1. Chapter 4: Newton’s second law of motion
Force Causes Acceleration
Friction
Mass and Weight
Mass Resists Acceleration
Newton’s Second Law of Motion
Free Fall
Non-Free Fall

2. The Force of Friction
CHECK YOUR NEIGHBOR
1) A chair is sitting on the floor, what would cause it to accelerate (change velocity)?
ANSWER – The application of a force
2) What is a force?
ANSWER – A push or a pull
3) What would cause the chair to accelerate a little (move slowly) vs. a lot (move quickly)?
D. all of the above.
ANSWER – The amount of force applied

3. Force causes Acceleration
Acceleration depends on the net force.
Acceleration is directly proportional to net force.
To increase the acceleration of an object, you must increase the net force acting on it.
More force = more acceleration
Acceleration ~ net force

4. The Force of Friction
CHECK YOUR NEIGHBOR
BOTH) Which chair would require the most amount of force to get it to accelerate (move)?
Rank the following from least force required to most force required– explain your choices.
D. all of the above. A B C D E

5. 4) Where is there a greater force of friction?
The Force of Friction
CHECK YOUR NEIGHBOR
4) Where is there a greater force of friction?
Between a cardboard box and a wood floor
Or Between a cardboard box and a concrete floor
– Due to the kind of materials (surfaces in contact) = μ
WHY?
5) Where is there a greater force of friction?
Between a 10 kg cardboard box and a concrete floor
Or Between a 20 kg cardboard box and a concrete floor
D. all of the above.
WHY?
– Due to how much they are pressed together
Force Normal = N

6. The Force of Friction (ffriction)
~ is due to tiny surface bumps and to “stickiness” of the atoms on a material’s surface.
The amount (Newtons) of the force or friction (f) depends on: ) Surfaces in contact (μ) = coefficient of friction (kinds of materials)
2) Force Normal (N) (how much they are pressed together)
3) Amount of surface area in contact (-- you will not be tested on #3 )
f = μN
Friction between a crate on a smooth wooden floor is less than that on a rough floor.

7. 6) The force of friction can occur
CHECK With your Neighbor
6) The force of friction can occur
A. with sliding objects.
in water.
in air.
All of the above.
Comment:
Friction can also occur for objects at rest. If you push horizontally on your book and it doesn’t move, then friction between the book and the table is equal and opposite to your push.
D. all of the above.

8. Net Force = Zero = acceleration
The Force of Friction
CHECK YOUR NEIGHBOR
7) What are the different forces that are being applied to the box in the image below? (EXPLAIN your thoughts)
8) How would we know if the box is moving at a constant velocity, accelerating or sitting still? (EXPLAIN)
Acceleration depends on the net force. FN
ffriction
Fpush
C. equal and opposite to Sanjay’s push.
Net Force = Zero
= Equilibrium
= No acceleration FW
Net Force = Zero = acceleration

9. Net Force = Zero FN ffriction Fpush = Equilibrium = No acceleration FW
The Force of Friction
CHECK YOUR NEIGHBOR
9) When Sanjay pushes a refrigerator across a kitchen floor at a constant speed, the force of friction between the refrigerator and the floor is… (EXPLAIN your thoughts)
A. less than Sanjay’s push.
equal to Sanjay’s push.
equal and opposite to Sanjay’s push.
more than Sanjay’s push. FN
ffriction
Fpush
C. equal and opposite to Sanjay’s push.
Net Force = Zero
= Equilibrium
= No acceleration FW

10. Fpush Acceleration is occurring ffriction The Force of Friction
CHECK YOUR NEIGHBOR
10) When Sanjay pushes a refrigerator across a kitchen floor at an increasing speed, the amount of friction between the refrigerator and the floor is… (EXPLAIN your thoughts)
A. less than Sanjay’s push.
equal to Sanjay’s push.
equal and opposite to Sanjay’s push.
more than Sanjay’s push.
Fpush
ffriction
Explanation:
The increasing speed indicates a net force greater than zero. The refrigerator is NOT in equilibrium.
Acceleration is occurring
A. less than Sanjay’s push.

