Chapter 5Forces

Force & Vectors

Forces

• Kinematics: Describes how an object moves

• Dynamics: Describes why an object moves

• Newton’s three laws of motion, describe the “dynamics” of why objects move

Forces and Interaction

• Force – a “push or pull”

• Contact Force – you physically push on a wall

• Long-range Force – like magnets or gravity

• Force – a vector quantity. Has what two parts.

• SI Unit – the Newton abbreviated as “N”

• Superposition of Forces : forces combine according to vector addition

4 Types Forces• Gravitational forces

• The Earth pulls and holds the moon in orbit• The moon pulls and causes tide changes

• Electromagnetic forces• due to electric charges, both static and moving.

• Strong Nuclear Forces • holds particles in the nucleus together. (Strongest

of the 4)• Weak Nuclear Forces

• Radioactive decay

Newton’s Three Laws of Physics

The apple was at rest, what started it in

motion?

Why did the apple accelerate?

Newton’s 1st Law

• An object at rest will stay at rest unless a force acts on it.• Here, the girl is at rest until acted on by the force imposed

by the cannonball.

Newton’s 1st Law

Newton’s 1st Law• An object at rest will stay at rest unless a force

acts on it.• Here, the skateboard/log combination is at rest

until acted on by the force imposed by the rocket.

Newton’s 1st Law• An object in motion will continue in a straight line until

acted on by some “outside” force.

• Consider a baseball that is pitched to a batter. What force causes the ball to change direction?

Hit

Newton’s 1st Law

• An object in motion will continue in a straight line until acted on by some “outside” force.

• Consider the space shuttle turning while in space flight. What produces the forces?

Newton’s 1st law• An object in motion will continue in a straight line

until acted on by some “outside” force.

• Consider the space shuttle when landing. What produces the forces?

Multimedia

• The car and the wall

• The motorcyclist

• The truck and the ladder

Weight and Mass

Mass:

A measure of the amount of matter in an object has.Symbol (m) Unit (kg)

Weight:

The gravitational force exerted on a body

Symbol (W) Unit (N Newton)

W mg

Weight

A Motor cycle weights 2450N. What is its mass?

W mg /m W g

2

2450

9.8 ms

Nm

250m kg

Homework

• WS 5a 1-10

• WS 5a (b) 1-11

Newton’s 2nd Law

Newton’s 2nd Law

• Acceleration is directly proportional to the magnitude of the net force.

• Acceleration is inversely proportional to the mass of the object.

Newton’s 2nd Law

netFam

F ma

• Acceleration depends on both mass and the net force

Acceleration depends on net force

• A force of 10N accelerates the box

Acceleration depends on net force

• A force of 20N accelerates the box twice as fast

Acceleration depends on mass

• A force of 10N accelerates the box

Acceleration depends on mass

• A force of 10N accelerates the smaller box faster

Free-body diagrams WS 5b #1

Draw the free-body diagram for a book is at rest on a table top. normalF

gravityF

A girl is suspended motionless from a bar which hangs from the ceiling by two ropes. A free-body diagram for this situation looks like this:

gravityF

tensionFtensionF

Free-body diagrams WS 5b #2

An egg is free-falling from a nest in a tree. Neglect air resistance. A free-body diagram for this situation looks like this:

gravityF

Free-body diagrams WS 5b #3

A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. A free-body diagram for this situation looks like this:

gravityF

normalF

appFfrictionF

If the net force is zero, there is no acceleration

If the net force is not zero, there is acceleration

Net Force

• If there is no movement–The net force is zero

• If there is no acceleration–The net force is zero

• If there is acceleration–The net force is not zero.

Homework

• WS 5b (FBD)– 3-10

Newton’s 1st Law Equilibrium Situation

• An object at rest will stay at rest unless a force acts on it.

• An object in motion will continue in a straight line until acted on by some “outside” force.

Newton’s Second Law – Non-Equilibrium Situation

• The result of a Non-Equilibrium situation is that the body, will begin to move.

amFFFF

...321

1F

1F

2F 1F F ma

1 2F F F ma

Newton’s Second Law – Non-Equilibrium Situation

• Two 50g masses are placed 40cm on either side of a fulcrum. What is the Net force?

