CHAPTER-6

6.1 Force and Motion Contact Versus Long-Range Forces Force = A push or pull exerted on an object. System = The object

Environment = The world around the object that exerts forces on it. Force has both magnitude and direction, ∴ force is a ___________ quantity. A: vector Contact force = Can only act on an object if it is directly touching the object. Example: book/desk, book/hand

Long-Range Force = A force that can be exerted on an object without actually touching it. Examples = Magnets, Gravity- long-range attractive force that exists on ALL objects due to the mass of the Earth. Agent = The actual cause of the force, if you cannot name it, then it does not exist

Free Body diagram = The object is represented by a dot and all of the forces operating on the object are drawn in the direction of the forces with their tails on the dot.

FBD Box on a Desk

FBD Ball on a rope/chain

FBD Ball in a Hand

FBD Box being pushed at a constant Velocity

FBD Box Sliding on an Incline Not Being Pushed

Hanging Traffic light

Newton’s Second Law of Motion The acceleration produced by a net force on an object is directlt proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.

Newton’s 2 nd Law Continued Basically means= If a force is applied to an object, the object will accelerate in the direction of the force. F = net force (N) F = net force (N) F = ma a = acceleration (m/s 2 ) a = F/m m = mass (kg)

Net Force (F net ) a) The vector sum of two or more forces b) The sum of ALL the forces acting on an object. c) When ALL the forces acting on an object are “resolved” (broken down) into their summation in each direction, their “component” vectors are added together to achieve some net force in a particular direction.

F net EXAMPLES HorizontalVertical Horizontal & Vertical together At some angle – then “RESOLVE”

Measuring Force: The Newton 1 Newton = 1 N kgm kgm 1 N = 1 s 2 F = maN = kg x m/s 2

Newton’s First Law of Motion An object at rest will remain at rest and an object in motion will remain in motion in a straight line with a constant speed unless a net force acts on it. AKA: Law of Inertia In other words an object tends to keep on doing what it’s already doing.

INERTIA = Is the tendency of an object to resist a change in its motion. If it is at rest it wants to remain at rest. If it is moving it wants to continue moving at the same speed and direction. Inertia depends on mass,  the more mass an object has = more inertia.

Equilibrium = When the net force acting on an object is equal to zero. This does not mean that there are NO FORCES acting on an object it simply means that if all the forces acting on an object are added together the sum would be zero. There may be many forces acting on the object. EXAMPLES

TERMINAL VELOCITY = The greatest speed that a “Free Falling” object can attain. Q: How does an object reach terminal velocity? Student examples.

TERMINAL VELOCITY Cont. As an object begins to fall faster the amount of air resistance increases proportionally. Once the object falls fast enough the force of gravity will become equal to the force of air resistance. At that point equilibrium is reached. The object will continue to fall, but will fall at the same speed, constant velocity, because there will be no net force acting on the object, forces on the object will be in equilibrium.

From page 123 Table 6-2 F f = frictional force F N = normal force, the force exerted by a surface on an object perpendicular to surface on an object perpendicular to the surface. the surface. F g = force of gravity F T = force of tension F SP = force of spring tension

6.2 Using Newton’s Laws Using Newton’s Second Law Aristotle – the heavier the object, the faster it falls (accelerates towards the center of the Earth)

Galileo – All objects fall at the same rate a = -g = -9.8m/s 2 All forces acting on an object must be considered such as air resistance, friction, …etc

Mass = The amount of matter an object has Weight = The force of gravity acting on an objects mass. Weight = F g = mg

Q: What does a scale actually measure? A: The scale actually measures the F N (normal force) or the upward force that opposes gravity perpendicular to the scale.

If you are standing on the scale, equilibrium is reached. F net = 0 F net = F scale -F g =0  the scale is measuring the magnitude of the upward force needed to offset F g, which is your weight. weight = F g = mg

Weighing yourself on a floor compared to weighing yourself in an accelerating elevator. Your mass = 75kg a) floor Weight = F = mg = (75kg)(9.8m/s 2 ) Weight = F = mg = (75kg)(9.8m/s 2 ) Weight = 735kgm/s 2 = 735N Weight = 735kgm/s 2 = 735N

b) elevator is accelerating upward at 3m/s 2. What does the scale register? F scale = F N + F net F scale = mg + ma (acc of elevator) F scale = m(g+a) F scale = 75kg(9.8m/s 2 + 3m/s 2 ) F scale = 75kg(12.8m/s 2 ) F scale = 960N

c) elevator is accelerating at 5m/s 2 downward. What is the apparent weight on the scale? F scale = F N + F net F scale = mg + ma F scale = m (g +a) F scale = 75kg(9.8m/s 2 -5m/s 2 ) F scale = 75kg(4.8m/s 2 ) F scale = 360N

Apparent Weight = the force exerted by the scale Elevator accelerating F scale = mg ± ma F scale = m(g ± a)

The Friction Force Friction = The force that acts to resist the motion of objects that are in contact with each other. Since friction opposes motion, the F f (frictional force) acts in the opposite direction of motion.

All surfaces have some friction, nothing is completely frictionless. Static Friction = The force exerted on one surface by another when there is no relative motion between them.

