PHYSICS UNIT 2: DYNAMICS(Explaining Motion)

FORCES Force: a "push" or a "pull“

unit: Newtons, N (1 N is about ¼ lb) vector - includes direction contact forces and field forces (act

over a distance) net force: total effect of all forces

acting on an object

FORCES Typical Forces

gravity, FG: object’s weight, always directed toward center of earth (FG=mg mass × acceleration due to gravity)

normal force, FN: supporting force a surface exerts on an object, always directed upward perpendicular to the surface

tension, FT: force transmitted by a rope or chain, directed along the rope, constant throughout the rope

FORCES Free body diagrams: show just one object &

the forces acting on the object (NOT forces the object is exerting on other things) example: car hitting a wall

Examples Apple on a table Rock under

water Block on a hill Water skier Child pulled

forward at an angle on a sled

NEWTON’S LAWS OF MOTION

The Law of Inertia (1st Law): an object’s velocity stays constant unless acted upon by a net external force inertia: resistance to change in

motion (mass is a measure of inertia, more mass = more inertia)

Example of Newton’s 1st Law

NEWTON’S 2nd LAW OF MOTION

The Law of Acceleration (2nd Law): a net force causes an acceleration proportional to the force, in the same direction, and inversely proportional to mass. Fnet = ma

Fnet: sum of all forces or net force (N), m: mass (kg), a: acceleration (m/s2) 1 N = 1 kg·m/s2

Second The greater the force, the greater the

acceleration The greater the mass, the greater the

force needed for the same acceleration Calculated by: F = ma (F = force, m = mass, a =

acceleration)

NEWTON’S 2nd LAW OF MOTION

NEWTON’S 3rd LAW OF MOTION

The Law of Interaction (3rd Law): for every action force from one object on another, there is an equal magnitude, opposite direction reaction force from the 2nd object back on the 1staction:

hammer hits anvilreaction: anvil hits hammer

NEWTON’S 3rd LAW OF MOTION

Law of Interaction (3rd Law) action & reaction forces do not

balance each other - they are on different bodies (ex: car pulling a trailer)

equal force does not mean equal acceleration - depends on mass (ex: person jumping off the ground)

Examples of Newton’s 3rd law

FORCES Finding the Net Force (total of all forces on an

object) draw a free body diagram identify & label x & y axes separate forces into x and y parts – Fx=Fcos

Fy=Fsin add all x forces, add all y forces equilibrium: no net force – x forces add up to

zero, y forces add up to zero

Example

LAB 2.3 – Elevator Scene 1

LAB 2.3 – Elevator Scene 2

LAB 2.3 – Elevator Scene 3

LAB 2.3 – Elevator Frame 1

LAB 2.3 – Elevator Frame 2

LAB 2.3 – Elevator Frame 3

LAB 2.3 – Elevator Frame 4

LAB 2.3 – Elevator Frame 5

LAB 2.3 – Elevator Frame 6

LAB 2.3 – Elevator Frame 7

QUIZ 2.1 Joe rolls a ball down a hill. The ball has a

mass of 0.500 kg. The force pulling the ball down the hill is 6.00 N. The hill is 100.0 m long. (a) What is the ball’s acceleration? (b) How fast is the ball going at the bottom of the hill, if it started at rest at the top? (c) If the force on the ball doubled, what would happen to the ball’s acceleration? (d) If instead the mass of the ball doubled, what would happen to its acceleration?

12.0 m/s2

49.0 m/s

doubles (24 m/s2)

halves (6 m/s2)

PHYSICS

UNIT 2: DYNAMICS(Explaining Motion)

NEWTON’S LAWS OF MOTION

Law of Inertia (1st Law) objects slow & stop, or require

continued force to keep moving, due to friction

FRICTION Friction Force, Ff:

resistance to motion between objects in contact with each other acts parallel to contact

surface, opposite to motion

caused by uneven surfaces, molecular attraction

FRICTION

static friction: resistance to starting motion (at rest) beneficial (walking, building, eating, wheels rolling)

kinetic friction: resistance to continued motion (sliding) undesirable (machines, moving furniture, wheels

skidding)

kinetic friction < static friction

FRICTION coefficient of friction,: constant

that depends on type of surfaces in contact s: coefficient of static friction k: coefficient of kinetic friction Ff = FN (friction force = ×

normal force)

