Forces A force is just a push or pull.

– an object’s weight

– tension in a rope

– a left hook to the schnozzola

– friction

– attraction between an electron and proton

Bodies don’t have to be in contact to exert forces on each other, e.g., gravity.

System/Environment

System--is the object that is being considered in situation…. p. 119 book– Book on desk– Ball hanging on rope– Ball held in hand

Environment– is the world around object that is exerting forces on the system

Contact vs. Long Range forces

Contact Forces act on body by touching it

Long Range Forces act at a distance, without contact.

Examples of each kinds of force…

1. Contact--actual touching

2. Long-Range—forces acting at a distance

Frictional ForceTensional ForceNormal ForceAir Resistance Applied ForceSpring Force

A GravitationalB. ElectromagneticC. Nuclear

Forces that could cause accelerationsForce Symbol Definition Direction

Friction FfThe contact force that acts to oppose sliding motion between surfaces

Parallel to the surface and opposite the direction of sliding

Normal FNThe contact force exerted by a surface on an object

Perpendicular to and away from the surface

Spring FspA restoring force, the push or pull a spring exerts on an object

Opposite the displacement of the object at the end of the spring

Tension FTThe pull exerted by a string, rope, or cable when attached to a body and pulled taut

Away from the object and parallel to the string/rope/cable at the point of attachment

Weight FW or FgLong range force due to gravitational attraction between two objects (generally Earth and an object)

Straight down toward the center of the earth

Fundamental Forces of Nature: Long Range Forces Gravity

– Attraction between any two bodies w/ mass– Weakest but most dominant

Electromagnetic – Forces between any two bodies w/ charge– Attractive or repulsive

Weak nuclear force – responsible for radioactive decay

Strong nuclear force – holds quarks together (constituents of protons and neutrons)

Agents

An Agent is a specific, identifiable, immediate cause of a force– Mass is the agent of gravity– Examine diagrams in book, page 119.– Identify the agents of each force– Now you try it….Practice problem #1,

p. 119

Free Body Diagram

Diagram showing all forces acting on an object.

Shows object as a dot.

Try a few…. What forces are acting on a “little, red wagon”

as it is being pulled at a constant velocity? What forces are acting on a steel anvil as it

falls through the air? (not at Terminal velocity) What forces are acting on an airplane in level

flight, at a constant velocity? What forces are acting on a person in an

elevator that is accelerating upward?

Fw or FgFw or Fg

Fw or FgFw or Fg

Flift Fapplied (causing acceleration)

Ffriction

Fdrag

FNormal

FNormal

FappliedFdrag

Wagon

Fthrust

Airplane

Anvil

Elevator

Newton’s 3 Laws of Motion

Newton’s 3 Laws of Motion

1. Inertia: “An object in motion tends to stay in motion; an object at rest tends to stay at rest.” (unless some force acts upon the object)

2. Fnet = ma3. Action – Reaction: “For every

action there is an equal but opposite reaction.”

2nd Law: Fnet = m a The acceleration an object experiences

is directly proportional to the net force acting on it and is inversely proportional to the mass of the object.

For a given mass, if Fnet doubles, triples, etc. in size, so does a.

For a given Fnet if m doubles, a is cut in half.

Fnet and a are vectors and always point in the same direction.

Units

Fnet = m a

1 N = 1 kg m/s2

The SI unit of force is the Newton.

A Newton feels like about a quarter pound.

1 lb = 4.45 N An apple weighs about 1N

What Newton was really saying…

Greater net forces cause greater accelerations

Greater masses require greater net forces to accelerate at equal rates

Greater accelerations can occur if an object is smaller

What is Net Force?

Net force (resultant force) is the vector sum of all the forces, e.g., the “net effect.”

F1

F2

F3

Fnet

If Net force acting on object is zero….forces are said to “balanced”

and the object will not experience a change in velocity (will have a zero acceleration)

Newton’s 1st law If net force is zero, then object could

either be moving (with a constant velocity), or stopped.

