Laws of Motion, Class 5, Unit 2

• Class 5 focuses on the Laws of Motion and forces as part of Unit 2.

Course Units:

• Motion (Kinematics).
• Forces (Dynamics).
• Energy.
• Waves.
• Electricity and Magnetism.

Key Question:

• What makes an object change its motion?

Revolutionary Science:

• 1687: Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy") published.
• The publication is one of the most important in science.
• Laid the foundation for classical mechanics (Newtonian mechanics) and calculus.
• Based heavily on works by Galileo and Johannes Kepler.
• Physics based on Newton's laws of motion has been successful in describing and predicting physical phenomena.

First Law of Motion:

• An object remains in its state of rest or uniform motion until a net external force is applied.
• Under the first law of motion, these equations are equivalent: Fnet = ∑F = 0, v = constant, a = 0.
• No net external force implies constant velocity and zero acceleration.
• Vector sum of all forces on the object is zero.
• Forces on the object are balanced.
• State of equilibrium.
• Constant velocity means constant magnitude and direction.
• Uniform motion.
• Object moves in a straight line.
• Zero acceleration.

Aristotle's view on motion:

• Prior to Galileo, motion understanding was primarily from Aristotle, who stated that any body in motion would naturally come to a state of rest.
• Aristotle's idea can seem to "make sense", for example, sliding a book across a table will eventually stop.
• Galileo pointed out that Aristotle's philosophy is ambiguous, as absolute rest cannot be determined because all motion is relative.

Absolute Rest:

• "Absolute rest" and "absolute motion" cannot be determined.
• An object stationary according to one observer can be moving relative to another (relative motion).
• A cup of water on an airplane tray table at cruising speed appears stationary to passengers but is moving relative to an outside observer.
• Uniform motion is indistinguishable from rest.
• Dropping a tennis ball on the ground results in the ball falling straight down.
• Repeating this on an airplane at 900 km/h yields the same result.
• The motion of the ball does not reveal whether one is at rest or in uniform motion.

Force:

• A force is a push or pull upon an object due to an interaction with another object.
• Interaction between two objects results in a force on the objects.
• Interaction can be by contact or at a distance.
• When the interaction ceases, the two objects no longer experience the force.
• The unit of force is the newton (N), defined as 1 N = 1 kg⋅m/s².
• Force is a vector, therefore direction matters.

First Law Examples:

• A marble is fired into a circular tube which is anchored onto a frictionless tabletop.
• A spacecraft lost in deep space drifting from point A to C with on-board rockets exerting constant perpendicular force will have its path altered depending on when and how long the thrust is applied.

Second Law of Motion

• The acceleration of an object is proportional to the net external force applied to it and is in the same direction as the net external force.
• The 1st & 2nd laws of motion can be summarized in a single equation: Fnet = ∑F = ma.
• Net force is a vector in the same direction as acceleration.
• This equation is correct only when mass is constant.

Mass:

• Mass is defined as the ratio between the magnitude of net force and the magnitude of acceleration: m = Fnet/a.
• An object's mass is an intrinsic property which remains constant regardless of location (Earth, underwater, Moon, space).

Third Law of Motion:

• For every action, there is an equal and opposite reaction; mutual actions of two objects on each other are directed to the other object.
• For every action force on an object (B) due to object (A), there is a reaction force equal in magnitude but opposite in direction on object (A) due to object (B): FAB = -FBA.
• Action/reaction forces act on different objects.
• Forces always exist as pairs.
• The third law of motion is an application of the first law.

Common Forces:

• Acceleration depends on the vector sum of all forces acting on an object.
• Common forces in Physics 11: Gravity (Fg), Normal force (Fn), Static and kinetic friction (Fs and Fk), Air resistance (drag) (Fd), and Tension force (Ft).

Gravitational Force:

• Gravitational force (Fg), or weight, is an attractive force between all objects with mass, proportional to the object's mass (m) and gravity (g): Fg = mg.
• Near Earth's surface, the average value of g = 9.81 m/s², but it varies by location and altitude.

