Chapter 4 The Laws of Motion

Sir Isaac Newton 1642 – 1727 Formulated basic concepts and laws of mechanics Universal Gravitation Calculus Light and optics

Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Conditions when Classical Mechanics does not apply very tiny objects (< atomic sizes) objects moving near the speed of light

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What Causes Motion? In the absence of any forces acting on it, an object will continue moving forever. Motion needs no “cause.” Slide 4-15

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What Is a Force? A force is a push or a pull.... acts on an object.... requires an agent.... is a vector.... is a contact force or a long-range force. Slide 4-17

Fundamental Forces Types Strong nuclear force – attractive force that binds quarks to form protons & neutrons (strongest force) Electromagnetic force – binding atoms and molecules to each other Weak nuclear force – binding force between protons and neutrons Gravity- attractive force between masses (weakest of all types of forces) Characteristics All field forces Listed in order of decreasing strength Only gravity and electromagnetic in mechanics

Units of Force SI unit of force is a Newton (N) US Customary unit of force is a pound (lb) 1 N = lb

Forces Usually think of a force as a push or pull Vector quantity May be a contact force or a field force Contact forces result from physical contact between two objects (a bat hitting a ball) Field forces act between disconnected objects (gravity or an electric field) Also called “action at a distance”

Contact and Field Forces a)Elastic force of a spring b) Component pulling force c) Component pushing force a)Gravitational force of two masses b) Electrical force of attraction c) Magnetic force

External and Internal Forces External force Any force that results from the interaction between the object and its environment Internal forces Forces that originate within the object itself (molecular cohesiveness, frictions) They cannot change the object’s velocity

Force Vectors Slide 4-18

A Short Catalog of Forces: Weight w  Slide 4-19

Spring Force F sp  Slide 4-20 The direction of the force is in the opposite direction of the motion of the object.

Tension ForceT  Slide 4-21

Normal Force n  Slide 4-22 Normal forces are forces that resist a motion, they do not cause a motion themselves.

Friction f k and f s   Slide 4-23

Drag D and Thrust F thrust  Slide 4-24

Identifying Forces Slide 4-25

Example Problem A block is dragged uphill by a rope. Identify all forces acting on the block. Slide 4-26

Reading Quiz 1. A “net force” is A.the sum of the magnitudes of all the forces acting on an object. B.the difference between two forces that are acting on an object. C.the vector sum of all the forces acting on an object. D.the force with the largest magnitude acting on an object. Slide 4-7

Answer 1. A “net force” is A.the sum of the magnitudes of all the forces acting on an object. B.the difference between two forces that are acting on an object. C.the vector sum of all the forces acting on an object. D.the force with the largest magnitude acting on an object. Slide 4-8

Reading Quiz 2.Which of the following is NOT one of the steps used to identify the forces acting on an object? A.Name and label each force the object exerts on the environment. B.Name and label each contact force acting on the object. C.Draw a picture of the situation. D.Identify “the system” and “the environment.” E.Name and label each long-range force acting on the object. Slide 4-9

Answer 2.Which of the following is NOT on of the steps used to identify the forces acting on an object? A.Name and label each force the object exerts on the environment. B.Name and label each contact force acting on the object. C.Draw a picture of the situation. D.Identify “the system” and “the environment.” E.Name and label each long-range force acting on the object. Slide 4-10

Reading Quiz 4.An action/reaction pair of forces A.point in the same direction. B.act on the same object. C.are always long-range forces. D.act on two different objects. Slide 4-13

Answer 4.An action/reaction pair of forces A.point in the same direction. B.act on the same object. C.are always long-range forces. D.act on two different objects. Slide 4-14

Newton’s First Law An object moves with a velocity that is constant in magnitude and direction, unless acted on by a nonzero net force The net force is defined as the vector sum of all the external forces exerted on the object

Mass A measure of the resistance of an object to changes in its motion due to a force As a quantity of mass increases, it becomes more resistant to changes in its motion and will require greater force to overcome the inertia Scalar quantity – direction does not matter SI units are kg

Inertia Is the tendency of an object to continue in its original motion Includes resting inertia and rotational inertia of a mass

Summary Slide 4-39

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Newton’s Second Law Slide 4-29

Weight The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object w = mg is a special case of Newton’s Second Law g is the acceleration due to gravity and has a value of 9.80 m/s 2 g can also be found from the Law of Universal Gravitation

More about weight Weight is not an inherent property of an object mass is an inherent property Weight depends upon location

Checking Understanding An object, when pushed with a net force F, has an acceleration of 2 m/s 2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be A.½ m/s 2. B.1 m/s 2. C.2 m/s 2. D.4 m/s 2.

