Physics Chapter 4 Newton s
Classical Mechanics 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
Forces Forces Commonly imagined as a push or pull on some object Vector quantities
Forces Forces May be a contact force Results from physical contact between two objects
Forces Forces May be a field force (long-range force) Field forces act between disconnected objects at a distance action at a distance
Forces Forces Fundamental forces All Field Forces In decreasing strength Strong nuclear force (holds atom together) Electromagnetic force (between electric charges) Weak nuclear force (radioactive processes) Gravitational force (between two objects)
Forces Contact and Field Forces A force acts on the object surrounded by the dashed lines. Something in the environment external to the boxed area exerts the force. We need to look at the system and the environment regarding the object.
Forces External and Internal 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 They cannot change the object s velocity
Sir Isaac Newton 1642 1727 Formulated basic concepts and laws of mechanics Universal Gravitation Calculus Light and optics
Newton s First Law of Motion An object moves with a velocity that is constant in magnitude and direction unless a nonzero net force acts on it. The net force is defined as the vector sum of all the external forces exerted on the object
Newton s First Law of Motion An object that is at rest will remain at rest or an object that is moving will continue to move in a straight line with constant speed, if and only if, the net force acting on the object is zero Equilibrium: when the net force is zero Two conditions: at rest, or constant velocity
Newton s First Law of Motion
Newton s First Law of Motion Thought experiment Hit a golf ball Hit a bowling ball with the same force Both resist changes in their motion Which one, the golf ball or bowling ball, goes further? Why? Newton s First Law of Motion is also know as the Law of Inertia
Inertia The tendency of an object to continue in its original state of motion Mass A measure of the object s resistance to changes in its motion due to a force Sometimes called Inertial Mass
Mass A measure of the resistance of an object to changes in its motion due to a force The larger the mass, the less it accelerates under the action of a given force Standard SI unit is the kilogram (kg) Scalar quantity
Newton s Second Law of Motion The acceleration of an object is directly proportional to the net force acting on it, in the direction of the net force, and inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object
Newton s Second Law of Motion Can be applied three-dimensionally Meaning in F x, F y, and/or F z Fx ma x Fy ma y Fz ma z
Newton s Second Law of Motion SI unit of force is a Newton (N) Newton force required to impart an acceleration of 1m/s 2 to a mass of 1 kg
Newton s Second Law of Motion US Customary unit of force is a pound (lb) 1 N = 0.225 lb 1 lb = 4.45N US Customary unit of mass is. the slug
Newton s Second Law of Motion Questions True or False An object can move even when no force acts on it.
Newton s Second Law of Motion Questions True or False If an object isn't moving, no external forces act on it.
Newton s Second Law of Motion Questions True or False If a single force acts on an object, the object accelerates.
Newton s Second Law of Motion Questions True or False If an object accelerates, at least one force is acting on it.
Newton s Second Law of Motion Questions True or False If an object isn t accelerating, no external force is acting on it.
Newton s Second Law of Motion Questions True or False If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction.
Notes about Forces Forces cause changes in motion All the forces acting on an object are added as vectors to find the net force acting on the object Mass x Acceleration (ma) is not a force itself Newton s Second Law is a vector equation This is important as it changes how we will solve problems using forces
Gravitational Forces Mutual force of attraction between any two objects Expressed by Newton s Law of Universal Gravitation: Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them
Gravitational Forces mm 1 2 where G 6.67 10 N m /kg 2 r 11 2 2
Gravitational Forces g G r M E 2 Think of gravity on Earth. Does it change with location? M E m w G r 2 What is weight? How does it compare to F g? w mg SI unit: N
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
Weight Weight is not an inherent property of an object Mass is an inherent property Weight depends upon location Weight decreases with elevation and latitude Force of Gravity is another name for weight F g = W
Weight Questions Solve What is the weight of a person on Earth who weighs 70.0kg?
Weight Questions Solve What is the weight of a person on the moon who weighs 70.0kg on Earth if the moons gravity is 16.5% that of Earth s?