• If left mass slides 20cm right, what happens?

• If the left mass slides 20cm right and grows to 100g, what type of situation is this?

amFFFF

...321

Newton’s 2nd law e.g.• What net force is required to accelerate a

1500kg race car at 3.0m/s2?

F ma21500 (3.0 / )F kg m s

4500F N

A truck with a mass of 710kg starts from rest and travels 40m in 3.0s

What Fnet acts on the car?

21

1

2d v t at

2

2da

t 2

2(40 )

3

ma

s

28.8 ms

a

6248F N

F ma

Newton’s 2nd law e.g.

Newton’s 2nd law e.g.

A 873kg dragster, starting from rest, accelerates to a speed of 26.3m/s in .59s

a) Find the acceleration

b) Find the average force on the dragster

2 1v v at 2 1v va

t

244.6 m

sa

F ma 38935F N

Newton’s 2nd law WS5d #1• An artillery shell has a mass of 55kg. The

shell leaves the 1.5m long barrel at a velocity of 770m/s.

• What is the force the gun applies to the shell?– Step 1 Find the acceleration– Step 2 Find the Net Force

Newton’s 2rd Law WS5d #1• What is the force the gun applies to the shell?

2 22 1 2v v ad

2 22 1

2

v va

d

2 2(770 ) (0 )

2(1.5)

m ms sa

m

F ma

2

555 (2 10 )ms

F kg x

71.1 10F x N2

52 10 ms

a x

Newton’s 2rd Law WS 5c #5

• A car, mass 1225kg traveling at 105km/hr slows to a stop in 53m.

• What is the size and direction of the force that acted on the car?

– Step 1 Unit conversion km/hr to m/s– Step 2 Find the acceleration– Step3 Find the Force

Newton’s 2nd Law WS 5d #51000 1

105 ( )( ) 29.21 3600

km mhr s

m hr

km s

2 22 1 2v v ad

2 22 1

2

v va

d

F ma

9800F N

28.0 ms

a

2 2(0 ) (29.2 )

2(53 )

m ms sa

m

Homework

• WS 5c– 1-5

• WS 5d– 1,2

Newton’s 3rd Law

Newton’s 3rd Law

• When one object exerts a force on a second object, the second exerts a force on the first that is equal in magnitude but opposite in direction.

• For every action there is an equal and opposite re-action.

• Action – Reaction force pair

Newton’s 3rd LawExample

• A book rests on a table• The force from the weight

of the book pushes down.• The table provides a

supportive force up.

• Normal force (N) is perpendicular to the surface

W mg

N mg

Friction

• Friction is a force like any other force

• Friction acts on materials that are in contact with each other

• Friction slows down motion

• Forces due to friction are always in the opposite direction of the motion.

Friction• There are two types of friction:

– Kinetic (Sliding) friction: The force that opposes the motion of a moving object

– Static friction: The force that oppose the start of motion.

Friction

• The force of friction depends on

1) The force pushing down (weight)

2) The surface materials in contact with each other

Friction

f NF F

fF force of friction

coeffiecient of friction

NF Normal force

• A horizontal force of 30N pushes a 12kg crate across a floor at a constant velocity. Find the coefficient of sliding friction.

Friction Example

gravityF

normalF

appFfrictionF

app fF F

f NF F f

N

F

F

2

30

12 (9.8 )ms

N

kg

.25

Friction e.g.• A 4kg block has a

coefficient of friction of .22 .

• What is the force of friction for the 4kg block?

• What is the Fnet? • What is the acceleration?

Fapp=20N4kg

f NF F

2.22(4 )(9.8 )mf sF kg

8.6fF N

net app fF F F

20 8.6 11.3netF N N N netF ma

22.8 ms

a

Homework

• WS 5e• 1-3

• p. 102• 13-16

• Quiz Newton’s 3 laws

Newton’s laws review• Newton’s First Law - An object remains at

rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposed force.

• Newton’s first law describes an Equilibrium Situation.

