1

Ch 4. Forces & Newton’s Laws of Motion

force = a push or a pull.

Unit of Force = Newton

net force = vector sum of all forces on object

Individual Forces

Net Force

10 N4 N

6 N

3 N

4 N

5 N 64Individual Net

F

net force =

Newton’s 1st Law:object – stays at rest – or constant speed in a straight line – if no net force.

Inertia = tendency of objectto stay at rest – or constant speed in a straight line – if no net force.

2

Mass (m) is the amount of “stuff” in an object

Unit of Mass: kilogram (kg)

Newton’s 2nd Law:Acceleration – proportional to Force – inversely proportional to mass

mF

a

aF

m

22 s

mkg

s

mkg

Unit of Force = Newton

Units

free-body-diagramrepresents object & forces

Net force: 275 N + 395 N – 560 N = +110 Nalong the + x axis

2sm059.0kg 1850

N110

m

Fa

Acceleration: mass of car = 1850kg

3

aFm

xx maF

yy maF Force x component y component

+17 N

+(15 N) cos67

0 N

+(15 N) sin67

+23 N +14 N

P

A

Net force:

forces

2sm 018.0kg 1300

N 23

m

Fa

x

x

2sm 011.0kg 1300

N 14

m

Fa yy

P

A

4

Newton’s 3rd Law:Action = ReactionForce from body-A to body-B = Force from body-B to body-A

Magnitude of force is 36 N. Mass of spacecraft is 11,000 kg. Mass of astronaut is 92 kg.

What are the accelerations?

PF

PF

astronaut On the

spacecraft On the

2sm0033.0

kg 11,000

N 36

ss m

Pa

2sm39.0

kg 92

N 36

AA m

Pa

5

Newton’s Law of Gravitation

masses m1 and m2 separated by distance r, gravitational force

221

r

mmGF

2211 kgmN10673.6 G

N 104.1

m 1.2

kg 25kg 12kgmN1067.6

8

22211

221

r

mmGF

12 kg 25 kg1.2 m

Weight = gravitational force earth attracts object

2r

mMGW E

mgW

2r

MGg E

2

26

242211

2

sm 80.9

m 106.38

kg 1098.5kgmN1067.6

E

E

R

MGg

On earth’s surface

6

Normal Force

N 26

0N 15N 11

N

N

F

F

from surface to object

Apparent Weight = normal force on scale by man

mamgFF Ny mamgFN

apparent weight

trueweight

7

Frictional Force static friction

MAXss ff NsF

coefficient of static friction.

Nkk Ff coefficient of kinetic friction

After motion begins

kg20sm80.9kg4005.0 2

mgFf kNkk

coefficient of kinetic friction = 0.05 mass = 40kg What is the kinetic frictional force?

8

Tension ForceCables and ropes transmit forces through tension.

0xF 0yF

Equilibrium

Reasoning Strategy

• select an object in equilibrium• draw free-body diagram

for object & forces• choose x,y axes • resolve forces into x,y comps• apply equilibrium equations• solve for unknown quantities

035sin35sin 21 TT

035cos35cos 21 FTT

Equilibrium

9

Equilibrium Force x component y component

1T

2T

W

0.10sin1T0.80sin2T

0

0.10cos1T0.80cos2T

W

N 3150W

080sin10sin 21 TTFx

080cos10cos 21 WTTFy

21 10sin

80sinTT

080cos10cos10sin

80sin22

WTT

80cos10cos10sin80sin

2

WT

N 5822 T N 1030.3 31 T

10

Non-EquilibriumWhen an object is accelerating, it is not in equilibrium.

xx maF yy maF

030sin30sin 21 TTFy

21 TT

x

x

ma

RDTTF

0.30cos0.30cos 21

TTT 21

N 1053.10.30cos2

5

DRmaT x

you are given m,a,R,D