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Newton’s Laws. The Study of Dynamics. Isaac Newton. Arguably the greatest physical genius ever. Came up with 3 Laws of Motion to explain the observations and analyses of Galileo and Johannes Kepler. Invented Calculus.

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Newton s laws

Newton’s Laws

The Study of Dynamics


Isaac newton
Isaac Newton

  • Arguably the greatest physical genius ever.

  • Came up with 3 Laws of Motion to explain the observations and analyses of Galileo and Johannes Kepler.

  • Invented Calculus.

  • Published his Laws in 1687 in the book Mathematical Principles of Natural Philosophy.


What is force
What is Force?

  • A force is a push or pull on an object.

  • Forces cause an object to accelerate…

    • To speed up

    • To slow down

    • To change direction


Newton s first law
Newton’s First Law

  • The Law of Inertia.

  • A body in motion stays in motion at constant velocity and a body at rest stays at rest unless acted upon by an external force.

  • This law is commonly applied to the horizontal component of velocity, which is assumed not to change during the flight of a projectile.


The first law is counterintuitive
The First Law is Counterintuitive

Aristotle firmly believed this.

But Physics B students know better!







Newton s second law
Newton’s Second Law

  • A body accelerates when acted upon by a net external force.

  • The acceleration is proportional to the net force and is in the direction which the net force acts.

  • This law is commonly applied to the vertical component of velocity.


Newton s second law1
Newton’s Second Law

  • ∑F = ma

    • where ∑F is the net force measured in Newtons (N)

    • m is mass (kg)

    • a is acceleration (m/s2)


Units of force
Units of force

  • Newton (SI system)

    • 1 N = 1 kg m /s2

  • 1 N is the force required to accelerate a 1 kg mass at a rate of 1 m/s2

  • Pound (British system)

    • 1 lb = 1 slug ft /s2


Newton s third law
Newton’s Third Law

  • For every action there exists an equal and opposite reaction.

  • If A exerts a force F on B, then B exerts a force of -F on A.


Step 1 draw the problem

FL

FM

20 kg

Working a Newton’s 2nd Law Problem

Step 1:Draw the problem

Larry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N. What is acceleration?


Step 2 diagram

N

N

FM

FL

FM

20 kg

FL

FG

FG

Working a Newton’s 2nd Law Problem

Step 2:Diagram

  • Force diagram

  • Free Body diagram


Step 3 set up equations

Working a Newton’s 2nd Law Problem

Step 3:Set up equations

  • F = ma

  • Fx = max

  • Fy = may

Always resolve two-dimensional problems into two one-dimensional problems.


Step 4 substitute

Working a Newton’s 2nd Law Problem

Step 4:Substitute

  • Make a list of givens from the word problem.

  • Substitute in what you know.


Step 5 solve

Working a Newton’s 2nd Law Problem

Step 5:Solve

  • Plug-n-chug.

  • Calculate your unknowns.

  • Sometimes you’ll need to do kimematic calculations following the Newton’s 2nd law calculations.


Gravity as an accelerating force
Gravity as an accelerating force

A very commonly used accelerating force is gravity. Here is gravity in action. The acceleration is g.


Gravity as an accelerating force1
Gravity as an accelerating force

In the absence of air resistance, gravity acts upon all objects by causing the same acceleration…g.


Gravity as an accelerating force2
Gravity as an accelerating force

The pulley lets us use gravity as our accelerating force… but a lot slower than free fall. Acceleration here is a lot lower than g.


2 dimensional problem

N

FL

FM

20 kg

FG

2-Dimensional problem

Larry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N.

a) What is the acceleration?

b) What is the normal force?


The problem of weight
The problem of weight

Are weight and mass the same thing?

  • No. Weight can be defined as the force due to gravitation attraction.

  • W = mg


Flat surfaces 1 d

N

mg

Flat surfaces – 1 D

N = mg for objects resting on horizontal surfaces.


Ramps 2 d

N

mgsin

mgcos

mg

Ramps – 2 D

The normal force is perpendicular to angled ramps as well. It’s always equal to the component of weight perpendicular to the surface.

