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**Forces and Newton’s Laws of Motion**

Chapter 4 Forces and Newton’s Laws of Motion

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**4.1 The Concepts of Force and Mass**

A force is a push or a pull. Arrows are used to represent forces. The length of the arrow is proportional to the magnitude of the force. 15 N 5 N

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**4.3 Newton’s Second Law of Motion**

SI Unit for Force This unit of force is called a newton (N).

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**4.1 The Concepts of Force and Mass**

Mass is a measure of the amount of “stuff” contained in an object. SI Unit of Mass: kilogram (kg)

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**4.2 Newton’s First Law of Motion**

Newton’s First Law (Law of Inertia) An object continues in a state of rest or in a state of motion at a constant Speed unless changed by a net force The net force is the SUM of all of the forces acting on an object.

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**4.2 Newton’s First Law of Motion**

The net force on an object is the sum of all forces acting on that object. Individual Forces Net Force 4 N 10 N 6 N

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**4.2 Newton’s First Law of Motion**

Individual Forces Net Force 5 N 3 N 4 N

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**4.3 Newton’s Second Law of Motion**

Mathematically, the net force is written as where the Greek letter sigma denotes the vector sum.

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**4.3 Newton’s Second Law of Motion**

When a net force acts on an object of mass m, the acceleration that results is directly proportional to the net force and has a magnitude that is inversely proportional to the mass. The direction of the acceleration is the same as the direction of the net force.

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**4.4 The Vector Nature of Newton’s Second Law**

The direction of force and acceleration vectors can be taken into account by using x and y components. is equivalent to

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**4.4 The Vector Nature of Newton’s Second Law**

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**4.4 The Vector Nature of Newton’s Second Law**

The net force on the raft can be calculated in the following way: Force x component y component +17 N +(15 N) cos67 0 N +(15 N) sin67 +23 N +14 N

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**4.4 The Vector Nature of Newton’s Second Law**

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**4.5 Newton’s Third Law of Motion**

Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.

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**4.5 Newton’s Third Law of Motion**

Suppose that the magnitude of the force is 36 N. If the mass of the spacecraft is 11,000 kg and the mass of the astronaut is 92 kg, what are the accelerations?

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**4.5 Newton’s Third Law of Motion**

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**4.7 The Gravitational Force**

Newton’s Law of Universal Gravitation Every particle in the universe exerts an attractive force on every other particle.

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**4.7 The Gravitational Force**

For two particles that have masses m1 and m2 and are separated by a distance r, the force has a magnitude given by

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**4.7 The Gravitational Force**

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**4.7 The Gravitational Force**

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**4.7 The Gravitational Force**

Definition of Weight The weight of an object on or above the earth is the gravitational force that the earth exerts on the object. The weight always acts downwards, toward the center of the earth. SI Unit of Weight: newton (N)

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**Definition of the Normal Force**

The normal force is the force that a surface exerts on an object with which it is in contact – It is ALWAYS perpendicular to the surface.

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4.8 The Normal Force A hand pushes down on a block with a force of 11 N. The block weighs 15N. What is the magnitude of the normal force? A rope is now used to lift the block with a force of 11 N. What is the magnitude of the normal force?

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4.8 The Normal Force Apparent Weight The apparent weight of an object is the reading of the scale. It is equal to the normal force the man exerts on the scale.

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4.8 The Normal Force true weight apparent weight

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**4.9 Static and Kinetic Frictional Forces**

When an object is in contact with a surface there is a force acting on that object. The component of this force that is parallel to the surface is called the frictional force.

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**4.9 Static and Kinetic Frictional Forces**

When the two surfaces are not sliding across one another the friction is called static friction.

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**4.9 Static and Kinetic Frictional Forces**

Note that the magnitude of the frictional force does not depend on the contact area of the surfaces. What does it depend on???

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**4.9 Static and Kinetic Frictional Forces**

Static friction opposes the impending relative motion between two objects. Kinetic friction opposes the relative sliding motion motions that actually does occur. is called the coefficient of kinetic friction.