11. f = μN fs = Static Friction fs = μsN fk = Kinetic Friction fk = μkN
The force of friction depends upon both the surfaces in contact (μ) and the normal force (N)
fs = Static Friction
fs = μsN
Net Force = Zero
= Equilibrium
= No acceleration
= No movement
fk = Kinetic Friction
fk = μkN

12. .
                                    
The force of friction depends upon both the surfaces in contact (μ) and the normal force and motion or static
surface-on-surface
hook velcro-on-fuzzy velcro
>6.0
>5.9
average tire-on-dry pavement
0.9
0.8
grooved tire-on-wet pavement
0.7
glass-on-glass
0.4
metal-on-metal (dry)
0.6
smooth tire-on-wet pavement
0.5
metal-on-metal (lubricated)
0.1
0.05
steel-on-ice
steel-on-Teflon
You should keep in mind that it isn't possible to give accurate values for the coefficient of frictions due to changing surface smoothness.  For example, not all pieces of metal have the same surface smoothness.  Some that are highly polished may be more slippery than others that are pitted or scratched.  These values are just meant to give you the approximate values.

13. f = μN fs = μsN fk = μkN The force of friction (f) depends upon:
surfaces in contact (μ) = coefficient of friction
normal force (N) (how hard they are pushed together)
Static μs vs. moving μk
f = μN
fs = μsN
fk = μkN
4) How things are moving
Not moving = Static
Sliding = kinetic (chair without wheels)
Rolling = kinetic (chair with wheels)
Fluid = kinetic (chair sinking in ocean)
Dry vs. Wet
Presence of a lubricant (oil, grease, silicon…)
Condition of surfaces (scratched, pitted, warped…)
Pencils Down! – We will NOT be studying these things, but I did want to mention them

14. Mass and Weight Mass (m): The quantity of matter in an object.
It is also the measure of the inertia or sluggishness that an object exhibits in response to any effort made to start it, stop it, or change its state of motion in any way.
Weight (W): The force upon an object due to gravity
Mass (matter) of an object will never change
Weight (force) will change based on the location of the object (on the moon, on Jupiter, mountain top)
SI unit for mass = kg (kilogram)
SI unit for weight = N (Newton)

15. Mass and Weight Greater inertia  greater mass Mass
A measure of the inertia of a material object
Independent of gravity
Greater inertia  greater mass
Unit of measurement is the kilogram (kg)
Weight
The force on an object due to gravity
Scientific unit of force is the newton (N)
Unit is also the pound (lb)

16. Mass—A Measure of Inertia
CHECK YOUR NEIGHBOR
11) If the mass of an object is halved, the weight of the object is (EXPLAIN)
A. halved.
twice.
depends on location.
None of the above.
A. halved.
Note: There is a mathematical equation for weight (FW), but we haven’t learned it yet

17. Mass and Weight Mass versus weight
Mass and weight in everyday conversation are interchangeable.
Mass, however, is different and more fundamental than weight.
Mass versus weight
on the Moon and Earth:
Weight of an object on the Moon
is less than on Earth.
Mass of an object is the same
in both locations.

