WHAT DO OBJECTS DO WHEN

NO FORCE IS ACTING ON THEM ??????

An Historical Overview

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Aristotle (384 -322 B.C.) :

objects would seek their natural resting places: apple on the ground and smoke high in the air like the clouds.

of CELESTIAL objects (Moon, planets, stars, Sun) was circular - without beginning or end.

no need for gravity to explain this motion – it is JUST NATURAL – what a life for physics

student!!!!

of TERRESTRIAL bodies (apple, smoke, you) was for light things to rise up and heavy things to

fall

was imposed motion – result of forces that pushed or pulled.

Important: violent motion had an external cause, it was not natural to the objects

THOUGHT FOR NEARLY 2000 YEARS: IF AN OBJECT WAS MOVING, IT IS AGAINST ITS NATURE AND THE FORCE OF SOME KIND WAS

RESPONSIBLE.

NO FORCE – NO MOTION, No wonder that most thinkers before the 16th century consider it obvious that the Earth must be in its natural resting place and

assumed that the force large enough to move it was unthinkable, it was clear that Earth did not move.

Conclusion: EARTH is THE CENTER OF UNIVERSE

And in this intellectual climate of the 15th century Nicolaus Copernicus (1473-1543) formulated, in secret to escape persecution, his famous HELIOCENTRIC THEORY – idea that was extremely controversial at the time - the Earth is just a small planet and together with other planets

circle around Sun.

Only in the final days of his life he sent his ideas to the printer. The first copy of his work, De Revolutionibus, reached him on the day of

his death.

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Lets look at animated model of solar system and universe in general Remember when we talked about speed of our Earth:

• 0.4 km/s (0.25 mi/s) rotating around the center of the Earth • 30 km/s relative to the Sun• at about 250 km/s relative to the center of our galaxy• together with the whole galaxy at 600 km/s (1.34 million mi/h) in the direction of the constellation Hydra.).

Here is a wonderful animation

http://www.youtube.com/watch?v=0jHsq36_NTU

Thank you Mr. Dyer -

One of his most outspoken supporters was Galileo Galilei, the foremost scientist of late-Renaissance Italy.

It took the genius of Galileo to claim that NO FORCE is needed to keep an object in the motion (straight-line, constant speed)

Galileo argued (brainstorm – just pure thought – no experimental proof) that forces only CHANGE THE MOTION, not cause the motion Left alone the things would travel in a straight line with constant speed forever. It is the force of friction that slows them down.

Aristotle: It is the nature of the ball to come to rest.Galileo: In the absence of friction the ball would keep on moving. No force needed to maintain the motion. The force changes the motion – velocity.

Every object resists change to its state of motion/velocity. To change it, the force must act on it. We

call this resistance INERTIA.

Galileo’s findings about motion and his concept of inertia discredited Aristotle’s theory of motion.

So why in the world do we STILL sometimes think the same way???

Think, Pair, ShareAristotle’s views of motion were

discredited almost 400 years ago. So why do we still tend to follow his thinking about motion?

On Christmas day in the year Galileo died

By the age of 24 he gave the world his famous three laws of motion.

Isaac Newton (1642-1727) was born.

Together, Galileo and Newton discredited the Aristotelian view of motion and developed the theories that still form the basis of mechanics today.

Forces throughout History

Before we talk about force, let us introduce inertia, mass and

weight.

Inertia is resistance an object has to a change of velocity. • sort of laziness (inerzia – laziness in Italian)

Important Vocab

Inertia is resistance an object has to a change of velocity. • sort of laziness (inerzia – laziness in Italian)

Mass is numerical measure of the inertia of a body • more mass – harder change of velocity is a measure of the amount of matter in the object • depends only on the number and kind of atoms in it. • doesn’t depend on the location of the object • If the object has mass of 1 kg here on earth it would have the mass of 1 kg on the moon, but it would weigh only one-sixth as much.Weight is the gravitational force acting on an object. • acting straight down toward the center of the earth (moon …) • depends on the location of the object. • depends on its mass and acceleration due to gravity:

W = mg unit: 1 N

unit: 1 kg

• An interaction between two objects involving a push or a pull

• Causes objects to accelerate

NOTE: ALL forces are INTERACTIONS between 2 objects

Forces are vector quantities, having both direction and magnitude.

unit: Newton (N) = kg m/s2

1 N is the force that causes a 1-kg object to accelerate 1 m/s2.

Forces

The net force – resultant force is the vector sum of all forces acting on ONE

object.

