1. HONORS PHYSICS
Good morning! Please…
• Take out your homework, to be checked
• Answer the warm-up question:
• A baseball is thrown straight down from a building that is 65 meters tall. Its
initial velocity is 3.0 m/s. What will its velocity be right before it hits the
ground?

2. AGENDA:
1. Physics in the News!
2. Finish projectile motion activity
3. Review
4. Review activities
NOTE: Midterm is Wednesday 9:45-11:45
- Bring a book or work to do if you finish the midterm early
• LAST DAY FOR HOT TASK/MIDTERM WILL BE WEDNESDAY.
• **Cheat sheet update***

3. MIDTERM TOPICS
Topics Suggested Study Techniques
1. Conversion, measurement, precision, • Look over all old tests & know how to
accuracy do every problem
2. One-dimensional motion: constant • Go over your notes from each unit –
speed be familiar with concepts
3. One-dimensional motion: accelerated • Re-do problems from the homework &
motion problems from the review sheet
4. Free-fall motion Format:
5. Vectors • 30 multiple choice
6. Projectile motion • 14 problems with multiple parts
7. Forces & Newton’s laws

4. 1. CONVERSION, MEASUREMENT, PRECISION,
ACCURACY
• Using factor label method to convert numbers
• What are some examples of SI units used in physics? English units?
• What are the significant figures for the following two numbers:
• 0.02003 54300
• What is precision? What is accuracy?
• How to convert between metric units
• Know kilo- to milli-

5. 2 & 3. ONE-DIMENSIONAL MOTION: CONSTANT
SPEED & ACCELERATION
• Graphing motion
• Identifying the information given on an x vs. t, v vs. t, a vs. t graph
• Slope of the lines on the graphs
• Area under the curve
• Solving problems using one-dimensional motion equations

6. 2. ONE-DIMENSIONAL MOTION: CONSTANT
SPEED
• Graphing motion

7. 4. FREE-FALL MOTION
• The acceleration of an object in free-fall
• Using motion equations to solve free-fall problems:
• An object dropped from rest
• An object dropped with an initial velocity
• An object thrown straight up in the air that comes back down.

8. 4. FREE-FALL MOTION
• Sample problem: a ball is thrown straight up into the air at 12.0 m/s.
• What is the velocity of the ball at its maximum height? What is its acceleration at
maximum height?
7.4 m
• What is the maximum height that the ball will reach?
• What will be the velocity of the ball after 2.0 seconds? -7.6 m/s

9. 5. VECTORS
• Difference between scalar and vector quantities
• What are some examples of each?
• Breaking vector into its components
• Solving for resultant vectors by adding or subtracting two vectors

10. 6. PROJECTILE MOTION
• Concepts behind projectile motion
• Projectile motion is anything that has an initial horizontal velocity that is under the
influence of free-fall
• X & y dimensions of motion are completely independent of one another
• What happens in the x-direction?
• What happens in the y-direction?
• What is range? At what angle does any object have maximum range?
• Problems with initial horizontal velocity
• Problems with projectiles launched at an angle.

11. 7. FORCES
• Newton’s laws and how they apply in various situations
• What is Newton’s first law? Second law? Third?
• Drawing free-body diagram
• Problems with friction on an inclined plane
• Problems with friction on a level surface
• Problems with a force applied at an angle
• Calculating coefficients of kinetic and static friction.

12. 7. FORCES
• A student moves a box of books down the hall by pulling on a rope attached to the box.
The student pulls with a force of 185 N at an angle of 25.0 degrees above the horizontal.
The box has a mass of 35.0 kg and the coefficient of friction between the box and floor is
0.27. Find the acceleration of the box.
-1.2 m/s2

13. 7. FORCES
• What is the net force on each object?
FN = 10 N
Ff = 3 N Fa = 5 N
Mg = 10 N
FN = 10 N FN = 10 N
Ff = 3 N Fa = 1 N Ff = 3 N Fa = 3 N
Mg = 10 N Mg = 10 N

14. HOT TASK
• What does the normal force do?
4.0 kg
• How can we find the normal in both
situations shown?
15o
15o

15. NEWTON’S ACTIVITIES
• When a constant force is applied to something, should the speed increase? Should it stay
the same?
• Use Newton’s Second law and think about the scooter activity – did speed change as
force was constant? Did acceleration change?
• Explain how Newton’s first law applies in a car when wearing a seatbelt vs. without a
seatbelt.

