve this equation for µ and predict what you think the units for µ will be
µ = Ff / FN
µ is unit-less
Inclined planes
• We will call this force FII
FN
Fg
FII
Inclined planes
• FII is a component of the object’s weight along
with F˔FN
Fg FII
F˔
Calculating FII and F˔Sin(θ) = FII / Fg FII = Fg sin(θ)
Cos(θ) = F˔ / Fg F˔ = Fgcos(θ)
What do FII and F˔ mean?
F˔ has the same magnitude as the normal force
FN
F˔θ
What do FII and F˔ mean?FII is the component of the weight that is parallel to the plane
FII
θ
FII = -Ff when FNet = 0N
FII
θ
Ff