11/12 do now – on a new sheet
• Sketch a set of graphs that relate the variables shown on
the axes for an object that is thrown off a building
horizontally.
Due today - Extra credit
Homework - Due Monday: Another Angle on F-m-a packet
Due Monday
Project (projectile simulator)
Packet (Projectile Motion) correction
Packet (Regents Physics Projectile Practice) corrections
Homework is posted on google classroom - code: nsdnlt
Forces in Two Dimensions - Objectives
know the procedures of
–
–
Addition of Forces
Resolution of Forces
Understand the conditions of
–
Equilibrium and Static
Be able to determine
–
–
The individual force acting on an object in
equilibrium
If equilibrium is achieved in a system
Force Vector review
•
magnitude
Force is a vector quantity, it has ____________
and
direction
___________.
•
The vector sum of all forces acting on an object is
known as _____________.
Net Force
•
m∙a
According to Newton’s 2nd Law: Fnet = ________
Adding forces
Graphical method
• Two ways to add vectors are ____________
Mathematical method
and _______________.
Head-tail or tail-tail (parallelogram)
• Graphical method: _____________________.
• Mathematical method (only if the vectors are
perpendicular to each other)
c 2 = a 2 + b2
– To determine magnitude, we use _____________.
SOH CAH TOA
– To determine direction, we use ______________.
Resolving Force Finding components
•
To determine the magnitudes of the
components of a force , we use ____________
the trig. functions.
y
A∙cosθ
Ax = _______________

A
Ay
θ
Ax
A∙sinθ
Ay = _______________
x
Equilibrium and Static
• When all the forces that act upon an object are
balanced, then the object is said to be in a state of
equilibrium.
_______________
0
0
∑F = ___,
a = ____
• An object at equilibrium is either ...
– at rest and staying at rest - "static equilibrium.”
– in motion and continuing in motion with the same
speed and direction – “dynamic equilibrium”
Force at an angle
• When ever you see a force at an angle acting on
an object, you must resolve it into its x and y
components. Then you can compare all the x
components and all the y components to
determine if an object is in equilibrium or
accelerating.
Example - determine If a system is in equilibrium
• Forces A, B, C acting on a point. Determine if they
produce equilibrium.
To determine if a system is in
equilibrium is to check if ∑F = 0
A=5N
36.9o
B=4N
x
C=3N
1. Resolve A into x and y components.
2. Compare all x components and compare all y
components. If ∑Fx = 0 and ∑Fy = 0, then the system
is in equilibrium.
Example – determine individual force
in an equilibrium
• When a sign is hung at equilibrium symmetrically, the downward
pull of gravity must be balanced by the upward pull of the wires.
The tension in each wire must be the same. The vertical component
of the tension in each wire must support half the weight of the
frame.
∑Fx = 0
What is the weight of the frame?
∑F = 0
y
The weight of the
frame is 50 N
In conclusion
• A vector is quantity which has _____________ and
______________.
• Two ways to add vectors are ______________ and
________________________.
• Vector resolution is use trigonometric functions to resolve a vector
into ________________________.
• Equilibrium is the state of an object in which all the forces acting
upon it are _____________. In such cases, the net force is ____
Newton. Knowing the forces acting upon an object, trigonometric
functions can be utilized to determine the _______________ and
______________ components of each force. At equilibrium, all the
vertical components must _______________ and all the horizontal
components must _________________.
Net Force Problems Revisited
• A force directed an angle can be resolved into two
components - a horizontal and a vertical component.
•
•
To determine Net Force, add all the forces by components,
then use Pythagorean Theorem to solve for the magnitude
and tangent function to determine direction
The acceleration of an object can be determined by using
Newton's second law.
Example - Determine the net force and
acceleration
Object moves in horizontal direction
Fnet = 69.9 N, right
m = (Fgrav / g) = 20 kg
a = (69.9 N) / (20 kg) =3.50 m/s/s, right
Example - Determine the net force and
acceleration
Object moves in horizontal direction
Fnet = 30.7 N, right
a = 1.23 m/s/s, right.
Procedures for adding vectors at an angle
with horizontal
1.
2.
3.
4.
5.
6.
7.
Resolve the vectors at an angle into x and y
components.
Add all the x components together
Add all the y components together
Use Pythagorean Theorem to find the resultant
(hypotenuse)
Resultant2 = x2 + y2
Use trigonometric function to determine the
direction: tanθ = opp / adj
Use Newton’s 2nd Law to determine acceleration.
Practice 1
A block of 10 kg mass is pushed
along a frictionless, horizontal
surface with a force of 100 N at an
angle of 30° above horizontal.