Applied forces Net force

the object accelerates as if only one force – net force is applied

Fnet or ΣF

Check your understanding

Galileo’s Law of inertia

if ΣF = 0, a = 0 no change in velocity, thenAn object continues in motion in a straight line at

constant speed or at rest unless acted upon by a net external force."

"How many ways can you state Newton's First Law?"

Remember: net force (sum of all forces acting on an object) causes acceleration /change in velocity of that object

BIG IDEA 1: Zero NET force means no acceleration / no change in velocity. Balanced forces will not cause acceleration.

BIG IDEA 2: An object is in equilibrium (i.e. it has zero net force) whenever it has constant velocity (including constant velocity of 0).

Definition:

If the net force acting on an object is zero, the speed and direction of the motion will not change (the object won’t accelerate). If it was at rest it will stay at rest, and if it was in motion it will continue the motion with constant velocity (in the straight line at constant speed) .

We say the object is in EQUILIBRIUM.

Translational equilibrium

Since velocity is constant, the body is in translational equilibrium:

2. object is moving at 3 m/s in a straight line.

Two forces are acting on it. Find

- which means that the object’s acceleration is zero - therefore net force is zero

● F = 8N, 00

how to apply concept of translational equilibrium: 1. Two forces are acting on a body. Describe the motion of the body.

Since the net force on this body is zero, it is in equilibrium:

- which means that the object is not accelerating - the body is either at rest, or is moving with a constant

velocity 8 N F

F

8 N 8 N

if = 0 then = 0, change in velocity = 0 and velocity is constant or zero

equilibrium math:

if velocity is constant or zero, then = 0, and = 0

Six force are acting on an object. What can you tell about the motion of that

object? Is it at rest? Is it moving? If it is moving, how?

The tendency of moving objects to continue in motion can have very unpleasant consequences.

Seat belts: Passenger and the vehicle share the same destiny. The seatbelt provides the force to keep the driver from moving out of the position

No seat belts: The passengers maintain their state of motion unless there is a force strong enough to stop them. The passengers can become projectiles and continue in projectile-like motion.

In a car accident, the safest place to be is in the car; yet in a motorcycle accident, the worst place to be is on

the motorcycle.

Car: Wear your seat belt. Remember it's the law - the law of inertia.

Law of inertia would safe you from sharing the fate of the motorcycle itself .

No functioning straps: the ladder in motion would continue in motion. Assuming a

negligible friction between the truck and the ladder, the ladder would slide off the

top becoming a projectile.

Imagine you have two baskets of strawberries. You place one on the passenger seat of the car, near the car door. The other you forget on top of the car. Oops!

Like pancakes for the French club meeting. Still remember

You then drive out of the parking lot, turning at a constant speed. What happens to each basket of strawberries, and why?

Although the car accelerates (changes direction!) , the baskets will tend to continue in the same straight line motion unless a force stops them.

greater mass – greater inertia (laziness) – smaller acceleration more force – greater acceleration

The acceleration of an object produced by a net force on that object is directly proportional to the net force applied, and inversely proportional to the mass of the

object.Direction of the acceleration is in the direction of the

net force,

The acceleration of an object produced by a net force on that object is directly proportional to the net force applied, and inversely proportional to the mass of the

object.Direction of the acceleration is in the direction of the

net force,

If net force is zero, acceleration is zero, velocity is constant (or zero).

The object is in translational equilibrium.

𝑎=∑𝐹

𝑚

Even Spiderman has the weight, right?Pulling him downward.what propels him upward?

His muscles? Hm…. No!!!!!!

Just imagine Spiderman hanging on a rope.

Can his muscles help him to climb up into the thin

air?????

To understand what propels us forward ( or, if someone choses backward) we’ll introduce third Newton’s law and come back to this problem later.

In every interaction, the forces always occur only in pairs, BUT these forces act on two different

bodies.

Common definition: - to every action there is an equal and opposite reactionis very dangerous, so please do not use it. It is not defined what is action and what is reaction, so it looks as if we were talking about one body, but that’s not true.These forces act on different bodies.

Whenever object A exerts a force on object B, object B exerts an equal in magnitude and

opposite in direction force on object A.

Whenever object A exerts a force on object B, object B exerts an equal in magnitude and

opposite in direction force on object A.