N = mgcos


Ramps 2 d1

N

mgsin

mgcos

mg

Ramps – 2 D

How long will it take a 1.0 kg block to slide down a frictionless 20 m long ramp that is at a 15o angle with the horizontal?

N = mgcos


Applied forces affect normal force
Applied forces affect normal force.

friction

applied force

weight

normal

N = applied force


Elevator ride going up

V > 0

A > 0

V = 0

A = 0

V > 0

A = 0

V > 0

A < 0

Heavy feeling

Normal feeling

Normal feeling

Light feeling

N

N

N

N

mg

mg

mg

mg

Between

floors

Ground

floor

Just

starting up

Arriving at

top floor

Elevator Ride – going up!


Elevator ride going down

V < 0

A > 0

V = 0

A = 0

V < 0

A = 0

V < 0

A < 0

Heavy feeling

Normal feeling

Normal feeling

Light feeling

N

N

N

N

mg

mg

mg

mg

Between

floors

Top

floor

Arriving at

Ground floor

Beginning

descent

Elevator Ride – going down!


Friction
Friction

  • The force that opposes a sliding motion.

  • Enables us to walk, drive a car, etc.

  • Due to microscopic irregularities in even the smoothest of surfaces.


There are two types of friction
There are two types of friction

Static friction

  • exists before sliding occurs

  • Kinetic friction

    • exists after sliding occurs

  • In general fk <= fs


  • Friction and the normal force
    Friction and the Normal Force

    • The frictional force which exists between two surfaces is directly proportional to the normal force.

    • That’s why friction on a sloping surface is less than friction on a flat surface.


    Static friction
    Static Friction

    • fssN

      • fs : static frictional force (N)

      • s: coefficient of static friction

      • N: normal force (N)

    • Static friction increases as the force trying to push an object increases… up to a point!


    A force diagram illustrating static friction
    A force diagram illustrating Static Friction

    Normal Force

    Frictional Force

    Applied Force

    Gravity


    A force diagram illustrating static friction1
    A force diagram illustrating Static Friction

    Normal Force

    Bigger Applied Force

    Bigger Frictional Force

    Gravity


    A force diagram illustrating static friction2
    A force diagram illustrating Static Friction

    The forces on the book are now UNBALANCED!

    Normal Force

    Frictional Force

    Even Bigger Applied Force

    Gravity

    Static friction cannot get any larger, and can no longer completely oppose the applied force.


    Kinetic friction
    Kinetic Friction

    • fk=kN

      • fk : kinetic frictional force (N)

      • k: coefficient of kinetic friction

      • N: normal force (N)

    • Kinetic friction (sliding friction) is generally less than static friction (motionless friction) for most surfaces.


    Determination of the coefficients of friction
    Determination of the Coefficients of Friction

    Coefficient of Static Friction

    • Set a block of one material on an incline plane made of the other material.

    • Slowly increase angle of plane until the block just begins to move. Record this angle.

    • Calculate s = tan.


    Determination of the coefficients of friction1
    Determination of the Coefficients of Friction

    Coefficient of Kinetic Friction

    • Set a block of one material on an incline plane made of the other material.

    • Slowly increase angle of plane until the block just begins to move at constant speed after giving it a slight tap. Record this angle.

    • Calculate k = tan.


    Magic pulleys

    N

    T

    mg

    T

    -x

    mg

    x

    Magic Pulleys

    m1

    m2


    Pulley problem
    Pulley problem

    Mass 1 (10 kg) rests on a frictionless table connected by a string to Mass 2 (5 kg). Find (a) the acceleration of each block and, (b) the tension in the connecting string.

    m1

    m2


    Pulley problem1
    Pulley problem

    Mass 1 (10 kg) rests on a table connected by a string to Mass 2 (5 kg) as shown. What must the minimum coefficient of static friction be to keep Mass 1 from slipping?

    m1

    m2


    Pulley problem2
    Pulley problem

    Mass 1 (10 kg) rests on a table connected by a string to Mass 2 (5 kg). If ms = 0.3 and mk = 0.2, what is a) the acceleration and b) the tension in the string?

    m1

    m2


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