1 4 outline Newton’s 2 nd Law friction dynamics of falling objects RQ: 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 24, 26, 27, 30, 31, 33. Ex: 2,

1

4 outline• Newton’s 2nd Law• friction• dynamics of falling objects

• RQ: 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21, 24, 26, 27, 30, 31, 33.

• Ex: 2, 3, 20, 31, 32, 33, 42, 43, 44.

• Problems: 2, 3, 8.

2

example uses

• design crumple zones (cars & barriers)

• power requirements for cars

• parachute design

• elevator design

• /

3

force & acceleration

• Net force acceleration

• acceleration ~ net force

• e.g. The net force on a car is doubled. The acceleration of the car will then also double in size.

(“~” means “directly proportional to”)

4

Newton’s Second Law: the acceleration of an object is proportional to the Net External Force acting on it, and inversely proportional to the object’s mass.

mass

forcenet acceleration

mass

forcenet

time

direction / speedin change

5

Effect of a Net Force

• object at rest begins to move

• moving object changes its:

• speed

• or direction

• or both.

• change in velocity is in the same direction as the net force on the object.

7

Finding Net Force Using Diagrams

• Example of adding two perpendicular Forces A = 3, B = 4:

• A) Walk 3 steps forward.

• B) Turn left or right, walk 4 steps in this direction.

• C) Walk directly between the starting and ending locations counting your steps.

• Distance in “steps” in (C) is the Net of the two forces.

8

Ex. Net Force Rightward

• Car moving to right

• net force is to right

• Speed increases

9

Ex. Net Force Leftward

• Car moving to right

• net force is directed left

• Car slows down

10

Ex. Net Force Downward

• Ball is tossed to right

• net force is down

• object turns downward

11

Mass and Weight

• Mass is the quantity of matter.• Mass measures “inertia”.• Mass is measured in kilograms (kg)• Weight is the force on mass due to gravity.• Weight is measured in newtons (N) or

pounds (lb).• Weight ~ Mass• 1 kg of mass has a weight of 2.2 lbs

12

Comparing Accelerations of Objects in Free Fall.

• Downward force is weight.

• a = weight/mass

• but an object with twice the mass will have twice the weight…

• so the accelerations are the same…

• We call this acceleration “g”.

• g is about 10m/s/s downward.

13

Friction

• Objects in contact “like each other”, i.e. they form a “bond”.

• They resist being moved when in contact.

• Ex. A Chest sitting on a wood floor seems “glued” down. It is harder to get it moving than it is to keep it moving.

• These resistance forces are called “frictional forces”.

14

Direction of Frictional Forces• Frictional forces oppose the direction of

motion of object if it is moving.

15

Direction of Frictional Forces (cont.)

• If the object is at rest there still may be a frictional force. If there is a frictional force then it is in a direction opposite to the direction of the net applied force due to other causes.

16

Free-Fall

• only force is object’s weight

• air drag is negligible in size

• Ex. A solid steel ball falling a short distance is in free-fall.

• Ex. A falling feather is not in free-fall since air drag is equal to its weight

17

Question

In a vacuum, a coin and feather fall side by side, at the same rate. Is it true to say that, in vacuum, equal forces of gravity act on both the coin and the feather?

NO! They accelerate together because the ratio weight/mass for each are same (=g)

18

Non Free Fall

• Whenever air drag is significant compared to weight the object will fall with acceleration less than 10m/s/s.

19

Terminal Speed/Velocity

• Air drag on falling objects increases…

• until equal to the objects weight…

• … resulting in balanced forces

• acceleration = 0, speed no longer changes

• This top speed is called the “terminal velocity” of the object…

• … and varies from object to object.

20

1. increases.2. decreases.3. remains

the same.

As she falls faster and faster through the air, her acceleration

21

1. increases.2. decreases.3. remains

the same.

As she falls faster and faster through the air, her acceleration

a

Fnet

m

(mg R)

m

22

4 summary

• Newton’s 2nd Law relates net force, mass, and acceleration. It also covers the 1st Law.

• frictional forces are proportional to the forces holding objects together

• falling objects accelerate until air drag equals their weight

23

p.11 practicing physics

• Mass is fundamental, does not depend on location

• Mass is not a vector and not a force, it is simply a number

• 1kg mass “weighs” 10N on earth (2.2lbs), less on the moon

• Weight = mg (earth g = 10m/s/s)

24

4 agenda

• lecture

• practicing physics: pages 11, 12-16, 17

• lab: acceleration on an air-track

• lab: Newton’s 2nd Law on air-track

25

1. A falling elephant, or

2. A falling feather?

Which encounters the greater force of air resistance—

26

1. A falling elephant, or

2. A falling feather?

Which encounters the greater force of air resistance—

air drag ~ size and speedair drag ~ size and speed

27

Categories of Friction

• Sliding Friction: exists when one object slides against a second object, e.g. box along floor.

• Static Friction: exists when a force is applied to an object, but that force is not large enough to break the frictional bond.

28

Size of Frictional Force:

• proportional to the force holding the objects in contact, e.g. weight of a box.

• does not depend on the area of contact. Box on different sides will have similar frictional forces.

• Static friction > Sliding friction

29

Example of Objects at Terminal Velocity

30

Fluid Friction

• Gases and Liquids are both “Fluids”

• Motion through air is a “fluid-drag” and is called “air resistance” or “air drag”.

• Fluid-drag usually proportional to velocity or velocity squared.

• Air-drag ~ v2.

Ex. Falling Motion

• M = 1kg, speed is small, f = 0.

• Weight of 1kg is about W = 10N.

• Net force = W – f = W – 0 = W.

• Acceleration, a = Net Force/Mass

• a = Weight/Mass = 10N/1kg = 10 m/s/s

• N/kg = m/s/s

Ex. Falling Motion

• M = 1kg, speed is large, e.g. f = 1/3 weight = 10N/3 =3.33N

• Weight of 1kg is about W = 10N.

• Net force = W – f = W – W/3 = (2/3)W.

• Acceleration, a = Net Force/Mass

• a = (2/3)W/Mass = 6.67N/1kg = 6.67m/s/s

• N/kg = m/s/s