YOU CAN’T TOUCH

WITHOUT BEING

TOUCHED

You push the water backward, the water pushes you forward.

action: tire pushes roadreaction: road pushes tire

action: foot pushes the groundreaction: the ground pushes the foot that propels the turtle forward

action: cannon pushes the cannonballreaction: cannonball pushes the cannon (recoil)The same force F (opposite direction), BUT

cannonball:

cannon:

a

=

Fm

a =

Fm

action: earth attracts ball a = F/m = 9.80 m/s2

reaction: ball attracts earth aE = F/ME ≈ 0

Koka, the clever horse, taught physics by Mrs. Radja says:

You taught me Newton's third law: to every action there is an equal and opposite reaction.

Please help me! Why don’t action and reaction forces cancel? Should I find myself a less educated horse, or should I teach

better?

It says that if I pull on the wagon, the wagon pulls me back. If these two forces are equal and opposite, they will cancel, so that the net force is zero, right? So the wagon can never move! Since it is at rest, it must always remain at rest! Get over here and unhitch me, since I have just proven that Newton's law says that it is impossible for a horse to pull a wagon!

Only the forces that act on the same object can cancel. Koka: when the ground pushes forward on the horse harder than the cart pulls backward Koka accelerate forward. (Fnet = F1

’ – F2’ > 0)

Cart : accelerates forward when horse force is greater the frictional force

When we want to find acceleration of one body we have to find all forces acting on that particular body.

Forces between roller-skaters

If one skater pushes another, they both feel a force.

The forces must be equal and opposite, but the acceleration will be different since they have different masses.

The person with a smaller mass will gain the greater velocity.

A roller-skater pushes off from a wall

The force on the girl causes her to accelerate

backwards.

The mass of the wall is so large compared to the girl’s mass that the force on it does

not effectively cause any acceleration.

It looks unbelievable but it is true.

when they clinch forces are equal – you would expect thatwhen they clinch forces are equal – would you expect that?

Sudden acceleration can kill

again, the same force but different acceleration

Our organs are not firmly attached to anything.

When head is hit it gains acceleration. But the brain was not hit.

It continues with the same velocity. Skull and brain crash!!!!!

again, the same force but different acceleration

So what propels him upward?Upward force exerted by the WALL !!!!Friction force!!!!!He is pushing wall downwards and the wall is …..

𝐹 𝑓𝑟

𝑚𝑔

𝑚𝑔

Exit Ticket

1. How many horizontal forces are acting on the person? Label them

2. Draw free body diagram for the cart?

physics

Tension: the force that the end of the rope exerts on whatever is attached to it. Direction of the force is along the rope.

T1T2

T2

Normal force (support force, normal reaction force)

The force which is preventing an object from falling through the surface of another body .

The normal force results from strong repulsive electromagnetic force between electrons of two bodies. The atoms in the

surface are compressed microscopically to create the normal force. The surface deforms slightly and produces a reaction

force equal to the force pressing the object into the surface.

That’s why normal force is always perpendicular (normal) to the surfaces in

contact.

Existence: by evidence – object is not accelerating in vertical direction,

therefore, the vertical net force must be zero

For an object sitting on a horizontal surface, the normal

force is equal to the weight of the object.

= m = 0

Fn – mg = 0

Fn = mg

For an object sitting on a horizontal surface, the normal

force is equal to the weight of the object.

= m = 0

Fn – mg = 0

Fn = mg

mg mg

𝐹

mg

𝐹

If there is a force F trying to lift up the object, it helps the normal force – the clever desk doesn’t need to

exert so much force

If there is a force F trying to lift up the object, it helps the normal force – the clever desk doesn’t need to

exert so much force

= m = 0

Fn + F – mg = 0

Fn = mg – F

= m = 0

Fn + F – mg = 0

Fn = mg – F

If there is push down force – the desk has to exert more

force

= m = 0

Fn – F – mg = 0

Fn = mg + F

If the desk can not exert enough force it will break

𝐹 𝑛 𝐹 𝑛

𝐹 𝑛

Friction force Ffr

NWWWWWWWWWWWWWW

Friction is a force that is created whenever two surfaces move or try to move across each other. 

Friction always opposes the motion or attempted motion of one surface across

another surface.

¨ Friction is dependent on the texture/roughness of both surfaces.

¨ Friction acts parallel to surface in direction opposed to intended motion.

Friction is also dependent on the force which presses the surfaces together, normal

force. 

Ffr = m Fn

coefficient of proportionality μ is called coefficient of friction

m has no units it is a measure of surface-to-surface roughness depends on characteristics of both surfaces

different values for static and kinetic coefficient of friction (tables). kinetic μ is smaller than static μ. You probably noticed that once you moved something from rest it becomes easier to push around.

