Newton’s Laws The Study of Dynamics. Introduction to Newton’s Laws Newton’s First Law.
Newton’s Second and Third Laws Chapter 4 Section 3.
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Transcript of Newton’s Second and Third Laws Chapter 4 Section 3.
![Page 1: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/1.jpg)
Newton’s Second and Third LawsChapter 4 Section 3
![Page 2: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/2.jpg)
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
![Page 3: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/3.jpg)
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.
![Page 4: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/4.jpg)
Force and Acceleration
• Acceleration is always in the direction of the net force.
![Page 5: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/5.jpg)
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.
![Page 6: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/6.jpg)
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.
![Page 7: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/7.jpg)
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
![Page 8: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/8.jpg)
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
![Page 10: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/10.jpg)
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
![Page 11: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/11.jpg)
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
![Page 12: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/12.jpg)
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
![Page 13: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/13.jpg)
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.
![Page 14: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/14.jpg)
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?
![Page 15: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/15.jpg)
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.
![Page 16: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/16.jpg)
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?
![Page 17: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/17.jpg)
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?
![Page 18: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/18.jpg)
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?
![Page 20: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/20.jpg)
Example Problem #2 Answer
• 2.1kg
![Page 21: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/21.jpg)
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?
![Page 22: Newton’s Second and Third Laws Chapter 4 Section 3.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649dd15503460f94ac756b/html5/thumbnails/22.jpg)
Example Problem #3 Answer
• 2 m/s2