18. A. weight of the ball. mass of the ball. volume of the ball. top
Mass and Weight
CHECK YOUR NEIGHBOR
12) When the string is pulled down quickly, the ______ string breaks, which best illustrates the
A. weight of the ball.
mass of the ball.
volume of the ball.
density of the ball.
top
Explanation:
It is the inertia “laziness” of the ball that tends to keep it at rest, resulting in the breaking of the bottom string
B. mass of the ball.
bottom

19. A. weight of the ball. mass of the ball. volume of the ball. top
Mass and Weight
CHECK YOUR NEIGHBOR
13) When the string is pulled down slowly, the _____ string breaks, which best illustrates the
A. weight of the ball.
mass of the ball.
volume of the ball.
density of the ball.
top
A. weight of the ball.
Explanation:
Tension in the top string is the pulling tension plus the weight of the ball, both of which break the top string.
bottom

20. 30 kg cart 20 kg cart Acceleration is inversely proportional to mass.
The Force of Friction
CHECK YOUR NEIGHBOR
Acceleration is inversely proportional to mass.
14) If each man pushes with the same magnitude of force (100N), who will win the race? (EXPLAIN)
Greater Mass = lower Acceleration
100 N Force 
10 kg cart
100 N Force 
Twice the mass produces
half the acceleration
20 kg cart
D. all of the above.
3 times the mass
produces 1/3 the
acceleration
100 N Force 
30 kg cart

21. Acceleration is directly proportional to force.
The Force of Friction
CHECK YOUR NEIGHBOR
Acceleration is directly proportional to force.
15) If each man pushes with the same magnitude of force (100N), who will win the race? (EXPLAIN)
Greater Force = Greater Acceleration
100 N Force 
10 kg cart
200 N Force 
Twice the force produces
twice the acceleration
10 kg cart
D. all of the above.
3 times the force
produces 3 times
the acceleration
300 N Force 
10 kg cart

22. Newton’s Second Law of Motion
Isaac Newton was the first to connect the concepts of force and mass to produce acceleration.

23. Newton’s Second Law of Motion
In equation form:
Example:
If net force acting on object is doubled  object’s acceleration will be doubled.
If mass of object is doubled  object’s acceleration will be halved.
1 N = kg*m/s2
net force
Acceleration 
mass
Force = 24 N
Mass = 12 kg
= 2 N/kg = 2 m/s2
Force = 48 N
Mass = 12 kg
= 4 N/kg = 4 m/s2
Force = 24 N
Mass = 24 kg
= 1 N/kg = 1 m/s2
Newton’s second law (the law of acceleration) relates acceleration to force.

24. Which Brick would win EACH race?
net force
Acceleration 
mass
1 hand = 12 N of FORCE
1 brick = 4 kg of INERTIA
Which Brick would win EACH race?
12 N
4 kg
= 3 m/s2
24 N
4 kg
= 6 m/s2
12 N
4 kg
= 3 m/s2
12 N
8 kg
= 1.5 m/s2
24 N
8 kg
= 3 m/s2
12 N
4 kg
= 3 m/s2
12 N
8 kg
= 1.5 m/s2
24 N
4 kg
= 6 m/s2

25. Newton’s Second Law of Motion
CHECK YOUR NEIGHBOR
16) Consider a cart pushed along a track with a certain force. If the force remains the same while the mass of the cart decreases to half, the acceleration of the cart
remains relatively the same.
halves.
doubles.
changes unpredictably.
Same force
Half the Mass
100 N
10 kg
= 10 m/s2
100 N
5 kg
= 20 m/s2 25

26. Newton’s Second Law of Motion
CHECK YOUR NEIGHBOR
17) Push a cart along a track so twice as much net force acts on it. If the acceleration remains the same, what is a reasonable explanation?
The mass of the cart doubled when the force doubled.
The cart experiences a force that it didn’t before.
The track is not level.
Friction reversed direction.
200 N
20 kg
= 10 m/s2
100 N
10 kg
= 10 m/s2 26

27. F = m*a F = m*g W = Fw = m*g Mass = 1kg Weight = _?_ .
net force
Acceleration 
mass F m
a 
F = m*a
F = m*g
(Falling objects) a = g = 10 m/s2
W = Fw = m*g
Force = Weight (W) = mass * g
W = Fw = 1kg*10m/s2
Mass = 1kg
W = Fw = 10 N
1 kg = 10 N = 9.8 N
2 kg = 20 N = 19.6 N
Weight = _?_ .
Weight is a Force (N).
1 N = kg*m/s2