FRICTION

Ff

FRICTION on horizontal surface:

mg

FN

FN = mg

(normal force = body weight) so Ff = mg

FRICTION on tilted surface:

mgmgcos

FN Ff

FN = mgcos so f = mgcos

PHYSICS

UNIT 2: DYNAMICS(Explaining Motion)

QUIZ 2.2 A 1200 kg car sits on a horizontal

road. (a) How much force does Joe need to push the car at a constant speed if the coefficient of kinetic friction is 0.600? (b) How much will the car accelerate if Joe uses a force of 10,000 N?a) 7060 N

b) 2.45 m/s2

PHYSICS

UNIT 2: DYNAMICS(Explaining Motion)

PROJECTILE MOTION Projectile motion: parabolic

trajectory (path) Two dimensions of motion: horizontal

(x), vertical (y)vy

vx

v

vx = vcos

vy = vsin

if a bullet was fired horizontally, andanother bullet was dropped from thesame height at the same time, whichwould hit the ground first?

PROJECTILE MOTION Vertical

Motion

constant vertical acceleration due to gravity(2nd Law)

PROJECTILE MOTION A monkey hangs from a

tree branch. A hunter aims his tranquilizer gun barrel straight at the monkey. When the hunter fires his gun, should the monkey keep holding on to the branch, or let go?

PROJECTILE MOTION Vertical Motion

position: y = h + visinit – ½gt2

a. for ground launch, h=0, y = visinit – ½gt2

b. for horizontal cliff launch, 0=0, y = h – ½gt2

speed: vy = visini – gt flight time, T: t when y=0

ground: cliff:gsinv2

T ii

gh2

T

A tank moving at constant speed fires ashell straight up into the air. Where willthe shell come back down?

PROJECTILE MOTION Horizont

al Motionconstant horizontal speeddue to no horizontal force(1st Law)

PROJECTILE MOTION A snowmobile fires a

flare, then slows down. Where does the flare land? If the snowmobile speeds up instead, where does the flare land?

PROJECTILE MOTION Horizontal Motion

position: x = vicosit

for horizontal cliff launch, i=0, x = vit

speed: vx = vicosi

range, R: x when t = T ground: cliff:

g)2sin(v

R i2i

gh2

vR i

PROJECTILE MOTION Example: A projectile is launched

from ground level with a velocity of 50 m/s at an angle of 30 degrees. What is its position and velocity 2 seconds later? What is its flight time? What is its range?

PHYSICS

UNIT 2: DYNAMICS(Explaining Motion)

A plane moving at constant speeddrops a flare. Describe the path ofthe flare.

RELATIVE MOTION Referenc

e Frames:

projectile motion in one reference frame can be vertical free fall in another reference frame (and vice versa)

PHYSICS

UNIT 2: DYNAMICS(Explaining Motion)

QUIZ 2.3Circle your answers! Watch sig. fig's & units!1. Joe throws a ball from ground level at an angle

of 41º and a speed of 19 m/s. (a) Find the ball's vertical position after 1.5 seconds. (b) Find the ball's horizontal speed after 1.5 seconds.

2. Jane throws a ball off a 95-m tall building horizontally at 19 m/s. (a) Find the ball's flight time. (b) Find the ball's range.

y = h + visinit – ½gt2 vy = visini – gt

x = vicosit vx = vicosi

7.67 m14.3 m/s

4.40 s 83.6 m

PHYSICS

UNIT 2: DYNAMICS(Explaining Motion)

UNIT 2 REVIEW Newton's Laws (Memorize!):

1st Law: velocity stays constant unless acted upon by a net force

2nd Law: net force = mass x acceleration

3rd Law: for every action force, there is an equal and opposite reaction force

UNIT 2 REVIEW

F = ma FG = mg

Ff = FN

vf = vi + at

x= vit + ½at2

vf2=vi

2 + 2ax

y = h + visinit – ½gt2

x = vicosit

vy = visini – gt

vx = vicosi

g)2sin(v

R i2i

gh2

vR i

gsinv2

T ii

gh2

T