Answer An object, when pushed with a net force F, has an acceleration of 2 m/s 2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be A.½ m/s 2. B.1 m/s 2. C.2 m/s 2. D.4 m/s 2. Slide 4-34

A 40-car train travels along a straight track at 40 mph. A skier speeds up as she skis downhill. On which is the net force greater? A.The train. B.The skier. C.The net force is the same on both. D.There’s not enough information to tell. Checking Understanding Slide 4-35

Answer A 40-car train travels along a straight track at 40 mph. A skier speeds up as she skis downhill. On which is the net force greater? A.The train. B.The skier. C.The net force is the same on both. D.There’s not enough information to tell. Slide 4-36

Checking Understanding 10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is A.greater than the force of Sarah on Jack. B.equal to than the force of Sarah on Jack. C.less than the force of Sarah on Jack. Slide 4-37

Answer 10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is A.greater than the force of Sarah on Jack. B.equal to than the force of Sarah on Jack. C.less than the force of Sarah on Jack. Slide 4-38

Summary Slide 4-40

Applications of Newton’s Laws Assumptions Objects behave as particles can ignore rotational motion (for now) Masses of strings or ropes are negligible Interested only in the forces acting on the object can neglect reaction forces

Solving Newton’s Second Law Problems Read the problem at least once Draw a picture of the system Identify the object of primary interest Indicate forces with arrows Label each force Use labels that bring to mind the physical quantity involved

Solving Newton’s Second Law Problems Draw a free body diagram If additional objects are involved, draw separate free body diagrams for each object Choose a convenient coordinate system for each object Apply Newton’s Second Law The x- and y-components should be taken from the vector equation and written separately Solve for the unknown(s)

Free-Body Diagrams

Free Body Diagram Must identify all the forces acting on the object of interest Choose an appropriate coordinate system If the free body diagram is incorrect, the solution will likely be incorrect

Free Body Diagram, Example The force is the tension acting on the box The tension is the same at all points along the rope are the forces exerted by the earth and the ground

Free Body Diagram, final Only forces acting directly on the object are included in the free body diagram Reaction forces act on other objects and so are not included The reaction forces do not directly influence the object’s motion

Equilibrium An object either at rest or moving with a constant velocity is said to be in equilibrium The net force acting on the object is zero (since the acceleration is zero)

Equilibrium cont. Easier to work with the equation in terms of its components: This could be extended to three dimensions

Equilibrium Example – Free Body Diagrams

Forces on an Atwood Machine Isolate each body of mass and its respective forces. The component forces of each mass relate together to determine the tension force, T f. a = F net / mass (total) a = m 2 g -  m 1 g (m 1 + m 2 )

Connected Objects Apply Newton’s Laws separately to each object The magnitude of the acceleration of both objects will be the same The tension is the same in each diagram Solve the simultaneous equations

Multiple Objects – Example When you have more than one object, the problem-solving strategy is applied to each object Draw free body diagrams for each object Apply Newton’s Laws to each object Solve the equations

Multiple Objects – Example, cont.

Inclined Planes Choose the coordinate system with x along the incline and y perpendicular to the incline Replace the force of gravity with its components

Forces on an Inclined Plane The box is moving up the frictionless incline plane at constant velocity. In the absence of acceleration, the force needed to move the box upward is equal to the horizontal component of the weight, mgsin . Likewise, the normal force, is equal to the vertical component of the weight, mgcos .

Forces of Friction When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion This is due to the interactions between the object and its environment This is resistance is called friction

More About Friction Friction is proportional to the normal force The force of static friction is generally greater than the force of kinetic friction The coefficient of friction (µ) depends on the surfaces in contact The direction of the frictional force is opposite the direction of motion The coefficients of friction are nearly independent of the area of contact

Static friction acts to keep the object from moving If F increases, so does ƒ s If F decreases, so does ƒ s ƒ s  µ n Static Friction, ƒ s

Kinetic Friction, ƒ k The force of kinetic friction acts when the object is in motion ƒ k = µ n Variations of the coefficient with speed will be ignored

Block on a Ramp, Example Axes are rotated as usual on an incline The direction of impending motion would be down the plane Friction acts up the plane Opposes the motion Apply Newton’s Laws and solve equations

Newton’s Third Law Slide 4-32

Newton’s Third Law If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1. Equivalent to saying a single isolated force cannot exist

Newton’s Third Law cont. F 12 may be called the action force and F 21 the reaction force Actually, either force can be the action or the reaction force The action and reaction forces act on different objects

Some Action-Reaction Pairs is the normal force, the force the table exerts on the TV is always perpendicular to the surface is the reaction – the TV on the table

More Action-Reaction pairs is the force the Earth exerts on the object is the force the object exerts on the earth

Forces Acting on an Object Newton’s Law uses the forces acting on an object are acting on the object are acting on other objects

Summary Slide 4-41