Ffr

Fn

mg

pulling force

surface-on-surface μs μk

hook velcro-on-fuzzy velcro >6.0 >5.9

avg tire-on-dry pavement 0.9 0.8

grooved tire-on-wet pavement 0.8 0.7

glass-on-glass 0.9 0.4

metal-on-metal (dry) 0.6 0.4

smooth tire-on-wet pavement 0.5 0.4

metal-on-metal (lubricated) 0.1 0.05

steel-on-ice 0.1 0.05

steel-on-Teflon 0.05 0.05You 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.

At the points of direct molecular contact, electrons become confused.They forget which object they belong to, and wind up trying to orbit nuclei in molecules of both! The resulting bond is called molecular adhesion or a “cold-weld.”Each time they form a bond between uneven surfaces, force is required to break this bond 

1. Mechanical interlocking of "rough" surfaces – teeth on the surfaces

Origin of friction :

On an atomic scale, few surfaces are very smooth. Bumps far smaller then we can see loom like mountains to an atom.

Thoughts of an electron with an identity crisis...

2. Microscopic level –

Air Resistance and Terminal Velocity

If a raindrops start in a cloud at a height h = 1200m above the surface of the earth they would hit us at 340mi/h; serious damage

would result if they did. Luckily:

When an object moves through air or any other fluid, the fluid exerts drag force on the moving object. Unlike the friction between

surfaces, however, this force depends upon the speed of the object, becoming larger as the speed increases. It also depends upon the size and the shape of the object and the density and kind of fluid.

A falling object accelerates due to the gravitational force, mg, exerted on it by the earth. As the object accelerates, however, its

speed increases and the drag on it becomes greater and greater until it is equal to the weight of the object. At this point, the net force on the falling object is zero, so it no longer accelerates. Its speed now

remains constant; it is traveling at its terminal speed. Terminal speed occurs when

the weight force (down) is equaled by the drag force (up).

Terminal velocity of table tennis ball is 9 m/s after approximately 10 m. A basketball has a terminal velocity of 20 m/s after approximately 47 m.; the terminal velocity of a baseball is 42 m/s after approximately 210 m. Skiers increase their terminal velocity by decreasing the drag force. They hold their bodies in egg shape and wear smooth clothing and streamlined helmets. How do skydivers control their velocity? By changing body orientation and shape, sky divers can both increase and decrease their terminal velocity. (60 m/s after approximately 430 m)

Parashoot – 5 m/s after approximately 3 m.

AND THE RAINDROP?How fast is a raindrop traveling when it hits the ground? It travels at 7m/s (17 mi/h) after falling approximately only 6 m. This is a much “kinder and gentler” speed and is far less damaging than the 340mi/h calculated without drag.

a. parachutist that has just stepped out of the airplane.

b. parachutist is falling at increasing speed.

a = g

c. parachutist is traveling downward with constant velocity (terminal velocity)

=

=

mg

mg

air

mg

air

Σ

Σ = 0

Σ𝐹=𝑚𝑔𝑎=𝑚𝑔𝑚

Fnet = 0

a < g

the speed is still increasing, and therefore air friction too until

Draw all forces that act on a parachutist. Find and acceleration for

Σ𝐹=𝑚𝑔−𝐹 𝑎𝑖𝑟𝑎=𝑚𝑔−𝐹𝑎𝑖𝑟

𝑚

a = 0

Forces are usually divided into two types or classes.

● Contact forces, arising because of physical contact between objects. For example when you push on a door to open it or throw or kick a ball, you exert a contact force on the door or ball.

● Field forces – there is no need for contact for these forces to act: for example if you sit on a tree there is gravitational force acting on you (by the way you are attracting the Earth by the force equal in magnitude but opposite in direction, only the earth is too big for any meaningful acceleration, unlike you. If the branch breaks there is no normal force acting on you – you are not in equilibrium any more, ΣF = mg, and you are falling with acceleration of 9.8 m/s/s)

Contact ForcesFrictional Force

Tension Force

Normal Force

Air Resistance Force – Drag Force

Applied Force

Spring Force

Field ForcesGravitational Force

attraction between objects due to their masses

Electromagnetic Forcebetween charges

Strong Nuclear Forcekeeps nucleus together

Weak Nuclear Forcearise in certain radioactive processes

At the atomic level – all contact forces are result of repulsive electromagnetic forces (at very small

distances)

That means that objects have no actual contact, but their electric fields (outer electrons repel each other)

Although there are many different contact forces, they are all some form of only four different fundamental field

forces existing in the nature.