Weight Questions True or False No force of gravity acts on an astronaut in an orbiting space station.
Weight Questions True or False At three Earth radii from the center of Earth, the acceleration of gravity is 1/9 its surface value.
Weight Questions True or False One kilogram of gold would have greater value on Earth than on the Moon.
Weight Questions Answer Which has a greater value, a newton of gold on Earth or a newton of gold on the Moon? The newton of gold on the Earth The newton of gold on the Moon The value is the same, regardless
Newton s Third Law of Motion 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 Forces in nature always exist as pairs Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first
Newton s Third Law of Motion
Newton s Third Law of Motion 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 for every action there is an equal and opposite reaction
Newton s Third Law of Motion Questions Answer A small sports car collides head-on with a massive truck. Which vehicle experiences the greater impact force (in magnitude)? The car The truck Neither, the force is the same on both
Newton s Third Law of Motion Questions Answer A small sports car collides head-on with a massive truck. Which vehicle experiences the greater acceleration? The car The truck Neither, both accelerations are the same.
Types of Forces Force Friction Normal Symbol F f F N f N Definition Contact force opposed sliding motion Contact force exerted by surface on object Direction Parallel to surface and opposite sliding direction Perpendicular to and away from surface Tension F T T Pull exerted by string, rope or cable Away from object and parallel to string Weight F g W Long range force due to gravity Straight down to the center of Earth Push/Pull (Applied) F P P Force by a person Direction of the push or pull
Force Assumptions Objects behave as particles Masses of strings/ropes are negligible The tension is the same at all points in the rope Ignore any frictional effects of the rope Interested only in the forces acting on the object
Free Body Diagrams A diagram of the forces acting on an object Must identify all the forces acting on the object of interest Choose an appropriate coordinate system X & Y Parallel & Perpendicular
Free Body Diagrams 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 Motion descriptors (velocity, acceleration, ) are not used.. but may be near the diagram to help show the motion involved
Free Body Diagrams Draw a free body diagram for a box sitting on a table. Draw a free body diagram for a box being pulled by a rope at constant velocity.
Equilibrium The net force acting on the object is zero ΣF = ma ΣF = 0 the acceleration is zero Two possibilities where this could happen Object is NOT moving Object is moving with constant velocity
Equilibrium Easier to work with the equation in terms of its components: This could be extended to three dimensions A zero net force does not mean the object is not moving, but that it is not accelerating A zero net force does not mean that there are no forces on the object, just that it is not accelerating.
Free Body Diagrams Draw a free body diagram for a box sitting on a table. ƩF y = ma y F g F N = 0 F g = F N
Free Body Diagrams Draw a free body diagram for a box being pulled by a rope at constant velocity. ƩF y = ma y F g F N = 0 F g = F N ƩF x = ma x F T F f = 0 F T = F f
Free Body Diagrams Draw a free body diagram for a box being pulled by a rope but not moving. ƩF y = ma y F g F N = 0 F g = F N ƩF x = ma x F T F f = 0 F T = F f
Free Body Diagrams Draw a free body diagram for a box being pulled by a rope at an angle ϴ above the horizon. ƩF y = ma y F g F N F py = 0 F g = F N + F p sin ϴ ƩF x = ma x F TX F f = 0 F t cos ϴ = F f
Free Body Diagrams Draw a free body diagram for a box being accelerated by pulled a rope. ƩF y = ma y F g F N = 0 F g = F N ƩF x = ma x F T F f = ma x
Free Body Diagrams Draw a free body diagram for a box sitting on a slope not moving. ƩF = ma Fg F N = 0 Fg = F N ƩF = ma Fg F f = 0 Fg = F f
Free Body Diagrams Draw a free body diagram for a box accelerating down a slope. ƩF = ma Fg F N = 0 ƩF = ma Fg F f = ma Fg = F N
Free Body Diagrams Draw a free body diagram for a box that is hanging by a rope. ƩF y = ma y Fg F T = 0 Fg = F T
Force 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 resistance is called friction
Force of Friction Friction is proportional to the normal force F f F F N f = µf N To calculate the Force of Friction, there needs to be a multiplier based on what two surfaces are in contact The coefficient of friction, µ, depends on the surfaces in contact [µ is called mu] The coefficient of friction is nearly independent of the area of contact; it depends on the surfaces
Force of Friction Two different types of friction Static friction (µ s ) Kinetic Friction (µ k ) The direction of the frictional force is opposite the direction of motion (or perceived motion)
Force of Friction The force of static friction is generally greater than (or equal to) the force of kinetic friction pg 95
Force of Friction - Static Static friction acts to keep the object from moving If F increases, so does ƒ s If F decreases, so does ƒ s 0 F fs µ s F N What we care about is the maximum the static friction can hold before the object starts to move F fs,max = µ s F N
Force of Friction - Kinetic The force of kinetic friction acts when the object is in motion F fk = µ k F N Variations of the coefficient with speed will be ignored
Force of Friction The graph as an object moves from static friction to Kinetic friction.
