Newton s second and third laws
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Newton’s Second and Third Laws. Chapter 4 Section 3. Newton’s First Law. From Newton’s 1 st Law of Motion an object with balanced external forces acting on it is in a state of equilibrium. Σ F = 0 No acceleration

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Newton s first law
Newton’s First Law

  • From Newton’s 1st Law of Motion an object with balanced external forces acting on it is in a state of equilibrium.

    • ΣF = 0

    • No acceleration

  • If the Forces are not balanced then there is a change in the motion of the object.

    • ΣF ≠ 0

    • Acceleration occurs

Acceleration and force
Acceleration and Force

  • Acceleration is directly Proportional to the Force

    • Acceleration ~ Force

  • If the Force is increased, then the acceleration must increase by the same ratio as long as mass is held constant.

Force and acceleration
Force and Acceleration

  • Acceleration is always in the direction of the net force.

Acceleration and mass
Acceleration and Mass

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

    • Acceleration ~ 1 / Mass

  • If the mass increases, then the acceleration decreases as long as the force remains constant.

    • If the mass is doubled, then the acceleration is cut in half.

Force mass and acceleration
Force, Mass and Acceleration

  • The acceleration is directly proportional to the Force divided by the Mass

    • Acceleration ~ Force / Mass

  • This is where Newton’s 2nd Law is created from.

Newton s 2 nd law of motion
Newton’s 2nd Law of Motion

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

    • ΣF = ma

Equation variables and units
Equation Variables and Units

  • Newton’s Second Law variables

    • Σ: Greek Letter Sigma meaning “The sum of”

    • F: Force (Newton – N)

    • m: Mass (Kilograms – kg)

    • a: Acceleration (meters per second² - m/s²)

What is a newton
What is a Newton?

  • A Newton is the amount of force needed to move a 1 kilogram mass at an acceleration of 1 meter per second squared.

    F = ma

    N = kg • m/s²


Example problem
Example Problem

  • What force is needed to move a 3.2kg book across a table with an acceleration of 2.1 m/s² to the right?

  • Answer: 6.7 N to the right

Solving problems with multiple forces
Solving Problems With Multiple Forces

  • It is often easier to break the Newton’s 2nd Law into components.

    • The sum of the forces in the x-direction equals the mass multiplied by the acceleration in the x-direction.

      • ΣFx = max

    • The sum of the forces in the y-direction equals the mass multiplied by the acceleration in the y-direction.

      • ΣFy = may

Net external force equals zero
Net External Force equals Zero

  • If the net external force is zero, then the acceleration is equal to zero regardless of how much mass is present.

    • ΣF = ma

    • ΣF = m • 0m/s²

    • ΣF = 0

Newton s 3 rd law
Newton’s 3rd Law

  • Newton’s Third Law – If two bodies interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction.

  • For every action, there is an equal and opposite reaction.

Forces always exist in pairs
Forces Always Exist in Pairs

  • Forces always exist in pairs, therefore there can not be a single isolated force.

    • If you push on a wall with 100N, the wall presses back on you with 100N.

      • Equal and opposite, as long as there is no acceleration.

  • If Earth is pulling you down with a force equal to your weight, what is the second force?

Action reaction pair
Action-Reaction Pair

  • Action-Reaction Pair – A pair of simultaneous equal but opposite forces resulting from the interaction of two objects.

    • The action and reaction occur at the same exact time.

Field forces
Field Forces

  • Field Forces also exist in pairs as well.

    • Field forces such as gravity and electromagnetism.

  • If you drop a ball the earth pulls down on the ball, but the ball pulls up on the earth by the same amount.

  • But why doesn’t the earth move and the ball does?

Example problems 1
Example Problems #1

  • The net external force on the propeller of a 0.75kg model airplane is 17N forward. What is the acceleration of the airplane?

Example problem 1 answer
Example Problem #1 Answer

  • 23m/s² forward

Example problem 2
Example Problem #2

  • A ball pushed with a force of 13.5N accelerates at 6.5m/s² to the right. What is the mass of the ball?

Example problem 3
Example Problem #3

  • Two people push on a box resting on a frictionless floor. One person pushes to the left with a force of 17N and the other person pushed with a force of 37N to the right. If the mass of the box is 10kg, what is the acceleration of the box?