Do Now:Do Now: 1. What is the formula to calculate weight?1. What is the formula to calculate weight? 2. A. Draw the resultant force and calculate it. 2. A. Draw the resultant force and calculate it. B. Calculate the angle.B. Calculate the angle.

4.15

7

N

NTan

7N

5N 5N

7NR = 8.6N

Θ=54.5°

)4.1(1Tan

5.54

Aim: How can we calculate forces Aim: How can we calculate forces acting on an object?acting on an object?

Free-Body diagramsFree-Body diagrams

FappFf

FN

Fg

Free-body diagrams – is a sketch that shows all of the Free-body diagrams – is a sketch that shows all of the forces acting on an object.forces acting on an object. Example1: Draw a free-body diagram of the forces acting Example1: Draw a free-body diagram of the forces acting on a text book sitting on a table.on a text book sitting on a table.Normal force – contact force exerted by the surface on the Normal force – contact force exerted by the surface on the object. (always perpendicular to the surface)object. (always perpendicular to the surface)

Fg

FN

Ex2: An .1 kilogram egg is free-falling from Ex2: An .1 kilogram egg is free-falling from a nest in a tree. Neglect air resistance. a nest in a tree. Neglect air resistance.

Fg

Ex3: A 50 newton object is suspended Ex3: A 50 newton object is suspended motionless from the ceiling by two ropes. motionless from the ceiling by two ropes.

Fg

FTFT

A rightward force is applied to a book in order to A rightward force is applied to a book in order to move it across a desk. Draw the free-body move it across a desk. Draw the free-body diagram.diagram.

Fg

Ff

FN

Fapp

Aim: How can we describe Aim: How can we describe objects in equilibrium?objects in equilibrium?

Explain equilibrium in one word.Explain equilibrium in one word.Determine the normal force of a 35 newton Determine the normal force of a 35 newton

object at rest on a table.object at rest on a table.

How can we define equilibrium?How can we define equilibrium? Forces are equal in a specific direction. (x-direction & Y-Forces are equal in a specific direction. (x-direction & Y-

direction) direction) Resultant force equals zero. (net force = 0N)Resultant force equals zero. (net force = 0N) Ex: A box has a mass of 10 kg. Calculate the magnitude of the Ex: A box has a mass of 10 kg. Calculate the magnitude of the

normal force.normal force.

Fg

FN

EquilibriumEquilibrium

At rest At constant velocity

Fnet = 0 Newtons

A student pushes a 15 newton box across A student pushes a 15 newton box across the table with 20 newtons of force at the table with 20 newtons of force at constant velocity. constant velocity.

***Constant velocity the net force equals ***Constant velocity the net force equals zero***zero***What does “a 15 newton box mean?”What does “a 15 newton box mean?”Sketch a free body diagram.Sketch a free body diagram.Determine the frictional force.Determine the frictional force.

A flying bird is gliding (no A flying bird is gliding (no wingwing flapsflaps) from a tree ) from a tree to the ground at constant velocity. Consider air to the ground at constant velocity. Consider air resistance. Draw a free-body diagram.resistance. Draw a free-body diagram.

Fg

Fair fric

A student holds a 4.5 kilogram object from A student holds a 4.5 kilogram object from a string. The object is motionless. a string. The object is motionless. Calculate the force of tension in the string.Calculate the force of tension in the string.

Fg

FT

Do Now:Do Now: 1. List three ways an object can have 1. List three ways an object can have

acceleration.acceleration. A 10 Newton force to the left is applied to a box. A 10 Newton force to the left is applied to a box.

Also, a 10 Newton force to the right is applied to Also, a 10 Newton force to the right is applied to the same box. The box must bethe same box. The box must be A) at restA) at rest B) in motionB) in motion C) either in motion or at restC) either in motion or at rest

How can we describe Newton’s How can we describe Newton’s 11stst law? law?

Introduction to Newton’s laws of Introduction to Newton’s laws of MotionMotion

Dynamics – is the branch of mechanics Dynamics – is the branch of mechanics that deals with how the forces acting on an that deals with how the forces acting on an object affect its motion. object affect its motion.

An object in dynamic equilibrium moves An object in dynamic equilibrium moves with with constant velocityconstant velocity. That means No . That means No NET Force! Net force equals zero. NET Force! Net force equals zero.

How can we apply Newton’s first How can we apply Newton’s first law of motion?law of motion?

A .5 kilogram mass is hanging from a A .5 kilogram mass is hanging from a spring. How can we determine the net spring. How can we determine the net force?force?

Equilibrium

Static Equilibrium Dynamic Equilibrium

Net force zero, object at rest Net force zero, object moving with constant velocity

How can we describe the two states of equilibrium?

How can we describe inertia?How can we describe inertia?

Inertia is the tendency of an object to Inertia is the tendency of an object to resist a change in state of motion. resist a change in state of motion.

Mass is used to measure inertia. Mass is used to measure inertia. (kilograms)(kilograms)

Inertia and mass are directly proportional. Inertia and mass are directly proportional. Example: The more Example: The more massmass an object has the an object has the

more more inertiainertia the object has. the object has.

Newton’s first law of motionNewton’s first law of motion – An object at – An object at rest will remain at rest and an object in rest will remain at rest and an object in motion (constant velocity) will remain in motion (constant velocity) will remain in motion unless acted on by an unbalanced motion unless acted on by an unbalanced force.force.

Have you ever experienced inertia in an Have you ever experienced inertia in an automobile while it is braking to a stop? automobile while it is braking to a stop?

Describe the following situation using Newton’s Describe the following situation using Newton’s first law.first law.