FN
FAY
FA
30˚
This applied force (FA)
o) = 87 N
FAxcan
= 100cos(30
be broken
into
F =COMPONENTS
100sin(30o) = 50 N
Ay
X verticalYforce must
The total
be 0, so
FAY
RyFAX
= FN + FAY
–Fg = 0
FN = Fg F–g FAY
FN
FAX
Fg
Total =R
FAX
= Rx Total
= Fax= 0
Acceleration depends only on
FAX
Lab – shoot for your grade
NAMES, DATE, TITLE
PURPOSE
How far will a horizontally launched ball land?
MATERIALS launcher, meter stick, target paper
PROCEDURE
• Write a paragraph to describe how the lab is done so that
anyone reading your procedure can duplicate this lab.
• Include the following with your paragraph:
– Draw a diagram of your experiment
– List quantity you need to measure and the tools you use to
make the measurement. Indicate these quantities in your
diagram
– State equations you need to use to solve for the impact point
distance velocity
11/13 do now
• Sketch a set of graphs that relate the variables shown on
the axes for an object that is launched at an angle.
Homework -aDue
Monday: AnothervAngle
on F-m-a packet
x
x
Due Monday
t
t
Project (projectile simulator)
Packet (Projectile Motion) correction
Packet (Regents
Physics Projectile
vy Practice) corrections
ay
Due Tuesday
t
t
Packet (worksheet 1.2.3)
Homework is posted on google classroom - code: nsdnlt
Practice 2
• A man pulls a 40 kilogram crate across a
smooth, frictionless floor with a force of 20 N
that is 45˚ above horizontal.
What is the net force on the sled?
How could the
Fnetacceleration
= FA cos θ be increased?
Fnet = (20
N)(cos
45°) F greater and
Pushing at a smaller
angle
will make
net
Fnetincrease
= 14.14acceleration.
N
therefore
What is the crate’s acceleration?
a = Fnet / m
a = (14.14 N) / (40 kg)
a = 0.35 m/s2
Pushing on an Angle
A block is pushed along a
frictionless, horizontal surface with a
force of 100 newtons at an angle of
30° below horizontal.
FAX
FAY
The total verticalg force must
N
be 0, Fso
= FgTotal
+ FAY
Total F
=N
FAX
=0
-30˚
FA
Fg
FAX
F
FN
FAY
This applied force (FA)
canXbe broken
Y into
COMPONENTS
Acceleration depends only on
FAX
Practice 3
• A girl pushes a 30 kilogram lawnmower
with a force of 15 N at an angle of 60˚
below horizontal.
Assuming there is no friction, what is the
acceleration of the lawnmower?
Fnet = FA cos θ
Fnet = (15 N)(cos 60°)
Fnet = 7.5 N
a = Fnet / m
a = (7.5 N) / (30 kg)
a = 0.25 m/s2
What could she do to reduce her acceleration?
Push at an greater angle
Practice 4
Practice 5
• A student moves a box of books by attaching a rope to the box
and pulling with a force of 90.0 N at an angle of 30.0 degrees.
The box of books has a mass of 20.0 kg, and the coefficient of
kinetic friction between the bottom of the box and the
sidewalk is 0.50. find the acceleration of the box.
determine the net force and acceleration
Fnet2 = (∑Fx)2 + (∑Fy)2
Fnet = 39 N
θ = tan-1(-23/32) = -36o
θ = 324o CCW
a = Fnet / m = 39 N / 5 kg = 8.0 m/s2,
same direction as the force
11/16 do now
Due
today:
• A
projectile passes through points A and B as
Project
(projectile
simulator)
it follows
the path
shown below.
Packet (Projectile Motion) correction
Packet (Regents Physics Projectile Practice) corrections
Due tomorrow
Another Angle on F-m-a packet
Due Wednesday
1. Compared to the horizontal speed at point A in the projectile’s
Worksheet packet 2.1.2B packet
path, the horizontal speed at point B is (greater, smaller, the same)
Due Friday
2. Compared to the vertical speed at point A in the projectile’s path,
Projectile test correction
the vertical speed at point B is (greater, smaller, the same)
worksheet 1.2.3 correction
3.
Compared is
to posted
the acceleration
at point
A in the-projectile’s
path,
Homework
on google
classroom
code: nsdnlt
the acceleration at point B is (greater, smaller, the same)
Inclined Planes
• Objects accelerate down inclined planes because of an
unbalanced force. The unbalanced force is caused by gravity.
• Note: the normal force is not directed in
the direction that we are accustomed to.
The normal forces are always directed
perpendicular to the surface that the
object is on.
Fg on Inclined Plane
An important idea
• The process of analyzing the forces acting upon objects on
inclined planes will involve resolving the weight vector (Fgrav)
into two perpendicular components.
• The perpendicular component of the force of gravity is directed
opposite the normal force and as such balances the normal force.
• The parallel component of the force of gravity is part of the net
force that is responsible to object’s motion along the incline.
Forces on an Incline Calculations
• Consider forces:
– Perpendicular
• F┴ = Fg cos θ
• Cancel out Normal (FN )
θ
– Parallel
• F// = Fg sin θ
• All the parallel components
(including the friction force)
add together to yield the net
force. Which should directed
along the incline.