Net Force & the 2nd LawWhen forces act in the same line, we can just add or subtract their magnitudes to find the net force.

2 kg

15 N 32 N

Fnet = 27 N to the right

a = 13.5 m/s2

10 N

Net Force and Newton’s 2nd Law

5 N10 kg

3N a=????

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/newtlaws/u2l3c.html

1

0

CD p16

4N

4NFnet =

Fnet =4N3N

5N

5N5N

5N

3N

CD p16

Fnet =3N

4N

3N

4N

Fnet =

5N2N

4N

Fnet = 5N

4N

2N

Fnet =

3N

9.9

9.9

07

CD p16

Find acceleration of the 10kg object…….

20.°80. °

50.N 150N

75N

A

B

C

Ax=hypCos20° Ay=hypSin20 °

=150NCos20° =150NSin20°

=140N =51N

Bx=hypCos100° By=hypSin100°

=50.NCos 100° =50.NSin100°

=-8.7N =49N

Cx=0NCy=-75N

Rx=140N + -8.7N

Ry=51N + 49N +-75N

Rx2 + Ry

2 = R2

R2=(131N)2 + (25N)2

R=133N, northeast

Fnet=maa= F m = 133N 10kg =13.3m/s2!!

W = mg, a specific application of F=ma

Weight = mass acceleration due to gravity.

This follows directly from F = m a. Weight is the force of gravity on a body. Near the surface of the Earth,

g = 9.8 m/s2.

Why, exactly, do heavier and lighter objects fall with the same acceleration???? Isn’t gravity pulling down on the heavier object more?? Shouldn’t it accelerate faster as a result of the larger force?

4. The force due to gravity on an object is called? weight

The quantity of matter in an object is called? mass

The amount of space an object occupies is called? volume

CD p12

5. The force due to gravity on 1-kg is 9.8 N

The force due to gravity on 5-kg is 49 N

The mass with a weight of 98 N is 10 kg

CD p12

w = mg

6. Find the weight of your physics book. Then complete the table.

Object Mass Weight

Melon 1 kg _____

Apple ______ 1 N

Physics Book ______ ______

Uncle Harry 90 kg ______

CD p12

0.1 kg

9.8 N

882 N

300 300

300150

CD p13

No!!!300150

100 300

CD p13

150

No!!!

500

830

1000

CD p13

Newton’s First Law of Motion

Is a variation of the 2nd Law, for cases of ZERO NET FORCE

An object with no net force acting on it is said to be in EQUILIBRIUM

An object in equilibrium will be stationary, or could be moving at a constant velocity.

Inertia

A moving body will continue moving in the same direction with the same speed until some net force acts on it.

A body at rest will remain at rest unless a net force acts on it.

Summing it up: It takes a net force to change a body’s velocity.

“An object in motion tends to stay in motion; an object at rest tends to stay at rest.”

What force acts on the ladder “in flight”?Draw a free-body diagram of the forces acting on the ladder

Mass and Inertia

Mass is the “origin” of inertia If an object has a large mass, then it will

have a large inertia If an object has a small mass, then it will

have a small inertia

Inertia Example 1

An astronaut in outer space will continue drifting in the same direction at the same speed indefinitely, until acted upon by an outside force.

Inertia Example 2If you’re driving at 65 mph and have an accident, your car may come to a stop in an instant, while your body is still moving at 65 mph. Without a seatbelt, your inertia could carry you through the windshield.

Inertia Demo

Inertia Demo

No Demo!!

1. An astronaut in outer space away from all forces throws a rock. What will happen to the rock?

The rock’s tendency to do this is called… inertia.

What is inertia?How is it measured?

CD p11

grams /kg.

CC

2. The rock is being whirled at the end of a string in a clockwise rotation.

What is the path of the rock when the string breaks?

A B

D

CD p11

7. Hit lead plate with hammer

CD p12

3. The bus is traveling at 100 km/h. Relative to the bus, the pencil is traveling at… 0 km/h.

Its horizontal velocity is100 km/h. As it drops, its horizontal velocity is 100 km/h.