While riding a skateboard (or bicycle), you fly While riding a skateboard (or bicycle), you fly forward off the board when hitting a curb which forward off the board when hitting a curb which abruptly halts the motion of the skateboard. abruptly halts the motion of the skateboard.

To dislodge ketchup from the bottom of a To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then and thrusted downward at high speeds and then abruptly halted. abruptly halted.

How can we apply Newton’s 2How can we apply Newton’s 2ndnd law?law?

A 6 kilogram box is being pushed with a A 6 kilogram box is being pushed with a 25 newton force to the left on a table. The 25 newton force to the left on a table. The box is moving with constant velocity.box is moving with constant velocity.

Sketch free body diagram and label all of Sketch free body diagram and label all of the forces.the forces.

How can we define Newton’s 2How can we define Newton’s 2ndnd law?law?

Newton’s second law states when an Newton’s second law states when an unbalanced force acts on an object, the object unbalanced force acts on an object, the object is accelerated in the same direction of the is accelerated in the same direction of the force. force.

The net force is The net force is NOT zeroNOT zero. NO Equilibrium.. NO Equilibrium. Formula: Formula:

FFnetnet (sum of forces), m (mass), a (sum of forces), m (mass), a

(acceleration). (acceleration).

maFnet

Describe the mathematical relationship Describe the mathematical relationship between acceleration and net force.between acceleration and net force.

Its acceleration is Its acceleration is directly proportionaldirectly proportional to the to the net forcenet force

Describe the mathematical relationship Describe the mathematical relationship between acceleration and mass.between acceleration and mass.

Its acceleration is Its acceleration is inversely proportionalinversely proportional to to the object’s the object’s massmass

A 5 kilogram box is pushed with a 20 A 5 kilogram box is pushed with a 20 newton force to the right on a frictionless newton force to the right on a frictionless surface. Determine the acceleration.surface. Determine the acceleration.

A 2 kilogram box at rest accelerates to a A 2 kilogram box at rest accelerates to a speed of 10 meters per second in 2 speed of 10 meters per second in 2 seconds. Calculate the net force.seconds. Calculate the net force.

How can we determine the net How can we determine the net force?force?

Determine net force using a pictureDetermine net force using a picture Example 1: A 2kg block is sitting on a table. A 10 N force Example 1: A 2kg block is sitting on a table. A 10 N force

is applied to the right and a 45 N force is applied to the left. is applied to the right and a 45 N force is applied to the left. A) Determine the net force acting on the block?A) Determine the net force acting on the block? B) Calculate the acceleration.B) Calculate the acceleration.

F net in the x direction is the difference between the two forces acting in the x direction.

NF

NNF

net

net

20

1030

to the left

Refer to example 1:Refer to example 1:

The net force acting on the box is 20 The net force acting on the box is 20 Newtons to the right.Newtons to the right.

Calculate the acceleration.Calculate the acceleration.

maFnet

akgN )2(20

kg

Na

2

20

2/10 sma to the left

A 20 newton force is applied to a 4 A 20 newton force is applied to a 4 kilogram object to the right accelerating it kilogram object to the right accelerating it at 4.5 meters per secondat 4.5 meters per second22. .

A) Determine the net force.A) Determine the net force.B) Calculate the frictional force.B) Calculate the frictional force.

A person pushes a 7.0 kg box on a frictionless A person pushes a 7.0 kg box on a frictionless surface. The box accelerates 5 m/ssurface. The box accelerates 5 m/s22. Calculate . Calculate the applied force on the box.the applied force on the box.

maFnet

)/5)(0.7( 2smkgFnet

NFnet 35 to the right

How can we use Newton’s 2How can we use Newton’s 2ndnd law law to solve motion problems?to solve motion problems?

Define Newton’s 1Define Newton’s 1stst law. law.Sketch the equilibrium diagram.Sketch the equilibrium diagram.Determine the net force on an object when Determine the net force on an object when

it is moving with constant velocity.it is moving with constant velocity.A 3 kilogram chair is being push with a 10-A 3 kilogram chair is being push with a 10-

newton force to the right. Sketch a free newton force to the right. Sketch a free body diagram.body diagram.

Cart demonstrationCart demonstration

As mass decreases, acceleration As mass decreases, acceleration _____________._____________.

How would you sketch a graph of How would you sketch a graph of acceleration vs. mass?acceleration vs. mass?

A 50 newton force is required to A 50 newton force is required to accelerate a 3.5 kilogram object at 8.6m/saccelerate a 3.5 kilogram object at 8.6m/s22 over a level floor. over a level floor. A) Sketch a free body diagram.A) Sketch a free body diagram.B) Determine the net forceB) Determine the net forceC) Calculate the magnitude of the frictional C) Calculate the magnitude of the frictional

force acting on the objectforce acting on the object

A 6.5 kilogram object is accelerating at 8.0 A 6.5 kilogram object is accelerating at 8.0 meters per secondmeters per second22. The magnitude of the . The magnitude of the frictional force is 10 newtons. frictional force is 10 newtons.

A) Sketch a free body diagram.A) Sketch a free body diagram.B) Determine the net force.B) Determine the net force.C) Calculate the applied force.C) Calculate the applied force.

**A constant 3,000 newton frictional force **A constant 3,000 newton frictional force is acting on a 1200 kilogram car. The car is acting on a 1200 kilogram car. The car is brought to rest in 20 seconds.is brought to rest in 20 seconds.

A) Identify the net force.A) Identify the net force.B) Calculate the deceleration.B) Calculate the deceleration.C) Calculate the initial velocity of the car.C) Calculate the initial velocity of the car.