One of the most significant intellectual achievements in the history of thought. It is universal – it applies to all objects regardless of their location anywhere in the Universe.

Every object in the universe attracts every other object. The force between two objects is proportional to their masses

and inversely proportional to the square of the distance between their centers. The force acts along the line joining

the two objects.

1 22

m mF = G

r G = 6.67x10-11 Nm2/ kg2 – “Universal gravitational constant” the same value anywhere in the universe - very small value – no significant forces of attraction between ordinary sized objects.

r

rE – Earth’s radius mE – Earth’s mass. E E

2 2E E

m m mF = G = G m = gm

r r

2E2E

mg = G = 9.80m/s

r

The force between an object of mass m close to the Earth surface and the Earth

Force between an object of mass m close to the Earth surface and the Earthis commonly called weight W = mg.

Now we can see that the gravitational acceleration g is a consequence of the gravitational force. Its magnitude depends on how far is the object from the center of the earth.

Double the distance from the centre, r = 2 rE , g is 4 times less, g = 2.45 m/s2 , and so is weight

STEPS

The most important one firstDraw free body diagram/force diagram

Draw free body diagram/force diagramDraw free body diagram/force diagram

sketch of an object and all forces acting on that object

No velocity on that diagram, no acceleration on that diagram,

only object (circle or a box, and you can write mass in it)

and all forces acting on that object

Second step is to find net force

Third step is to apply second newton’s law

How to draw a force diagram

2. Make a simple sketch of the system – point system

1. Choose ONE body to be isolated

dog or the cart?

FWWWWWWWWWWWWWW

fr

mgWWWWWWWWWWWWWW

FWWWWWWWWWWWWWW

dog

3. Identify forces that act on the system Label them on diagram

4. Find out the net force by adding the force vectors

decision: cart

5. Apply Newton’s second law

netF = ma

𝐹 𝑛

ΣF

VECTOR EQUATION ??????

So

1. Add all vectors to get net force

2. Apply newton's second law

Don’t worry, there is an easy way out.

Are you kidding me??

= m

Separate everything into vertical and horizontal components/motion

And remember that magnitudes of forces are positive

Howard, the soda jerk at Bea’s diner, slides a 0.60-kg root beer from the end of the counter to a thirsty customer. A force of friction of 1.2 N brings the drink to a stop right in front of the customer. a) What is the acceleration of root beer? b) What is the coefficient of kinetic friction between the glass and the

counter?c) If the glass encounters a sticky patch on the counter, will this spot have a

higher or lower coefficient of friction?

Ffr = Fn Ffr / = 1.2/6.0

= 0.20 (no units)

0.60 kg

Ffr

Fn

mg = 6N

Vertical acceleration = 0Vertical force ΣF = 0

Fn – mg = 0

Fn = mg = 6.0 N

Vertical direction: Horizontal direction:Resultant force = friction forceΣF = Ffr =1.2 N

ΣF = ma1.2 = 0.60 = 2.0 m/s2

c. higher

ΣF

We read this as : SUM of (all) forces, not as SOME of forces

Although they sound the some, there is a HUGE difference

Thank you Mr. Bruhn for clarifying possible confusion -

A boy exerts a 36-N horizontal force as he pulls a 52-N sled across a cement sidewalk at constant speed. What is the coefficient of kinetic friction between the sidewalk and the metal sled runners? Ignore air resistance.

W = mg = 52 N m = 5.2 kg

Vertical direction:

Vertical acceleration

= 0

Vertical ΣF = 0

Fn–mg = 0

Fn = 52 N Horizontal direction: v is constant, a = 0 and ΣF = 0 Ffr = F = 36 N

Ffr = μ Fn Ffr / = 36/52

= 0.69

A force of 40.0 N accelerates a 5.0-kg block at 6.0 m/s2 along a horizontal surface.a. How large is the frictional force?b. What is the coefficient of friction?

m = 5.0 kg F = 40.0 N a = 6.0 m/s2

Vertical direction:

a = 0, so ΣF = 0

Fn = mg = 50 N → Ffr = μ Fn

= 50 μ horizontal direction: a = 6.0m/s2 ΣF.= ma F – Ffr = ma 40.0 – Ffr = 30 Ffr = 10 N

Ffr / = 10/50 = 0.2

Ffr = μ Fn

Luke Skywalker starts to pull a sled with Princess Leia across a large ice pond with the force of 100 N at an angle of 30.0° with the horizontal (with nails on his shoes). Find normal force and initial acceleration if the weight of sled and Princess Leia is 800 N and the friction force is 40 N.

free body diagram components

mg = 800 N m = 80 kg F = 100 N Ffr = 40 N

vertical direction :ΣF=0 F sin θ + Fn–mg

= 050 + Fn = 800 Fn = 750 N

Horizontal direction: ΣF= ma F cos θ – Ffr = ma

86.6 – 40 = 80 a

a = 0.58 m/s2

INCLINE

An object is on incline θ.