28. Free Fall All objects fall with an acceleration of g = 10 m/s2
The greater the mass of the object…
the greater its force of attraction toward the Earth.
the smaller its tendency to move i.e., the greater its inertia.
So, the acceleration is the same.
It is equal to the acceleration due to gravity: 10 m/s2
(precisely g = 9.8 m/s2).
All objects fall with an acceleration of g = 10 m/s2
(If air resistance is negligible)

29. Free Fall When acceleration is g—free fall
Newton’s second law provides an explanation for the equal accelerations of freely falling objects of various masses.
Acceleration is equal when air resistance is negligible.
Acceleration depends on force (weight) and inertia.

30. Free Fall CHECK YOUR NEIGHBOR
At one instant, an object in free fall has a speed of 40 m/s. Its speed 1 second later is
A. also 40 m/s.
45 m/s.
50 m/s.
None of the above.
C m/s.

31. Free Fall CHECK YOUR ANSWER
At one instant, an object in free-fall has a speed of 40 m/s. Its speed 1 second later is
A. also 40 m/s.
45 m/s.
50 m/s.
None of the above.
Comment:
We assume the object is falling downward.
C m/s.

32. Free Fall CHECK YOUR NEIGHBOR
A 5-kg iron ball and a 10-kg iron ball are dropped from rest. For negligible air resistance, the acceleration of the heavier ball will be
A. less.
the same.
more.
undetermined.
B. the same.

33. Free Fall CHECK YOUR ANSWER
A 5-kg iron ball and a 10-kg iron ball are dropped from rest. For negligible air resistance, the acceleration of the heavier ball will be
A. less.
the same.
more.
undetermined.
B. the same.

34. Free Fall CHECK YOUR NEIGHBOR
A 5-kg iron ball and a 10-kg iron ball are dropped from rest. When the free-falling 5-kg ball reaches a speed of 10 m/s, the speed of the free-falling 10-kg ball is
A. less than 10 m/s.
10 m/s.
more than 10 m/s.
undetermined.
B m/s.

35. Free Fall CHECK YOUR ANSWER
A 5-kg iron ball and a 10-kg iron ball are dropped from rest. When the free-falling 5-kg ball reaches a speed of 10 m/s, the speed of the free-falling 10-kg ball is
A. less than 10 m/s.
10 m/s.
more than 10 m/s.
undetermined.
B m/s.

36. Non-Free Fall
When an object falls downward through the air it experiences
force of gravity pulling it downward.
air drag force acting upward.

37. Non-Free Fall When acceleration of fall is less than g, non-free fall
occurs when air resistance is non-negligible.
depends on two things:
1) speed and
2) frontal surface area.

38. Non-Free Fall
When the object is moving fast enough that force of gravity equals its air resistance
Then no net force
No acceleration
Velocity does not change

39. Non-Free Fall Terminal speed Terminal velocity
occurs when acceleration terminates (when air resistance equals weight and net force is zero).
Terminal velocity
same as terminal speed, with direction implied or specified.

40. Non-Free Fall—Example
A skydiver jumps from plane.
Weight is the only force until air resistance acts.
As falling speed increases, air resistance on diver builds up, net force is reduced, and acceleration becomes less.
When air resistance equals the diver’s weight, net force is zero and acceleration terminates.
Diver reaches terminal velocity, then continues the fall at constant speed.

41. Non-Free Fall CHECK YOUR NEIGHBOR
When a 20-N falling object encounters 5 N of air resistance, its acceleration of fall is
A. less than g.
more than g.
C. g.
terminated.
A. less than g.

42. Non-Free Fall CHECK YOUR ANSWER
When a 20-N falling object encounters 5 N of air resistance, its acceleration of fall is
A. less than g.
more than g.
C. g.
terminated.
Comment:
Acceleration of a non-free fall is always less than g. Acceleration will actually be (20 N – 5 N)/2 kg = 7.5 m/s2.
A. less than g.