16. Example: force applied at an angle
Suppose a 10.0 kg box is pulled at an angle of 30.0 degrees with a force
of 50.0 Newtons. F ¹ mg! N
a) Calculate the normal force of the box å FY = 0 ® FN + Fay - Fg = 0
FN + Fay = mg
FN = mg - Fay ® (10)(9.8) - 50sin30
FN = 73N
a) If the block is accelerating at 1.5 m/s/s, calculate the coefficient of friction.
FN Fa = 50 N å Fx = Fnet = ma
Fay = 50sin(30) Fax - Ff = ma
Ff 30
Fax = 50cos(30) 50 cos30 - m FN = (10)(1.5)
mg
43.3- m (73) = 15
m = 0.39

17. EXAMPLE: FORCE APPLIED AT ANGLE
#5 from handout last week:
A 120.0 N force is applied at an angle of 45 degrees to a 40.0 kg box. The coefficient of
friction between the two surfaces is 0.15. Find
(b) The force due to gravity and normal force
(c) The force due to friction
(d) The acceleration
(e) How fast the object is moving in 10.0 sec
(f) How far it will move in 10.0 sec

18. NEWTON’S THIRD LAW

19. NEWTON’S THIRD LAW
“For every action there is an EQUAL and OPPOSITE reaction.
• This law focuses on action/reaction pairs (forces)
• They NEVER cancel out
All you do is SWITCH the wording!
•PERSON on WALL
•WALL on PERSON

20. NEWTON’S THIRD LAW
• How does this law apply when there is a collision
between two objects, like a train and a truck??

21. NEWTON’S THIRD LAW
This figure shows the force during a collision
between a truck and a train. You can clearly see
the forces are EQUAL and OPPOSITE. To help
you understand the law better, look at this
situation from the point of view of Newton’s
Second Law.
Ftruck = Ftrain
What about mass & acceleration just after collision?
mtruck Atruck = Mtraina train
There is a balance between the mass and acceleration. One object usually
has a LARGE MASS and a SMALL ACCELERATION, while the other has a
SMALL MASS (comparatively) and a LARGE ACCELERATION.

22. N.T.L EXAMPLES
Action: HAMMER HITS NAIL
Reaction: NAIL HITS HAMMER
Action: Earth pulls on YOU
Reaction: YOU pull on the earth

23. NEWTON’S FIRST LAW
Concepts Problems
• What is it? • What type of problems apply?
• An object in motion will remain in
motion, or an object at rest will
remain at rest unless acted upon 4.0 kg
by an unbalanced force.
• Fnet = 0
• What conditions can occur?
4.0 kg
• Object can be at rest
• Object can be in constant motion
at a constant speed

24. NEWTON’S SECOND LAW
Concepts Problems
• What is it? • What type of problems apply?
• Fnet = ma or re-arranged as..
a = Fnet
4.0 kg
m
• Fnet = ma
• Describe the motion of the object
when Newton’s 2 nd law applies 4.0 kg

25. ATWOOD’S MACHINE
Draw the following FBDs if mass 1 = 1.0
kg, mass 2 = 2.0 kg:
• An FBD of the entire system
• An FBD of mass 1
• An FBD of mass 2
• Which direction will the masses
move?
• Use the FBDs to find the net force
equations for each FBD
• Calculate the acceleration

26. FREE-BODY DIAGRAMS
• Draw a Free-body diagram of an elevator accelerating up, and then one of an elevator
accelerating down. Write the equation for the net force on the elevator for each.

27. FREE-BODY DIAGRAM
• A block is pushed across a frictionless plane, and released when the block reaches a
speed of 2.0 m/s. Draw the FBD of the block AFTER it is released.
4.0 kg

29. HOMEWORK
24. A 650 N force acts in a northwesterly direction. A second 650-N force must be exerted in
what direction so that the resultant of the two forces points westward?

30. HOMEWORK
*26. Sketch the free-body diagram of a baseball (a) at the moment it is hit by the bat, (b) after
it has left the bat and is flying toward the outfield

31. HOMEWORK
27. USE figure from book: two forces F1 and F2 act on a 27.0 kg object on a frictionless
tabletop. If F1 = 10.2 N and F2 = 16.0N, what is the net force on the object and its
acceleration in both situation (a) and (b)
F1
F2

32. HOMEWORK
32. A window washer pulls herself upward using the bucket-pulley apparatus shown. Mass =
65 kg.
(a) how hard must she pull downward to raise herself slowly at constant speed?
(b) If she increases this force by 10%, what will her acceleration be?