Ffr

Fn

Ffr

Fn

We know that acceleration perpendicular to the surface is zero; acceleration can be only parallel to incline.

Now instead of three forces,

we have four forces

direction perpendicular to the incline: ΣF = ma = 0 → Fn–mg cos θ = 0 → Fn = mg

cos θ

Force pressing the object into the surface is not full weight mg, but only part of it, So the normal force acting on the object is only part of full weight mg: Fn = mg cos θ

If the surface is horizontal: θ = 00 → Fn = mg

If the object is in free fall not pressing the surface: θ = 900 → Fn = 0

Therefore the most natural choice of coordinate system / components is:

● one parallel to the incline ● one perpendicular to the incline.

A cute panda, m = 60 kg, is sliding down an iced incline 300. The ice can support up to 550 N. Will bear fall through the ice? If the coefficient of the friction is 0.115, what is the acceleration of the bear?

m = 60 kg θ = 300

= 0.115 g = 10 m/s2

Perpendicular direction: ΣF = ma = 0 Fn - mg cos θ = 0 Fn = 520 N < 550 Nice can support him, but he should not eat too much

Parallel direction: ΣF = ma mg sin θ – Ffr = ma 300 – 60 = 60 a a = 4 m/s2

cute panda is speeding up!!!!

Ffr = μ Fn = 60 N

Question:

How does the apparent weight of a person in an elevator depend on the motion of that elevator?

What will the scale show if the elevator is

1. at rest or moving up with constant speed

2. speeding up ( ↑ )

3. slowing down ( ↓ )

m = 65 kg

Newton’s 3. law: Force with which the person acts on the scale (reading of the scale) is equal to the normal force on the person.

So, if we find normal force we know the reading of the scale, so called APPARENT WEIGHT

1. draw free body diagram 2. choose upward positive 3. apply Newton’s 2. law : ΣF = ma

mgWWWWWWWWWWWWWW

Fn – mg = ma = 0 → Fn = mg = 650 N

apparent weight = weight = 650 N

+

1. elevator is at rest or moving up with constant speed

1.2. elevator is speeding up: ( ↑ )

mgWWWWWWWWWWWWWW

Fn – mg = ma → Fn = mg + ma = 845 N

apparent weight > weightthe scale would show more, and you would feel heavier

1.3. elevator is slowing down: ( ↓ )

mgWWWWWWWWWWWWWW Fn – mg = ma → Fn = mg + ma = 650 N – 195 N = 455 N

apparent weight < weightthe scale would show less, and you would feel lighter

Fn

Fn

Fn

A system of two cables supports a 150-N ball as shown.

a) What is the tension in the right-and cable?b) What is the tension in the horizontal cable?

mg=150N

𝑇 1𝑇 2

x: ΣF = 0 T1 cos 300 – T2 = 0 T2 = 260 N

y: ΣF = 0 T1 sin 300 – 150 = 0 T1 = 300 N

WHEN THERE ARE TWO BODIES YOU HAVE TO DRAW TWO BODY

DIAGRAMS !!!!!!

Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find a) the magnitude of the acceleration of each block b) tension force on the blocks

the same string – the same tensionthe same acceleration, except that 110 g accelerate down, and 90 g accelerate up.

ΣF = ma a is upT – mg = ma T – 0.9 = 0.09a first equation

ΣF = ma a is downmg – T= ma 1.1 – T = 0.11a second equation

two equations with two unknowns

T – 0.9 = 0.09a (1) 1.1 – T = 0.11a (2)

(1) + (2): 0.2 = 0.2 a a = 1 m/s⟹ 2

T = 0.09a + 0.9 T = 0.99 N ⟹

A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right.

 

a) What is the magnitude of the acceleration of the 40-kg block?b) What is the magnitude of the tension T in the rope that connects the two blocks? As these two objects are connected

with the same rope, tension is the same and acceleration is the same for two objects.

ΣF = maT = 10a a is to the right

50 – T = 40a a is to the right

2 EQS with 2 unknowns 50 – 10a = 40a a = 1 m/s2 T = 10a T = 10 N

Click me