Force & Newton’s Force & Newton’s Laws of MotionLaws of Motion

FORCEFORCE • Act of pulling or pushingAct of pulling or pushing• Vector quantity that causes an Vector quantity that causes an

acceleration when unbalancedacceleration when unbalanced• Forces can cause objects to…Forces can cause objects to…

• Start movingStart moving• Stop movingStop moving• And/or change directionAnd/or change direction

NEWTONNEWTON

* SI Unit for Mass = kilogram (kg)* SI Unit for Mass = kilogram (kg)

* SI Unit for Acceleration = meters/second* SI Unit for Acceleration = meters/second22

* SI Unit for Force = Newton (N)* SI Unit for Force = Newton (N)

* * Newton:Newton: Amount of force that, when Amount of force that, when acting on a 1 kg mass, produces an acting on a 1 kg mass, produces an acceleration of 1 m/sacceleration of 1 m/s22

* 1 N = 1 kg x 1 m/s* 1 N = 1 kg x 1 m/s22

NEWTON’S FIRST LAWNEWTON’S FIRST LAW

Objects move at constant velocity Objects move at constant velocity unless acted upon by a net forceunless acted upon by a net force

** Every object continues in a state of rest, or of motion ** Every object continues in a state of rest, or of motion in a straight line at constant speed, unless it is in a straight line at constant speed, unless it is compelled to change that state by forces exerted upon compelled to change that state by forces exerted upon itit

MASSMASS Measures an object’s resistance to change Measures an object’s resistance to change

velocityvelocity Quantity of matter in an objectQuantity of matter in an object Mass is NOT weightMass is NOT weight

Gravitational Force:Gravitational Force:WEIGHT WEIGHT

Force of gravity on an objectForce of gravity on an object Downward pointing vectorDownward pointing vector W = mgW = mg

Weight = mass x acceleration due toWeight = mass x acceleration due to gravitygravity

QUESTIONQUESTION

* What is Frank’s weight on Earth?* What is Frank’s weight on Earth?

(HINT: His mass = 80.0 kg)(HINT: His mass = 80.0 kg)

Answer:Answer:

W = mgW = mg

W = (80 kg)(9.8 m/sW = (80 kg)(9.8 m/s22))

W = 784 NW = 784 N

NET FORCENET FORCE

* In the * In the absenceabsence of of force…force…

- Objects at rest, remain at rest- Objects at rest, remain at rest

- Objects in motion, continue in motion - Objects in motion, continue in motion

* * NET FORCE:NET FORCE:

- Combination of all forces acting on an object- Combination of all forces acting on an object

- Net force - Net force Changes an object’s state of motion Changes an object’s state of motion

NET FORCE NET FORCE *Remember *Remember Force = Vector, represented by an arrow Force = Vector, represented by an arrow

Applied ForcesApplied Forces Net ForcesNet Forces5 N

10 N15 N

10 N5 N 5 N

5 N5 N0 N

• An object is in equilibrium when it has zero acceleration

• Net force on the object equals zero

EQUILIBRIUMEQUILIBRIUM

5 N 5 N

NEWTON’S SECOND LAWNEWTON’S SECOND LAW

Acceleration of an objectAcceleration of an object Directly proportional to the net force acting Directly proportional to the net force acting

on the objecton the object Inversely proportional to the object’s massInversely proportional to the object’s mass

Net force = mass x accelerationNet force = mass x acceleration

(Newtons)= (kg) x (m/s(Newtons)= (kg) x (m/s22) )

Rearranged:Rearranged:

€

ra =

r F ∑m

aFm

QuestionQuestion

What is the box’s acceleration?What is the box’s acceleration? Mass of the box = 15 kgMass of the box = 15 kg F = 158 NF = 158 N a = ?a = ?

QuestionQuestion

What is the box’s acceleration?What is the box’s acceleration?