33. LAST NIGHT’S HOMEWORK
23. a) 40 N, b) 10 N, c) 0
38. 100 N, no force
*39. (a) μs=0.82 (b) μk=0.74
40. diagrams
41. μs=0.41
42. μs=2.3

34. HOMEWORK: FRICTION PROBLEMS
*23. A box weighing 10 N rests on a table. A rope tied to the box runs vertically upward over a
pulley and a weight is hung from the other end. Determine the force that the table exerts on
the box if the weight hanging on the other side of the pulley weighs (a) 30 N, (b) 60 N, and ©
90 N.
a) 40 N, b) 10 N, c) 0
70N

35. HOMEWORK: FRICTION PROBLEMS
38. The coefficient of Friction between a 35 kg crate and the floor is 0.30, what horizontal
force is required to move the crate at a steady speed across the floor? What horizontal force
is required if μk is zero? (100 N, no force)

36. HOMEWORK: FRICTION
*39. A force of 40.0 N is required to start a 5.0 kg box moving across a horizontal concrete
floor. (a) what is the coefficient of static friction between the box and the floor? (b) if the 40.0
N force continues, the box accelerates at 0.70 m/s2. What is the coefficient of kinetic friction?
(a) μs=0.82 (b) μk=0.74
FN
Ff Fa
mg

37. HOMEWORK: FRICTION
*40. (a) a box sits at rest on a rough 30 degree inclined plane. Draw the free-body diagram,
showing all the forces cting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

38. HOMEWORK: FRICTION
41. A 2.0-kg silverware drawer does not slide readily. The owner gradually pulls with more and
more force. When the applied force reaches 8.0 N, the drawer suddenly opens, throwing all
the utensils to the floor. Find the coefficient of static friction between the drawer and the
cabinet. (μs=0.41)

39. HOMEWORK: FRICTION
42. Drag race tires in contact with an asphalt surface probably have one of the highest
coefficients of static friction in the everyday world. Assuming a constant acceleration and no
slipping of tires, estimate the coefficient of static friction for a drag racer that covers the
quarter mile in 6.0 s. (μs=2.3)

40. CALCULATING COEFFICIENTS OF STATIC &
KINETIC FRICTION
You can calculate μs and μk between two surfaces Materials needed:
by…
• Brick of known mass with string
• Finding out the MAXIMUM force required to attached
begin moving an object
• Spring scale
Fmax = μsFN
• Finding out the force required to move an object
at a constant speed Directions:
• Have TWO different people take readings
F f = μkFN from the force scales & take the average
of the two
In both of these cases, the object is in
equilibrium, so • Use equations to solve for coefficients
• NOTE: Spring scale reads in Pounds –
Fa = Ff & Fa = Fmax you will have to conver units to Newtons
(using 2.2 lbs = 1 kg, W = mg)

41. FORCES ON AN INCLINED PLANE
Ff = μFN
FN
So to find Ff, we must find FN first!
Steps to solving these problems…
1. FBD
2. Sum forces in y-direction (to
find Fn)
FG
3. Solve for Ff
4. Find the net force in the x- θ
direction (direction of motion)

42. WORKSHEET PROBLEM #1 12 kg
1. A 12-kilogram block is place on a 25 o inclined plane.
25o
s= 0.15 and k= 0.11
(a) Draw a Free Body Diagram showing mg, F , FN ,
FII & Ff.
(b) Calculate for mg, FII , FN for the block.
(c) Calculate the forces of static & kinetic friction.
(d) Solve for the net force on the block.
(e) Solve for the acceleration of the block.
(f) How far will it slide in 1.0 seconds?

43. WORKSHEET PROBLEM #1 12 kg
1. A 12-kilogram block is pushed up a 25o inclined
plane, then the applied force is removed. Answer the 25o
following questions for the block AFTER it is released,
but while it is still traveling UP the incline.
s= 0.15 and k= 0.11
(a) Draw a Free Body Diagram showing mg, F , FN ,
FII & Ff.
(b) Calculate for mg, FII , FN for the block.
(c) Calculate the forces of static & kinetic friction.
(d) Solve for the net force on the block.
(e) Solve for the acceleration of the block.
(f) How far will it slide up the incline if the initial
velocity is 2.0 m/s2?