Kinetic Friction = The force exerted on one surface by another when the surfaces are in relative motion. Static Friction Force (F fs ) 0≤F fs ≤μ s F N Kinetic Friction Force (F fk ) F fk = μ k F N μ = coefficient of friction F N = mg

Table 6-3 Page 131 Surfaceμsμk Rubber on concrete Rubber on wet concrete Wood on wood Steel on steel (dry) Steel on steel (with oil) Teflon on steel

Example Problem Friction #1 A 25kg box is pulled across a floor at a constant 32m/s. What is the force of the pull if the coefficient of static friction is and kinetic friction is 0.114?

SOLUTION PROCESS 1. FBD 2. Table of known/unknown 3. Equation 4. Plug in #’s 5. Steps showing ALL work 6. Solution/final answer in box/circle

FBD Table of known/unknown m = 25kg d i = 0 v i = 32m/sd f = X v f = 32m/sa = 0 t i = 0μ k = t f = Xμ s = t f = Xμ s = F net = 0 F net = 0

Equation = ? F P = F kf F P = F N μ k F P = mgμ k F P = (25kg)(9.8m/s 2 )(0.114) F P = 27.93kgm/s 2 F P = 27.93N

Example Problem Friction #2 If the force of the pull were doubled what would the acceleration be? Differences…? F net = some value F f remains the same  there will be an acceleration

Solution F net = F P –F f ma = F P – F f a = (F P – F f ) / m a = (55.86N – 27.93N) / 25kg a = 27.93kgm/s 2 / 25kg a = 1.12m/s 2

Periodic Motion Periodic Motion = The back and forth motion over the same path. Examples: Swinging, stretched spring with a mass, pendulum

Pendulum The pendulum will swing back and forth forever until some net force other than gravity acts on it.

Q: What F net will eventually cause the pendulum to stop moving? A: air resistance

Simple Harmonic Motion = Motion that returns an object to its equilibrium position as a result of a restoration force acting on the object that is directly proportional to the object’s displacement.

Restoration Force = A net force attempting to bring the object back to equilibrium, it is in the opposite direction of the object’s displacement.

Period (T) = The time needed to repeat one complete cycle of simple harmonic motion. Amplitude = The maximum distance the object moves from equilibrium.

Period of a Pendulum T = 2π√(l/g) T= time of period in seconds l = length of string in meters g = acceleration of gravity, 9.8m/s 2

Q: what is the only factor that determines the period of a pendulum? A: l, the length of the string.

Resonance = Applying a net force to the swing in the same direction the swing is moving will increase the amplitude of the swing (causing the swing to go higher).

Mechanical Resonance = When small forces are applied at regular intervals to a vibrating or oscillating object, the amplitude of the vibration increases. The time interval between applications of the force is equal to the period of oscillation.

6.3 INTERACTION FORCES Identifying Interaction Forces Pitcher & catcher When the ball is stopped by the catcher what forces are present?

A: The forces present are… ball on the catcher and catcher on the ball Q: how do the forces compare? A: they are equal and opposite

Interaction Forces Present F ball on hand F A on B F hand on ball F B on A Action-Reaction force pairs One does not cause the other The two forces exist together or not at all

Newton’s Third Law According to Newton, an interaction pair is two forces that are opposite in direction but have equal magnitudes. Ex: The force of the catcher’s hand on the ball is equal to the force of the ball on the catcher’s hand.

Newton’s Third Law = Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

Pairs Of Forces Transparency from text book How does a car accelerate

Force Pair Example Ball / Earth If a 0.18kg tennis ball is dropped: a) What is the force of the Earth on the ball? b) What is the downward acceleration of the ball? c) What is the upward acceleration of the Earth?

Draw diagram & FBD m ball = 0.18kg m Earth = 6 x kg g = 9.8m/s 2 a) = (F = ma) F Earth on ball = F ball on Earth = mg mg = (0.18kg)(9.8m/s 2 ) mg = 1.764N

b) = Downward acceleration = -g = -9.8m/s 2 c) = upward acceleration of Earth (a E ) F = ma E a E = F/m a E = 1.764N / (6 x kg) a E = m/s 2 a E = 2.94 x m/s 2

Four Fundamental Forces 1. Gravitational Interaction = Every object in the universe exerts a gravitational force on every other object in the universe. 2. Electromagnetic = The force that holds atoms and molecules together, they are responsible for all contact forces.

3. Strong Nuclear = The force that holds protons and neutrons together. This is the strongest known force in the universe. 4. Weak Nuclear = Responsible for some types of radioactive decay.

Forces of Ropes and Strings Newton’s 3 rd Law states that the forces are part of an interaction pair.

F T – F g = 0  F T = F g The tension (T) in the rope/chain is equal to the weight of all the objects below it.

Q: What is the tension in the rope? Neither team is moving, each team pulls with a force of 5000N.

Answer: Since neither team is moving F net = 0 = equilibrium F T(team A on rope) - F T(team B on rope) = 0  F TA = F TB = 5000N The two tensions are part of an interaction pair.  Pairs are = but opposite  Each Tension (T) = 5000N

Pully Ex prob-1 W 1 = 50N W 2 = 40N Neglect friction What is the acceleration of the boxes? What is the tension in the cord?

Pully Ex prob-2 W 1 = 100N W 2 = 45N Neglect friction What is the acceleration of the boxes? What is the tension in the cord?

Pully Ex prob-3 m 1 = 85kg m 2 = 110kg μ k = μ s = What is the acceleration of the boxes? What is the tension in the cord?

Pully Ex prob-4 m 1 = 85kg m 2 = 110kg μ k = μ s = What is the acceleration of the boxes? What is the tension in the cord?