Where will the pencil strike the floor?

Where will the pencil strike the floor if the bus is at rest?

Directly below where dropped.

Directly below where dropped.

CD p11

Newton’s 3rd Law…Action-Reaction

For every action force, there is an opposite, but equal reaction force

Action - Reaction If you hit a tennis ball with a racquet,

the force on the ball due to the racquet is the same as the force on the racquet due to the ball, except in the opposite direction.

If you drop an apple, the Earth pulls on the apple just as hard as the apple pulls on the Earth.

If you fire a rifle, the bullet pushes the rifle backwards just as hard as the rifle pushes the bullet forwards.

“For every action there’s an equal but opposite reaction.”

Apple pulls up on earth

Earth Pulls downOn apple

Forces are equal, but opposite

Earth / Apple 2

a = mm a

Apple’s big acceleration

Apple’s

little mass Earth’s little acceleration

Earth’s

big mass

The products are the same, since the forces are the same.

Action Reaction force Pair????

CD p15

The forces on the ball are…?

Lost in Space

Suppose an International Space Station astronaut is on a spacewalk when her tether snaps. Drifting away from the safety of the station, what might she do to make it back?

Demolition Derby

When two cars of different size collide, the forces on each are the SAME (but in opposite directions). However, the same force on a smaller car means a bigger acceleration!

Horse Cart ProblemAs a horse pulls forward on a cart, according to Newton’s Third Law, the cart must be pulling backward on the horse.

Newton’s Law also says that each of these forces must act in opposite directions, but be equal in magnitude

So…..it seems as if the forces are balanced, and that the horse and cart should not move (or accelerate). But they do….. Why???

Consider only the forces acting on the HORSE……

If net force is not zero, then horse will accelerate!!!

What about the wagon?? Consider only the forces acting on it.

Misconceptions If an object is moving, there must be

some force making it move. Wrong! It could be moving without accelerating.

If v = 0, then a, and Fnet must be zero. Wrong! Think of a projectile shot straight up at its peak.

An object must move in the direction of the net force. Wrong! It must accelerate, not move, that way.

Inertia is a force. False

Misconceptions 2 Heavy objects must fall faster than light

ones. Wrong! The rate is the same in a vacuum.

When a big object collides with a little one, the big one hits the little one harder than the little one hits the big one. Wrong! The 3rd Law says they hit it each just as hard.

If an object accelerates, its speed must change. Wrong! It could be turning at constant

speed.

Forces & Kinematics

1. Find net force (by combining vectors).

2. Calculate acceleration (using 2nd law).

3. Use kinematics equations:

vf = v0 + a t

x = v0 t + a t2

vf2 – v0

2 = 2 a x

Sample Problem 1

1. Fnet

2. a

3. v after 5 s

4. x after 5 s

Goblin 400 N Ogre 1200 N

Troll 850 N

Treasure 300 kg

= 50 N left

= 0.167 m/s2 left

= 0.835 m/s left

A troll and a goblin are fighting with a big, mean ogre over a treasure chest, initially at rest. Find:

= 2.08 m left

6.2 Using Newton’s Laws

Apparent Weight

The weight of an object that is sensed as a result of contact forces on it.

Weightlessness

Means there are NO contact forces acting on the object

Scales

A scale is NOT a weight meter. A scale is a normal force meter. A scale might lie about your weight if

– you’re on an incline.– someone pushes down or pulls up on you.– you’re in an elevator.

Your actual weight doesn’t change in the above cases.

Weight in a Rocket

U S A

You’re on a rocket excursion standing on a purple bathroom scale. You’re still near enough to the Earth so that your actual weight is unchanged.

The scale, recall, measures normal force, not weight. Your apparent weight depends on the acceleration of the rocket.

U S A

During the countdown to blast off, you’re not accelerating. The scale pushes up on you just as hard as the Earth pulls down on you. So, the scale reads your actual weight.