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**4.9 Static and Kinetic Frictional Forces**

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**4.9 Static and Kinetic Frictional Forces**

The sled comes to a halt because the kinetic frictional force opposes its motion and causes the sled to slow down.

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**4.9 Static and Kinetic Frictional Forces**

Suppose the coefficient of kinetic friction is 0.05 and the total mass is 40kg. What is the kinetic frictional force?

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**4.3 Newton’s Second Law of Motion**

A free-body-diagram is a diagram that represents the object and the forces that act on it.

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**The net force in this case is: 275 N + 395 N – 560 N = +110 N **

4.3 Free Body Diagrams The net force in this case is: 275 N N – 560 N = +110 N and is directed along the + x axis of the coordinate system.

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**4.6 Types of Forces: An Overview**

Examples of different forces: Friction force Tension force Normal force Weight (Force due to gravity) Gravitational Force Magnetic Force Electric Force

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**Cables and ropes transmit forces through tension.**

4.10 The Tension Force Cables and ropes transmit forces through tension.

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**This diagram shows four forces acting upon an object**

This diagram shows four forces acting upon an object. There aren’t always four forces, For example, there could be one or more forces.

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Problem 1 A book is at rest on a table top. Diagram the forces acting on the book.

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Problem 1 In this diagram, there are normal and gravitational forces on the book.

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Problem 2 An egg is free-falling from a nest in a tree. Neglect air resistance. Draw a free-body diagram showing the forces involved.

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**Gravity is the only force acting on the egg as it falls.**

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Problem 3 A rightward force is applied to a book in order to move it across a desk. Consider frictional forces. Neglect air resistance. Construct a free-body diagram. Let’s see what this one looks like.

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**Note the applied force arrow pointing to the right**

Note the applied force arrow pointing to the right. Notice how friction force points in the opposite direction. Finally, there is still gravity and normal forces involved.

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Problem 4 A block is at rest on an incline and stays in place because of static friction. Draw a free-body diagram

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A skier is standing motionless on a horizontal tow rope, which is about to pull her forward. The skier’s mass is 59kg and the coefficient of static friction between the skis and the snow is Draw a free body diagram. What is the magnitude of the maximum force that the tow rope can apply to the skier without causing her to move.

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**Objects in Equilibrium**

Objects that are either at rest or moving with constant velocity are said to be in equilibrium This means that the net force acting on the object is zero Equivalent to the set of component equations given by

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**4.11 Equilibrium Application of Newton’s Laws of Motion**

Reasoning Strategy Draw a free-body diagram. Choose a set of x, y axes for each object and resolve all forces in the free-body diagram into components that point along these axes.

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**4.11 Equilibrium Application of Newton’s Laws of Motion**

What is the Tension in Rope 1 and 2? The engine has a weight of 3150 N

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**4.11 Equilibrium Application of Newton’s Laws of Motion**

Force x component y component

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**4.11 Equilibrium Application of Newton’s Laws of Motion**

The first equation gives Substitution into the second gives

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**4.11 Equilibrium Application of Newton’s Laws of Motion**

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**4.12 Nonequilibrium Application of Newton’s Laws of Motion**

When an object is accelerating, it is not in equilibrium.

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**4.12 Nonequilibrium Application of Newton’s Laws of Motion**

The mass of the supertanker is 1.5 x 108 kg. There is a drive force with magnitude 75000 N and an opposing force of N. The tanker moves with an acceleration of 2.0 x 10-3 m/s2. Solve for the Tension in each of the ropes. The acceleration is along the x axis so

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**4.12 Nonequilibrium Application of Newton’s Laws of Motion**

Force x component y component

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**4.12 Nonequilibrium Application of Newton’s Laws of Motion**

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**4.12 Nonequilibrium Application of Newton’s Laws of Motion**

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Chapter 4 Dynamics: Aim: How can we describe Newton’s Laws of Motion? © 2014 Pearson Education, Inc.

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