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**Newton’s Second and Third Laws**

Chapter 4 Section 3

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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

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**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.

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**Force and Acceleration**

Acceleration is always in the direction of the net force.

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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.

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**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.

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**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

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**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)

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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

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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

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**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

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**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

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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.

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**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?

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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.

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**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?

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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?

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**Example Problem #1 Answer**

23m/s² forward

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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?

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**Example Problem #2 Answer**

2.1kg

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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?

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**Example Problem #3 Answer**

2 m/s2

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