Rocket:

At rest on the launch pad

mg

N

m

a = 0

v = 0

U S A

mg

Rocket: Blasting Off

N

During blast off your acceleration is up, so the net force must be up (no matter which way v is).a

v Fnet = m a

N - mg = m a

N = m (a + g) > mg

Apparent weight > Actual weight

Rocket: Cruising with constant velocity

U S A

mg

N

m

If v = constant, then a = 0. If a = 0, then Fnet = 0 too. If

Fnet = 0, then N must be equal in magnitude to mg.

This means that the scale reads your normal weight (same as if you were at rest) regardless of how fast you’re going, so long as you’re not accelerating.

a = 0

v

Rocket: Engines on low

U S A

mg

m

a

v

As soon as you cut way back on the engines down, the Earth pulls harder on you than the scale pushes up. So you’re acceleration is down, but you’ll still head upward for a while. Choosing down as the positive direction,

NFnet = m a

mg - N = m a

N = m (g - a) < mg

Apparent weight < Actual weight

Friction Friction is the force bodies exert on each other

when in contact. The friction forces act parallel to the contact

surface Exerted against motion (opposite direction) The forces shown are an action-reaction pair.

Acme Hand Grenades

Fapplied

Ffriction constant v

Friction Facts Caused by

– electrostatic attraction between the atoms of the objects in contact

– microscopic particles banging into each other.

Like any force, can cause acceleration. Often results in waste heat/wear and

tear on parts Comes in action-reaction pairs.

Good or Bad?

Two Kinds of Friction Static friction

– Must be overcome in order to budge an object

– Present only when there is no relative motion between the bodies, e.g., the box & table top

Kinetic friction– Weaker than static friction– Present only when objects

are moving with respect to each other (skidding)

FAFs

FAFk

a to the right

v left or right

objects still or moving together

Coefficients of Friction

Static coefficient … s.

Kinetic coefficient … k.

Both depend on the materials in contact.– Small for steel on ice or scrambled egg on

Teflon frying pan– Large for rubber on concrete or cardboard box

on carpeting

The bigger the coefficient of friction, the bigger the frictional force.

Surface μs

Rubber on asphalt, dry 1.07Rubber on asphalt, wet 0.95Rubber on ice 0.005Rubber on concrete, dry 1.02Rubber on concrete, wet 0.97Steel on steel – dry 0.41Steel on steel – lubricated 0.12Steel on ice 0.01

Lubrication

Reduces friction by – separating two surfaces so

“high points” don’t hit each other

– Changing coefficient of friction to a lower value with a different material

– Includes using oil, graphite, teflon, etc.

Normal force Force exerted between two surfaces in

contact, perpendicular to the surface. If level surface, and object is resting on

surface, then……..

mg

FN FN = mg.

and, Fnet = 0;

hence a = 0.

m

Normal forces aren’t always up“Normal” means perpendicular. A normal force is always perpendicular to the contact surface.

But it isn’t always equal to mg!!!!!

N

mg

Normal force directions Up

– You’re standing on level ground.

– You’re at the bottom of a circle while flying a loop-the-loop in a plane.

Sideways– A ladder leans up against a wall.

– You’re against the wall on the “Tom’s Twister” ride when the floor drops out.

At an angle– A race car takes a turn on a banked track.

Down– You’re in a roller coaster at the top of a loop.

Cases in which N mg

N

mgmg

N

mg

N FA

a

1. Mass on incline

2. Applied force acting on the mass

3. Nonzero acceleration, as in an elevator or launching space shuttle

When does N = mg ?

If the following conditions are satisfied, then N = mg:

The object is on a level surface.

There’s nothing pushing down or pulling it up.

The object is not accelerating vertically.

Friction MagnitudeThe magnitude of the friction force is

proportional to: how hard the two bodies are pressed

together (the normal force, N). the materials from which the bodies are

made (the coefficient of friction, ).