Force Questions Answer If you press a book flat against a vertical wall with your hand, in what direction is the friction force exerted by the wall on the book? Upwards Downwards Out from the wall Into the wall
Force Questions Answer A crate is sitting in the center of a flatbed truck. As the truck accelerates to the east, the crate moves with it, not sliding on the bed of the truck. In what direction is the friction force exerted by the bed of the truck on the crate? East West
Force Questions Answer Suppose your friend is sitting on a sled and asks you to move her across a flat, horizontal field. You have a choice of (a) or (b)
Force Questions Answer (a) pushing her from behind by applying a force downward on her shoulders at 30 below the horizontal, or (b) attaching a rope to the front of the sled and pulling with a force at 30 above the horizontal. Which option would be easier?
Solving Force Problems Read the problem carefully (identify the system) Draw a picture of the system (Free Body Diagram) Start with Newton s Second Law Separate the components (if needed) Substitute variables based on the system Solve for the unknown
Force Example Problems Example #1 You push a 25kg wooden box across a wooden floor at a constant speed of 1.0m/s. How much force do you exert on the box?
Force Example Problems Example #2 What happens (what is the acceleration) when a person pulls a string upwards which is attached to a 9kg box with a 100N force?
Force Example Problems Example #3 Who wants to bet?
Force Example Problems Example #3 A 168N sign is supported motionless by two ropes that each make a 22.5 o angle with the horizontal. What is the tension in each of the ropes?
Force Example Problems Example #4 A truck weighing 562N is resting on a plane inclined 30.0 o above the horizon. Find the components of the weight force parallel and perpendicular to the plane.
Force Example Problems Example #5 A pack of three Artic wolves are fighting over the carcass of a dead polar bear. To the right is a top view of the forces. Determine the movement of the 750kg polar bear carcass.
Force Example Problems Example #6 Who wants to bet?
Force Example Problems Example #6 What is half the ratio of the coefficient of static friction for a wood to wood contact that you then multiply by the force normal, divide by the force of the push and finally solve by multiplying by zero?
Force Example Problems Example #7 A 62kg person on skis is going down a hill sloped at 37 o below the horizon. The coefficient of kinetic friction between the skis and the snow is 0.15. How fast is the skier going 5.0s after starting from rest?
Chapter 4 Homework Homework (next slide) Copied work (for a grade) Free Body Diagrams [DONE] Labs - Newton s First Law Lab - Newton s Second Law Lab - Equilibrium Lab - Static and Kinetic Friction Lab - Air Resistance Lab (???)
Homework for Chapter 2 Chapter 4 Homework Homework (collected) pgs 114-120 # 2, 3, 7, 10, 11, 15, 19, 22, 23, 24, 27, 29, 31, 34, 36, 39, 43, 46, 50, 52, 54, 60, 66, 76, 86 (25) [bet won-2; bet lost-82]