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Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Chapter 4 Newton’s Laws of Motion

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Copyright © 2012 Pearson Education Inc. Goals for Chapter 4 To understand the meaning of force in physics To view force as a vector and learn how to combine forces To understand the behavior of a body on which the forces “balance”: Newton’s First Law of Motion: if there is no NET force on an object it will remain in the same state of motion

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Copyright © 2012 Pearson Education Inc. Goals for Chapter 4 To learn the relationship between mass, acceleration, and force: Newton’s Second Law of Motion: F = ma a = F/m To relate mass (quantity of matter) and weight (force on that matter from gravity)

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Copyright © 2012 Pearson Education Inc. Goals for Chapter 4 To see the effect of action-reaction pairs: Newton’s Third Law of Motion Force on object a from object b is EQUAL in magnitude (and opposite in direction) to Force on object b from object a

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Copyright © 2012 Pearson Education Inc. What are some properties of a force? A force is a push or a pull A force is an interaction between two objects, or between an object and its environment A force is a VECTOR quantity, with magnitude and direction.

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Copyright © 2012 Pearson Education Inc. There are four common types of forces #1: The normal force: When an object pushes on a surface, the surface pushes back on the object perpendicular to the surface. This is a contact force.

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Copyright © 2012 Pearson Education Inc. There are four common types of forces #2: Friction force: This force occurs when a surface resists sliding of an object and is parallel to the surface. Friction is a contact force.

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Copyright © 2012 Pearson Education Inc. There are four common types of forces II #3: Tension force: A pulling force exerted on an object by a rope or cord. This is a contact force.

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Copyright © 2012 Pearson Education Inc. There are four common types of forces II #4: Weight: The pull of gravity on an object. This is a long-range force, not a contact force, and is also a “field” force.

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Copyright © 2012 Pearson Education Inc. What are the magnitudes of common forces?

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Copyright © 2012 Pearson Education Inc. Drawing force vectors Use a vector arrow to indicate the magnitude and direction of the force.

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Copyright © 2012 Pearson Education Inc. Superposition of forces Several forces acting at a point on an object have the same effect as their vector sum acting at the same point.

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Copyright © 2012 Pearson Education Inc. Decomposing a force into its component vectors Choose coordinate system with perpendicular x and y axes. F x and F y are components of force along axes. Use trigonometry to find force components.

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Copyright © 2012 Pearson Education Inc. Notation for the vector sum Vector sum of all forces on an object is resultant of forces The net force.

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Copyright © 2012 Pearson Education Inc. Superposition of forces Force vectors are added using components: R x = F 1x + F 2x + F 3x + … R y = F 1y + F 2y + F 3y + …

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Copyright © 2012 Pearson Education Inc. Newton’s First Law “An object at rest tends to stay at rest, an object in motion tends to stay in uniform motion.”

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Copyright © 2012 Pearson Education Inc. Newton’s First Law Mathematically, “A body acted on by zero net force moves with constant velocity and zero acceleration.”

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Copyright © 2012 Pearson Education Inc. Newton’s First Law II In part (a) net force acts, causing acceleration. In part (b) net force = 0 resulting in no acceleration.

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Copyright © 2012 Pearson Education Inc. When is Newton’s first law valid? You are on roller skates in a stopped BART car… The car starts to accelerate forwards. What happens to you? If no net force acts on you, you maintain a constant velocity (0!)

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Copyright © 2012 Pearson Education Inc. When is Newton’s first law valid? You are on roller skates in a moving BART car… The car starts to slow - accelerate backwards. What happens to you? If no net force acts on you, you maintain a constant velocity

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Copyright © 2012 Pearson Education Inc. When is Newton’s first law valid? If no net force acts on you, you maintains a constant velocity (a vector!) But as seen in the non- inertial frame of the accelerating vehicle, it appears that you are being pushed to the outside! Newton’s first law is valid only in non-accelerating inertial frames.

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Copyright © 2012 Pearson Education Inc. Newton’s Second Law If the net force on an object is zero, the object will not accelerate.

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Copyright © 2012 Pearson Education Inc. Newton’s Second Law If the net force on an object is not zero, it causes the object to accelerate.

