FORCES AND CIRCULAR MOTION

A. Definition: a push or pull acting on a mass1. Force is a vector quantity with both magnitude (numeric value) and direction2. Force can be broken down into horizontal and vertical components3. Symbol:4. Units:

I. FORCE

Newtons ! (N)

F

B. Concurrent Forces: many forces acting on the same object at the same time.1. Treat all forces individually to find a resultant force (break into components)2. This resultant of all concurrent forces is called the Net Force

FnetSymbol:

C. Free Body Diagram: represents concurrent forces acting on an object

Two Physics students try pushing a car to see who is stronger. One student pushes west with a force of 500 Newtons. The other pushes East with a force of 700 Newtons.

Draw a free body diagram of the situation.

What is the Net Force?

What way does the car move?

EXAMPLE 1: NET FORCE

Two Physics students are again arguing and this time are in a tug of war. They are pulling on a box. One student pulls 30 degrees toward the northeast with a force of 400 Newtons and the other pulls at 20 degrees toward the Northwest with 500 Newtons.

Draw a free body diagram of the situation.

What is the Net Force?

EXAMPLE 2: NET FORCE

What is net force on a box of mice being pulled with a force of 20 Newtons due West toward a snake pit and another force of 30 Newtons pulling due East toward an alley filled with cats, a 50 Newton force pulling due North toward a cliff, and a 50 Newton force pulling due South toward a large pond? Draw a Free Body Diagram 1st!!!

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D. Static Equilibrium: reached when the resultant of all forces acting on an object is ZERO (balanced)

1. At Equilibrium, objects remain at rest or constant velocity.

Fnet = ZeroFnet ≠ Zero

2. Net Force is equal to ZERO in static situations

Fnet =0

What forces MUST be added in order to produce static equilibrium in the free body diagram below?

EXAMPLE: STATIC EQUILIBRIUM

II. DYNAMICS

A. Newton’s First Law: An object maintains a state of equilibrium unless acted on by an unbalanced force. (at rest or constant velocity)

1. Any unbalanced force (Fnet ≠ 0) will produce a change in an object’s velocity…either speed, direction, or both.• the object will ACCELERATE

2. Newton’s First Law is also known as the Law of Inertia• Inertia: the resistance of an object to a change in its motion More Mass = More Inertia

Effects of forces acting on objects (Newtons Laws of Motion)

• Masses resist changes in motion…

What has more inertia? A 10 kg bag of feathers sitting still or a 5 kg gold bar moving along at 10 m/s?

What has more inertia? A 20 kg baseball sitting on a stand, or a 5 kg bowling ball moving along at 30 m/s?

EXAMPLES: INERTIA

B. Newton’s Second Law: the acceleration of an object is directly proportional to the net external force acting on an object and inversely proportional to the object’s mass.

• force is related to mass and acceleration using the famous expression:

• acceleration is produced by force(s)• increasing force will increase the

acceleration

maFnet

1. Units for Force…Yay!! Dimensional Analysis!

a. Newtons are the SI unit of force and are a derived unit (combination of fundamental units)

b. 1 Newton is equal to the force required to accelerate a 1 kilogram mass 1 meter per second squared

maFnet 2smkg N1

2. Increasing mass will increase the force needed to accelerate that mass

maFnet

larger m larger Fnet

*The equation must balance!

mFa net

m a

3. If the force is constant, then increasing the mass of an object will decrease the resulting acceleration

Fnet a

4. Graphing Fnet = ma :

Force (N)

Acce

lera

tion

(m/s

2 ) Direct Relationship: Increasing Force produces more acceleration

A capybara with a mass of 100kg is tackled by a Jaguar with a steady force of 100 N along the ground. Assuming no friction, what is the acceleration of the rodent?

EXAMPLE: NEWTON’S 2ND LAW

C. Newton’s Third Law: when one object exerts a force on a second object, the second object exerts a force on the first that is equal in magnitude, but opposite in direction.

For every action there is an equal and opposite reaction!

• What happens to a boat when you step onto a dock?

Newton’s 3 rd Law!!!

Newton’s 3rd Law also applies in space when making objects move

A. Weight: gravitational force exerted on a small mass by a planet/large body

1. Weight CHANGES based on what planet/object you are on… MASS does NOT CHANGE

2. Symbol:

3. Units:

4. Equation:

III. NATURAL FORCES

mgFg

Newtons ! (N)

How much do you weigh?

EXAMPLE: WEIGHT

The fattest, ugliest Capybara has a mass of 66 kg. What is the weight of the rodent on Earth?

Convert the mass to pounds if 1 kilogram = 2.2 pounds

B. Newton’s Universal Law of Gravitation: Describes the force of attraction between different masses. Any two bodies attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them

221

rmGmFg

221

rmGmFg

Fg = Gravitational Force

G = Universal Gravitational Constant = 6.67 x 10 -11

N•m2/kg2

m1 = mass of object 1

m2 = masses of object 2

r = distance between the two masses

On Your Reference Tables!!

(Front Cover)

• Graphical Representation:

What is the force of gravitational attraction between the Earth and the Moon?

m1 = Earth = 5.98 x 1024 kg

m2 = Moon = 7.35 x 1022 kgr = 3.84 x 108 mG = 6.77 x 10 -11 N•m2/kg2

221

rmGmFg

EXAMPLE: NEWTON’S UNIVERSAL LAW OF GRAVITATION

221

rmGmFg 28

222411

)1084.3()1035.7)(1098.5)(1067.6( 2

2

mkgkgkg

mN

2217

2237

1047.1)1093.2(

kgmkgmN

NFg201099.1

2. Gravitational Fields: vectors are used to show gravitational force

A “unit test mass” will accelerate along gravitational field lines, toward the center of the source of gravity