44. INTRO TO FRICTION!
What do you already know about friction?
When is friction useful?
When is it harmful?
Write a short paragraph about a friction-free world!

45. FRICTIONAL FORCES
• There are two types of frictional forces:
Type of friction Definition Equation
Static Friction A force that acts parallel to the two surfaces & Fmax = μsFN
(used for stationary objects) keeps an object from moving.
Kinetic Friction A force that acts opposite to the direction of an
(used for moving objects) Ff = μkFN
object’s motion.
Fmax is the maximum force that can
be applied to an object before it Ff is the frictional force
begins to move
The greek symbol “μ” is pronounced “mu”

46. NEW FREE-BODY DIAGRAM
• Now we include the force of friction!
FN
Ff Fa
mg

47. HOW TO CALCULATE COEFFICIENTS OF
FRICTION (WHEN NET FORCE = 0)
• When an object is moving at a CONSTANT SPEED,
we can find the force of friction due to the coefficient
of kinetic friction.
Constant speed means that acceleration = 0
FN
So Fnet = 0
SO…. Fa – Ff = 0
Ff Fa
Ff = Fa
mg
• When a force is applied that causes an object to
JUST BEGIN TO MOVE, we can find the force of
friction due to the coefficient of static friction
Once again…. Ff = Fa

48. Example: Net force = 0
A 10-kg box is being pulled across the table to the right at a constant speed with a force
of 50N.
a) Calculate the Force of Friction Fa = Ff = 50N
a) Calculate the Force Normal mg Fn (10)(9.8) 98N
a) Calculate the coefficient of kinetic friction
Ff = mk FN
FN
Fa
50 = m k (98)
Ff
50
mg m k = = 0.51
98

49. Example: Net force = 0
Suppose the same box is now pulled at an angle of 30 degrees above the horizontal.
a) Calculate the Force of Friction
Fax Fa cos 50cos30 43.3N
Ff Fax 43.3N
a) Calculate the Force Normal
FN m g!
FN Fay mg
FN Fa FN m g Fay (10)(9.8) 50 sin 30
Fay FN 73N
Ff 30
Fax
mg

50. EXAMPLE: NET FORCE = MA
A 50 N applied force drags an 8.16 kg log to the right across a horizontal
surface. What is the acceleration of the log if the force of friction is 40.0 N?
Fn a FNET = ma
50 N
40 N Fa - Ff = ma
mg 50 - 40 = 8.16a
10 = 8.16a
a= 1.23 m/s/s

51. EXAMPLE: NET FORCE = MA
A sled is being accelerated to the right at a rate of 1.5 m/s/s by a rope at a 33
degree angle above the + x . Calculate the acceleration of the sled if the
Frictional Force is 26.8 N, the mass of the sled is 66 kg and the tension in
the rope is 150 N.
a
FN
Tsin
Tcos
FNET = ma
Ff T cosq - Ff = ma
mg
T cosq - ma = Ff
150 cos33- (66)(1.5) = Ff
Ff = 1.5 m/s/s

52. An Atwood's machine is a device where
two masses, m2 and m1, are connected by
ATWOOD’S MACHINE a string passing over a pulley.
• Assume the pulley is frictionless and
massless, which means the tension is
the same everywhere in the string.
• To solve these problems:
• Make three FBDs: one for each
mass, and one for the overall
system.
• So you can make 3 Fnet=ma
equations.
• To find Tension: use the FBDs of
individual masses
• To find acceleration: use either
both FBDs of individual masses,
or one of the overall system

53. If mass 1 is 200 kg, and mass 2 is 30 kg,
what is the acceleration of the system?
ATWOOD’S MACHINE
a = 3.27 m/s2
• Make FBDs
• Have the direction of acceleration be
positive
• Use Newton’s 2 nd law to find
acceleration

54. HOMEWORK SOLUTIONS
Pg. 104 # 1-8
1. 69 N
Free Body Diagrams
2. 116 kg
3. 883 N a. A projectile in motion in the presence
of air resistance.
4. 1260 N
5. (a) 648 N b. A car at the instant it hits a brick wall.
(b) 112 N c. A heavy crate being pushed across a
(c) 244 N surface (neglect surface friction).
(d) 0 N d. A shopping cart being pushed at a 30°
6. (a) W = 196 N, Fn = 196 N angle with horizontal (neglect surface
friction).
(b) Fn on 20 kg box: 294 N, Fn on 10 kg from
20 kg = 98 kg
7. 3443 N
8. F = 153 N