Tilt you head method
θ
Essential Knowledge
• What happens to the component of weight that is
perpendicular to the plane as the angle is increased?
Decreases – Fg perpendicular
• What happens to the component of weight that points
ALONG the plane as the angle is increased?
Increases – Fg parallel
• What happens to the normal force as the angle is
increased?
Decreases – depends on Fg perpendicular
• What happens to the friction force as the angle is
increased?
Decreases – depends on normal force
Example
Fg = 50N
30°
• What is the magnitude of the normal force?
FN = Fg perpendicular = Fg cos θ = 43.3 N
• If the box is sliding with a constant velocity,
what is the magnitude of the friction force?
Ff = Fg parallel = Fg sin θ = 25 N
Example 1
• The free-body diagram shows the forces acting upon a 100-kg
crate that is sliding down an inclined plane. The plane is inclined
at an angle of 30 degrees. The coefficient of friction between the
crate and the incline is 0.3. Determine the net force and
acceleration of the crate.
Fg┴ = Fgrav∙cos30o = 850 N
Fg// = Fgrav∙sin30o = 500 N
In perpendicular direction:
Fnorm = F┴ = 850 N
In parallel direction:
Fnet = F// - Ff
Fnet = 500 N - µFnorm
Fnet = 235 N
a = Fnet / m = 2.35 m/s2
Example
practice
1.
An 8.0-newton block is accelerating down a frictionless ramp inclined at
15° to the horizontal, as shown in the diagram below. What is the
magnitude of the net force causing the block’s acceleration?
2.
A child pulls a wagon at a constant velocity along a level sidewalk. The
child does this by applying a 22-newton force to the wagon handle, which
is inclined at 35° to the sidewalk as shown below. What is the magnitude
of the force of friction on the wagon?
3.
The diagram below shows a 1.0 × 105-newton truck at rest on a hill that
makes an angle of 8.0° with the horizontal. What is the component of the
truck’s weight parallel to the hill?
4.
A block weighing 10.0 newtons is on a ramp inclined at 30.0° to the
horizontal. A 3.0-newton force of friction, Ff , acts on the block as it is
pulled up the ramp at constant velocity with force F, which is parallel to
the ramp, as shown in the diagram below. What is the magnitude of force
F?
5.
a.
b.
A force of 60. newtons is applied to a rope to pull a sled across a horizontal
surface at a constant velocity. The rope is at an angle of 30. degrees above the
horizontal.
Determine the magnitude of the frictional force acting on the sled.
Calculate the magnitude of the component of the 60.-newton force that is
parallel to the horizontal surface.
6. The diagram below represents a block at rest on an incline. Draw arrows to
indicate the directions of friction force (Ff), normal force (FN), and gravity (Fg)
7. The diagram shows a sled and rider sliding down a snowcovered hill that makes an angle of 30.° with the horizontal.
Draw an arrow from the center of the rider to indicate the
direction of normal force.
8. A book weighing 20. newtons slides at a constant velocity down a ramp
inclined at 30.° to the horizontal as shown in the diagram below. What
is the force of friction between the book and the ramp?
11/17 do now
• A box with mass m is at rest on an rough plane
inclined at angle θ with horizontal.
1. Draw a free body diagram on the box.
In terms of m, g and θ
2. Determine Fg┴ and Fg//
3. Determine FN
4. Determine Ff
5. Determine Fnet
objective
Review
Finish Lab
• Due today:
– Another Angle on F-m-a packet
• Due tomorrow
– worksheet 2.1.2B – Forces on Angles Packet
– Castle Learning Test – Due tomorrow night
• Due Friday
– Projectile Projectile test correction
– Project: projectile simulator correction
– Worksheet 1.2.3 ground launched projectile packet correction
• Homework is posted on google classroom - code: nsdnlt
11/7 do now
1. A ball is projected horizontally with an initial
velocity of 20. meters per second east, off a cliff
100. meters high. How many seconds does the ball
take to reach the ground? [Neglect air resistance.]
2. The diagram below shows a 4.0-kilogram object
accelerating at 10. meters per second2 on a rough
horizontal surface. What is the magnitude of the
frictional force Ff acting on the object?
11/16 do now
Due today:
Fg =Angle
60N on F-m-a packet
Another
Project (projectile simulator) 30°
Packet (Projectile Motion) correction
Packet (Regents Physics Projectile Practice) corrections
• What
is the magnitude of the normal force?
Due
tomorrow
Packet
1.2.3)
FN =(worksheet
Fg perpendicular
= Fg cos θ = 52 N
Homework is posted on google classroom - code: nsdnlt
• If the box is sliding with a constant velocity,
what is the magnitude of the friction force?
Ff = Fg parallel = Fg sin θ = 30N