Acceleration Due to Gravity

• The value of g varies depending on location on Earth, mainly due to Earth's rotation along its axis.
• g for the North Pole is 9.8322 m/s² = 0 m altitude and 6357km radius.
• g for the Equator is 9.7805 m/s² = 0 m altitude and 6378km radius.
• g for the Peak of Mt. Everest is 9.7647 m/s² = 8848 m altitude and 6387km radius.
• g for the Bottom of Mariana Ocean Trench is 9.8331 m/s² = -11034 m altitude and 6367km radius.
• g for the International Space Station is 9.0795 m/s² = 250,000m altitude and 6628m radius.

Weightlessness:

• Weightlessness in the ISS is due to being in free fall with the same acceleration, despite still experiencing gravity in orbit.

Gravity on Other Planets:

• Acceleration due to gravity on other planets can be calculated using the law of universal gravitation.
• Average g (m/s²) for Earth is 9.81.
• Average g (m/s²) for the Moon is 1.64.
• Average g (m/s²) for Mars is 3.72.
• Average g (m/s²) for Jupiter is 25.9.
• Gravitational attraction (Fg) between two point masses (m1, m2) at a distance (r) is given by: Fg = Gm1m2/r².

Normal Force:

• When two objects are in contact, they exert a force on each other at the interface.
• Contact force called normal force (Fn).
• Normal force is perpendicular to the interface.
• points away from the contact surface, always exists as an action-reaction pair, as required by the 3rd law of motion.
• On a slope, normal force remains perpendicular to the interface.
• Finding the magnitude of the normal force is part of the problem-solving process.
• An object can be in contact with multiple objects, resulting in multiple normal forces.
• At the interface between masses m3 and m1 there is one normal force, N13.
• For mass m2, in contact with the bottom surface and with m1, there are two normal forces.
• For mass m1, in contact with m2, m3, and the bottom surface, there are three normal forces.
• N21, N1, and N31 act are normal forces on mass m1.
• N21 and N12 is an action-reaction pair of forces with equal magnitude and opposite direction
• N31 and N13 is an action-reaction pair

Friction:

• Friction is a resistive force between two surfaces that opposes sliding motion at the surface.
• Overcoming friction and inertia is necessary when first moving an object.
• Static friction is between surfaces that are not moving relative to each other.
• Kinetic friction is friction exists when the object is moving and is approximately constant.
• Static friction depends on the applied force (Fa) and is at maximum when the surfaces are just about to slide against each other.
• Static Friction coefficent: Fs ≤ μsFn (Fs = Magnitude of static fricton, μs = Coefficient of static friction, Fn = Magnitude of normal force)
• Kinetic Friction: Fk = μkFn (Fk = Magnitude of kinetic friction, μk = Coefficient of kinetic friction, Fn = Magnitude of normal force) For anything to move, it must be that μk ≤ μs
• Free-body diagrams are used to represent forces acting on an object.
• The friction plus inertia must be overcome when an object is first moved.
• Example friction coeffients: Rubber on dry solid surface μs = 1-4, μk = 1.00

Tires

• Friction can slow things down, and can speed things up. For example, the forward acceleration of a car is caused by the static friction tires and the road.
• Tires generate rolling resistance as they deform under the car's weight.

Drag:

• Aircraft, bicycles, cars, and submarines moving through fluids experience drag force (Fd).
• Drag force opposes the velocity vector's direction.
• Drag depends on the speed and shape of the moving object.
• Fd = ½ ρV∞2 CDAref (Fd = Magnitude of drag ,ρ = Density of the fluid, V∞= Free-stream velocity, Aref = Reference area, CD = Drag coefficient)
• Drag coefficient (CD) depends on the object's shape and surface smoothness.
• For bluff bodies, Aref is the frontal area; for streamlined objects, the Aref is the planform (top-view) area.

Tension Force:

• Tension is the force transmitted through stretchable objects such as ropes when pulled.
• Examples include ropes, cables, and strings.
• Tension force in a cable can only be transmitted if it is in an extended state.
• One cannot push on a rope.
• Pulleys can be used to change the direction of the tension force.