• An Equilibrium Situation is one in which the acceleration of a body is equal to zero.

Newton’s laws review

• Newton’s Second Law – If there is a non-zero net force on a body, then it will accelerate.

• Newton’s Second Law describes a Non-equilibrium Situation.

• A Non-equilibrium Situation is one in which the acceleration of a body is not equal to zero.

Newton’s laws review

• Newton’s Third Law - for every action force there is an equal, but opposite, reaction force.

• Newton’s Third Law says forces must come in pairs.

• Paired force internal to a system have a Net Force of zero.

Quiz

• A horizontal force of 35N pushes on a two block system as shown. If the coefficient of sliding friction is .25, what is the acceleration of the system?

Friction Example

gravityF

normalF

appFfrictionF

2.25(4 5 )(9.8 )mf sF kg kg

f NF F

net app fF F F

35 22.1netF N N 22.1fF N

4kg5kg

Two block system

12.95

9

Na

kg

21.44 ms

a

Friction e.g.• Two blocks are in contact with each other. The 4kg

block has a coefficient of friction of .22 . The two blocks are accelerated together at 1.2m/s2.

• What is the force of friction for the 4kg block? • What is the Fnet? • What is the coefficient of friction for the gold block?

Fapp=30N4kg

5kg

appFfF

W

N

Homework

• WS 5f– #’s1-3

Newton’s 2nd law

• Three identical blocks of 15kg are connected as shown and have a coefficient of friction of 0.3. If the system is pulled to the right, what is the tension at T1?

• At T2?• At T3?

• A block rests on a table and is attached to a hanging mass suspended by a pulley.

• Does the block move?• What might stop the block from moving?

FPull

Newton’s 2nd Law e.g

• A 2kg block rests on a table and is attached to a hanging .7kg mass suspended by a pulley.

• The coefficient of sliding friction is .25, if the block was set in motion, would it continue to move?

• Use the direction of motion as positiveFPull

Newton’s 2nd Law e.g

.7kg

2W m g

T

1W m g

N

fF T

Newton’s 2nd Law e.g • A 2kg block rests on a table and is attached to a

hanging .7kg mass suspended by a pulley. The coefficient of friction between the block and table is

2.25(2 )(9.8 )mf sF kg

.7kg

0.25

4.9fF N

2.7 (9.8 )ms

W kg

6.8W N

fFnet T W F T

6.8 4.9Fnet N N

FPull

.7kg

2W m g

T

1W m g

N

fF T

Newton’s 2nd Law e.g

net fF T F W T

net fF W F

total fm a W F

1 2 2 1( )a m m m g m g

2 1

1 2

m g m ga

m m

• Two unequal masses are suspended on either side of a pulley. What will happen?

• Draw the FBD for each mass.

gravityF

tensionF

gravityF

tensionF

2 2netF T m g

2 2m a T m g

1 1netF m g T

1 1m a m g T

Direction of positive motion

1 1T m g m a 2 2T m a m g

• Two unequal masses are suspended on either side of a pulley. What will happen?

Direction of positive motion

1 1T m g m a 2 2T m a m g

1 1 2 2m g m a m a m g

1 12 2m g m g m a m a

1 12 2( ) ( )g m m a m m

1

1

2

2

( )

( )

g m ma

m m

• Two unequal masses are suspended on either side of a pulley. What will happen?

• Draw the FBD for each mass.

gravityF

tensionF

gravityF

tensionF

1 2netF W T T W

Direction of positive motion

1 2netF W W

1 2tm a m g m g

1 2

1 2

( )g m ma

m m

Homework

• WS 5g 4-5

• WS 5f 1-3

1) What upward force does the mass exert on the scale when the elevator is not moving?

2) What force is exerted when the elevator accelerates upward at 1.5m/s2

500g

500g

500g

A spring scale hangs in an elevator and supports a 4.9N package.

4.9Fscale W N

2) What force is exerted when the elevator accelerates upward at 1.5m/s2

21.5 ms

a

500g

500g

500g

A spring scale hangs in an elevator and supports a 4.9N package.