Answer:Answer:

ΣF = maΣF = ma

F + (−mg) = maF + (−mg) = ma

a = (F − mg)/ma = (F − mg)/m

a = (158 N −147 N)/(15 kg)a = (158 N −147 N)/(15 kg)

a = 0.73 m/sa = 0.73 m/s22 (upward) (upward)

NEWTON’S THIRD LAWNEWTON’S THIRD LAW

Forces come in action-reaction pairsForces come in action-reaction pairs• Equal in strength, opposite in directionEqual in strength, opposite in direction• Forces act on different objectsForces act on different objects

FFabab = −F = −Fbaba

Force of a on b = opposite of force of b on aForce of a on b = opposite of force of b on a

QuestionQuestion The weight of the apple is 1.5 N. When the The weight of the apple is 1.5 N. When the

apple hits the ground, what force does it apple hits the ground, what force does it exert on the Earth?exert on the Earth? Answer: 1.5 N upwardAnswer: 1.5 N upward

Equilibrium:Equilibrium: When the Net Force Equals Zero When the Net Force Equals Zero

• What forces act on a motionless block What forces act on a motionless block sitting on a table?sitting on a table?

NORMAL FORCE (FNORMAL FORCE (FNN))• Occurs when 2 objects are in direct contactOccurs when 2 objects are in direct contact• Acts at right angles to the surfaceActs at right angles to the surface

• Perpendicular to the surfacePerpendicular to the surface

TENSION (FTENSION (FTT))

Force conveyed through a string, chain, Force conveyed through a string, chain, rope, tendon, etc. rope, tendon, etc.

A massless rope will transmittension undiminished from oneend to the other.

If the rope passes around amassless, frictionless pulley, thetension will be transmitted tothe other end of the ropeundiminished.

Free-body DiagramsFree-body Diagrams Shows all external forces acting on a Shows all external forces acting on a

bodybody Force vectorsForce vectors

• Point in the direction of the forcePoint in the direction of the force• Often drawn from the originOften drawn from the origin

Net force on the car:

275 N + 395 N – 560 N = +110 N

Directed along the + x axis of the coordinate system.

If the mass of the car is 1850 kg then, by Newton’s second law, the acceleration is

2sm059.0kg 1850

N110

m

Fa

FRICTIONFRICTION Resistive force Resistive force Acts in a direction opposite to the direction of Acts in a direction opposite to the direction of

the relative motion of 2 contacting surfacesthe relative motion of 2 contacting surfaces• Varies by materials in contactVaries by materials in contact

• Proportional to the normal force between the objectsProportional to the normal force between the objects Draw vector Draw vector parallelparallel to the surface to the surface

Note that the magnitude of the frictional force doesnot depend on the contact area of the surfaces.

The Force of FRICTIONThe Force of FRICTION Static Friction:Static Friction:

Force that resists the Force that resists the initiationinitiation of sliding of sliding motion between 2 surfaces that are in contact motion between 2 surfaces that are in contact and and at restat rest

ffs, max s, max = = ssFFNN

• ffs, max s, max = Maximum static friction force= Maximum static friction force

s s = Coefficient of static friction= Coefficient of static friction

• FFN N = Normal force= Normal force

When the two surfaces are not sliding across one anotherthe friction is called static friction.

The Force of FRICTIONThe Force of FRICTION Kinetic Friction:Kinetic Friction:

The force that The force that opposes opposes the movement of 2 the movement of 2 surfaces that are in contact and are surfaces that are in contact and are slidingsliding over each otherover each other

ffk k = = kkFFN N

• ffk k = Force of Kinetic Friction = Force of Kinetic Friction

k k = Coefficient of Kinetic Friction= Coefficient of Kinetic Friction

• FFN N = Normal Force= Normal Force

The sled comes to a halt because the kinetic frictional forceopposes its motion and causes the sled to slow down. Supposethe coefficient of kinetic friction is 0.05 and the total mass is 40kg. What is the kinetic frictional force?

Suppose the coefficient of kinetic friction is 0.05 and the total mass is 40kg. What is the kinetic frictional force?

Nkk Ff N = mg = (40kg)(9.8m/s2) = 392 N

fk = (0.05)(392N) = 19.6N

xx maFyy maF

The direction of force and acceleration vectorscan be taken into account by using x and ycomponents.

aFm

is equivalent to

4.11 4.11 Equilibrium Application of Newton’s Laws of MotionEquilibrium Application of Newton’s Laws of Motion

Definition of EquilibriumAn object is in equilibrium when it has zero acceleration.

0xF

0yF