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Newton’s Second and Third Laws

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 Second and Third Laws

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  1. Newton’s Second and Third Laws Chapter 4 Section 3

  2. 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

  3. 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.

  4. Force and Acceleration • Acceleration is always in the direction of the net force.

  5. 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.

  6. 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.

  7. 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

  8. 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)

  9. 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 N=kgm/s²

  10. 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

  11. 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

  12. 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

  13. 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.

  14. 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?

  15. 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.

  16. 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?

  17. 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?

  18. Example Problem #1 Answer • 23m/s² forward

  19. 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?

  20. Example Problem #2 Answer • 2.1kg

  21. 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?

  22. Example Problem #3 Answer • 2 m/s2

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