Fm

a 2

4.9500

9.8 /

Nm g

m s

2.5 (1.5 / ) .75elevatorF kg m s N

.75 4.9 5.65netF N N N

Newton’s 2rd Law e.g.

• A bowling ball and a baseball are simultaneously dropped from the top of a football stadium.

• Use Newton’s 2nd Law to predict which ball will hit the ground first.

Newton’s 2rd Law e.g. • Use Newton’s 2nd Law to predict which ball will

hit the ground first.– Step 1 draw the FBD for both objects– Step 2 Calculate the net force for both objects– Step 3 Calculate the acceleration for both

Newton’s 2nd Law e.g. • Use Newton’s 2nd Law to predict which ball will

hit the ground first.

bowlingW baseW

25 (9.8 )ms

W kg49W N

21.0 (9.8 )ms

W kg

9.8W NF

am

F

am

25 (9.8 )

5

ms

kga

kg 21.0 (9.8 )

1.0

ms

kga

kg

A 4500kg helicopter accelerates upward at 2m/s2.What lift force is exerted?

2 24500 (2 ) 4500 (9.8 )m mlift s sF kg kg

Flift

W

net liftF F W

netF ma

liftF ma W

53100liftF N

Inclined Plane Problems• Draw the FBD for the piano on the inclined plane.

• Resolve the Normal Force (N) and the force of friction (Ff) into their x and y components.

Inclined Plane Problems• We can do this problem by resolving only one force.• Rotate the FBD so that the N is in the y plane and the Ff

is in the x plane.

N

W

W

W

cosW W

sinW W

Inclined Plane Problems

Inclined Plane Problems

sinF W cosF W

A 120kg create rest on an incline plane at 35o.

W

fFN N

fF

W

sinF W cosF W

N

fF

Inclined Plane Problems

sinF W cosF W

cosN W

A 120kg create rest on an incline plane at 35o.sinF W

2120 (9.8 )sin 35ms

F kg

674.6F N

cosF W 2120 (9.8 )cos35ms

F kg

963.3F N W

fFN

WS 5H #1A hockey puck (m = 0.5kg) is placed on an icy incline (no friction) shown below. The puck is then released and allowed to slide.

•Draw the FBD•Draw the modified FBD

24 cosF W

N

sinF W

fFN

fF

W

WS 5H #1

sinF W cosF W

cosN W

A hockey puck (m = 0.5kg) is placed on an icy incline (no friction) shown below. The puck is then released and allowed to slide. sinF W

2.5 (9.8 )sin 24ms

F kg

1.99F N

cosF W 2.5 (9.8 )cos 24ms

F kg

4.47F N

W

fFN

24

Net fF W F

FBD• A boy pushing a lawn mower with 125N of force at an

angle of 25o ?

• Draw the Free Body Diagram.

Fnorm

W=mg

Ffric

Fapp

Fnorm

W=mg

Ffric

Fapp

Homework

• WS 5i 1-5

• Chapter test

FF

WF

FF

WF

8kg 4kg 2kg

4kg5kg

Two block system

F

WF

F

Inclined Plane Problems

A car is coasting to the right and slowing down. A free-body diagram for this situation looks like this:

Free Body diagrams

• If the net forces are zero, the FBD is balanced

Forces cont.

• FBD’s to Fnet

• Fnet to F=ma

• Horizontal pulley example

• Atwood’s pulley example

Home Work

• P106 # 5,7,13

Home Work

• P106 # 22,24

Homework

• P. 106 #’s 27,28

A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. A free-body diagram for this situation looks like this:

A skydiver is descending with a constant velocity. Consider air resistance. A free-body diagram for this situation looks like this:

A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. A free-boy diagram for this situation looks like this

A football is moving upwards towards its peak after having been booted by the punter. A free-body diagram for this situation looks like this:

Examples of zero net force?

• A book on a desk

• A sky diver with a parachute open

• A bike moving at a constant speed.

Free Body diagrams

• If the net forces are NOT zero, the FBD is NOT balanced

Examples of non zero net force

• A book sliding across a desk

• A sky diver falling without a parachute

C

BA