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Copyright © 2012 Pearson Education Inc. Newton’s Second Law If the net force on an object is not zero, it causes the object to accelerate.

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Copyright © 2012 Pearson Education Inc. An object undergoing uniform circular motion An object in uniform circular motion is accelerated toward the center of the circle. So net force on object must point toward the center of the circle.

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Copyright © 2012 Pearson Education Inc. Force and acceleration Magnitude of acceleration of an object is directly proportional to the net force on the object. | | = F/m

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Copyright © 2012 Pearson Education Inc. Mass and acceleration Magnitude of acceleration of an object is inversely proportional to object’s mass if net force remains fixed. | | = F/m

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Copyright © 2012 Pearson Education Inc. Newton’s second law of motion The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to the mass of the object. The SI unit for force is the newton (N). 1 N = 1 kg·m/s 2

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Copyright © 2012 Pearson Education Inc. Using Newton’s Second Law Ex. 4.4 Worker pushes box of mass 40 kg, with constant force of 20N. What is acceleration?

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Copyright © 2012 Pearson Education Inc. Using Newton’s Second Law Ex. 4.4

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Copyright © 2012 Pearson Education Inc. Using Newton’s Second Law II—Example 4.5 Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?

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Copyright © 2012 Pearson Education Inc. Using Newton’s Second Law II—Example 4.5 Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?

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Copyright © 2012 Pearson Education Inc. Using Newton’s Second Law II—Example 4.5 We know: Displacement in x = +1.0 m Initial x velocity = +2.8 m/s Final x velocity = 0 m/s THREE THINGS!

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Copyright © 2012 Pearson Education Inc. Using Newton’s Second Law II—Example 4.5 v f 2 = v i 2 + 2a x So… a = (v f 2 - v i 2 )/2 x a = - 3.9 m/s 2 NOTE a points in the direction of f! +x

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Copyright © 2012 Pearson Education Inc. Systems of units (Table 4.2) In MKS (SI) system force is measured in Newtons, distance in meters, mass in kilograms.

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Copyright © 2012 Pearson Education Inc. Systems of units (Table 4.2) In British system, force is measured in pounds, distance in feet, mass in slugs. In cgs system, force in dynes, distance in centimeters, and mass is in grams.

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Copyright © 2012 Pearson Education Inc. Mass and weight The weight of an object (on Earth) is gravitational force that Earth exerts on it. The weight W of an object of mass m is W = mg The value of g depends on altitude. On other planets, g will have an entirely different value than on the earth.

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Copyright © 2012 Pearson Education Inc. A euro in free fall

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Copyright © 2012 Pearson Education Inc. A bit coin in free fall?

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Copyright © 2012 Pearson Education Inc. Don’t confuse mass and weight! Keep in mind that the Newton is a unit of force, not mass. A 2.49 x 10 4 N Rolls-Royce Phantom traveling in +x direction makes an emergency stop; the x component of the net force acting on its -1.83 x 10 4 N. What is its acceleration?

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Copyright © 2012 Pearson Education Inc. Newton’s Third Law If you exert a force on a body, the body always exerts a force (the “reaction”) back upon you. A force and its reaction force have the same magnitude but opposite directions. These forces act on different bodies.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects at rest An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects at rest An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects at rest An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects at rest An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects in motion A person pulls on a block across the floor. Identify the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects in motion A person pulls on a block across the floor. Identify the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects in motion A person pulls on a block across the floor. Identify the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. Applying Newton’s Third Law: Objects in motion A person pulls on a block across the floor. Identify the action-reaction pairs.

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Copyright © 2012 Pearson Education Inc. A paradox? If an object pulls back on you just as hard as you pull on it, how can it ever accelerate?

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Copyright © 2012 Pearson Education Inc. Free-body diagrams A free-body diagram is a sketch showing all the forces acting on an object.

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Copyright © 2012 Pearson Education Inc. Free-body diagrams A free-body diagram is a sketch showing all the forces acting on an object.

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Copyright © 2012 Pearson Education Inc. Free-body diagrams A free-body diagram is a sketch showing all the forces acting on an object.

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