Attributes that have little or no effect: sliding speed contact area

FF= FN

Static Friction ForceFs s N

static frictional force coefficient of

static friction

normal force

Fs, max = s N

maximum force of static

friction

fs, max is the force you must exceed in order to budge a resting object.

Static friction force varies Fs, max is a constant in a given problem, but Fs varies.

Fs matches FA until FA exceeds Fs, max.

Example: In the picture below, if s for a wooden crate on a tile floor is 0.6, Fs, max = 0.6 (10 Kg ) (9.8m/s2) = 58.8 N.

10 kgFA = 27 NFS = 27 N

10 kgFA = 43 NFs= 43 N

10 kgFA = 66 N

finally budges

Fk

Kinetic Friction

Once object budges, forget about s.

Use k.

fk is a constant so long as the materials

involved don’t change. There is no “maximum fk.”

Fk = k N

kinetic frictional force coefficient of

kinetic friction

normal force

values

Typically, 0 < k < s < 1.

This is why it’s harder to budge an object than to keep it moving.

If k > 1, it would be easier to lift an object and carry it than to slide across the floor.

Dimensionless (’s have no units, as is apparent from FF = N).

Friction Example 1

Barrel o’ Monkeys 14.7 kg

You push a giant barrel o’ monkeys setting on a table with a constant force of 63 N applied sideways. If k = 0.35 and s =0.58, when will the barrel have moved 15 m?

answer: Never, since this force won’t even budge it!

63 < 0.58 (14.7) (9.8) 83.6 N

A desk has a mass of 30. kilograms. If the coefficient of static friction between the desk and the floor is 0.48, what force must be used to move the desk from rest? 141N

Once the desk above is in motion, what force must be used to keep it moving at a constant velocity if the coefficient of kinetic friction is 0.32? 94N

What will the acceleration of the box be if a force of 120N is applied sideways to the box?

First, calculate NET force acting on the box…

Then, use F=ma to find acceleration

0.87m/s2

Drag

Friction-like force exerted on objects moving through a fluid such as air or water.

Acts in opposition to motion

Apollo 15 returning to earth

Model of Leonardo da Vinci’s parachute

Air Resistance R depends on:

– Relative velocity (approximately proportional to v2)

• Faster speed = greater drag

– cross-sectional area• Larger area = greater drag

– air (fluid) density– other factors like shape

R is not a constant; it changes as the speed changes

mg

m

R

Turbulent flow

Streamlined/laminar flow

a streamline is a line which is everywhere tangent to the velocity of flow

Airplane wing in “stall”, which is a condition of loss ofLift due to turbulence over wing instead of laminar flow

1921 Rumple, drag coeff. .27, compared to 1984 average of .40

Traveling as fast as it can…..Draw a Free Body diagram. Include engine thrust, friction, drag.

Terminal Velocity

As an object falls faster, the amount of drag force increases.

When the drag force equals the force due to gravity of the object, the object will be in equilibrium

The object ceases to accelerate, and has reached “Terminal Velocity”

Period (Harmonic) Motion

Simple Harmonic motion is caused by a “Restoring Force” that results from a displacement of some object or material from rest position.

The distance of the displacement is called the “Amplitude”

The “period” is the length of time (T) needed to complete one cycle of motion

The period is independent of the mass.

The period depends only on the pendulum’s length.

The period = T = 2

Facts about the Simple Pendulum

gL

Restoring force on pendulum is gravity!

Don’t confuse the symbol T, which is used for both period and tension.

Mass on Spring

Spring Oscillator Applet

T = periodm= massk = spring constant (larger for stiffer springs)

Harmonic Motion 1

Resonance

Sometimes, when small forces are applied repeatedly to an object, the object will vibrate with larger and larger displacements….this is resonance

Tacoma Narrows Bridge video

The relatively new bridge over the Tacoma Narrows collapsed in 1940 as a result of mechanical resonance brought on by wind blowing through substructure of bridge.

Wind caused eddy currents which applied alternating forces which ultimately destroyed the bridge.