43. Non-Free Fall CHECK YOUR NEIGHBOR
If a 50-N person is to fall at terminal speed, the air resistance needed is
A. less than 50 N.
50 N.
more than 50 N.
None of the above.
B N.

44. Non-Free Fall CHECK YOUR ANSWER
If a 50-N person is to fall at terminal speed, the air resistance needed is
A. less than 50 N.
50 N.
more than 50 N.
None of the above.
Explanation:
Then, F = 0 and acceleration = 0.
B N.

45. Non-Free Fall CHECK YOUR NEIGHBOR
As the skydiver falls faster and faster through the air, air resistance
A. increases.
decreases.
remains the same.
Not enough information.
A. increases.

46. Non-Free Fall CHECK YOUR ANSWER
As the skydiver falls faster and faster through the air, air resistance
A. increases.
decreases.
remains the same.
Not enough information.
A. increases.

47. Non-Free Fall CHECK YOUR NEIGHBOR
As the skydiver continues to fall faster and faster through the air, net force
A. increases.
decreases.
remains the same.
Not enough information.
B. decreases.

48. Non-Free Fall CHECK YOUR ANSWER
As the skydiver continues to fall faster and faster through the air, net force
A. increases.
decreases.
remains the same.
Not enough information.
B. decreases.

49. Non-Free Fall CHECK YOUR NEIGHBOR
As the skydiver continues to fall faster and faster through the air, her acceleration
A. increases.
decreases.
remains the same.
Not enough information.
B. decreases.

50. Non-Free Fall CHECK YOUR ANSWER
As the skydiver continues to fall faster and faster through the air, her acceleration
A. increases.
decreases.
remains the same.
Not enough information.
Comment
If this question were asked first in the sequence of skydiver questions, many would answer it incorrectly. Would this have been you?
B. decreases.

51. Non-Free Fall
CHECK YOUR NEIGHBOR
Consider a heavy and light person jumping together with same-size parachutes from the same altitude. Who will reach the ground first?
A. The light person.
The heavy person.
Both will reach at the same time.
Not enough information.
B. The heavy person.

52. Non-Free Fall
CHECK YOUR ANSWER
Consider a heavy and light person jumping together with same-size parachutes from the same altitude. Who will reach the ground first?
A. The light person
The heavy person
Both will reach at the same time.
Not enough information.
B. The heavy person.
Explanation:
They both have the same drag force (for the same speed).
The man (heavier) has a greater downward force than the woman (lighter).
The man has to drop farther to receive drag force equal to his downward force, so a higher terminal velocity.

53. Free Fall vs. Non-Free Fall
Coin and feather fall with air present
Feather reaches terminal velocity very quickly and falls slowly at constant speed, reaching the bottom after the coin does.
Coin falls very quickly and air resistance doesn’t build up to its weight over short-falling distances, which is why the coin hits the bottom much sooner than the falling feather.

54. Non-Free Fall CHECK YOUR NEIGHBOR
When the air is removed by a vacuum pump and the coin and feather activity is repeated,
A. the feather hits the bottom first, before the coin hits.
the coin hits the bottom first, before the feather hits.
both the coin and feather drop together side-by-side.
Not enough information.
C. both the coin and feather drop together side-by-side.

55. Non-Free Fall CHECK YOUR ANSWER
When the air is removed by a vacuum pump and the coin and feather activity is repeated,
A. the feather hits the bottom first, before the coin hits.
the coin hits the bottom first, before the feather hits.
both the coin and feather drop together side-by-side.
Not enough information.
C. both the coin and feather drop together side-by-side.

56. Free Fall vs. Non-Free Fall
Coin and feather fall in vacuum
There is no air, because it is vacuum.
So, no air resistance.
Coin and feather fall together.