Lecture notes and guidelines used during times of my profession as a private tutor/lecturer.
Kinematics Schedule
Kinematics
- Uniform motion: movement at a constant speed in a straight line
- Nonuniform motion: movement involves in speed and/or direction
- Base units and derived units
- Scalar quantity: magnitude only
- Instantaneous speed: speed at a particular instant
- Average speed = total distance / time
- Vector quantity: both magnitude and direction
- Position(d): distance and direction of an object from a reference point
- Displacement(Δd): change in position of an object in a given direction
- Resultant displacement(ΔdR) = Σ(Δd)
- (Pythagorean theorem example)
- Velocity: rate of change in position
- Average velocity(ν) = Δd(change of position) / Δt(time interval)
- Acceleration: rate of change in velocity
- Instantaneous acceleration
- Average acceleration(a) = Δv(change of velocity)/Δt
- Calculus application
- Derivatives and integral
- calculation of uniform acceleration from position-time graph
- tangent technique
- a = Δv / Δt
- vf = vi + a*Δt
- Δd = ½(vi+vf)Δt (integral)
- Δd = viΔt + ½a(Δt)²
- Δd = ½(vi+vf)(vf-vi)/a
- Δd = (vf²-vi²)/2a
Forces and Motion
- Force: simply push or pull
- Gravitational force: force of attraction between all objects in the universe
- mass: quantity of matter in an object
- weight: force of gravity on an object
- Law of Universal Gravitation: the force of gravitational attraction between any two objects is directly proportional to the product of the masses of the objects, and inversely proportional to the square of the distance between their centres.
- FG = Gm₁m₂/d² G=6.67 x 10e-11 N*m²/kg²
- Normal force: force perpendicular to the surfaces of the objects in contact
- Friction = μ x FN
- static friction: force that tends to prevent a stationary object from starting to move
- kinetic friction: force that acts against an object's motion in a direction opposite to the direction of motion
Newton's First Law of Motion: the law of inertia
- If the net force acting on an object is zero, the object will maintain its state of rest or constant velocity
- Objects at rest tend to remain at rest (e.g. acceleration in moving vehicle)
- Objects in motion tend to remain in motion (e.g. de-acceleration in moving vehicle)
- If the velocity of an object is constant, the net external force acting on it must be zero.
- If the velocity of an object is changing in either magnitude and/or direction, the change must be caused by a net external force acting on the object.
- Inertia: property of matter that causes a body to resist changes in its state of motion; directly proportional to the mass
Newton's Second Law of Motion
- If the net external force on an object is not zero, the object accelerates in the direction of the net force. The magnitude of the acceleration is proportional to the magnitude of the net force and is inversely proportional to the object's mass
Newton's Third Law of Motion: action-reaction
- For every action force, there is a reaction force equal in magnitude, but opposite in direction
- e.g. Earth and an apple
Energy, Work, Power
- Energy: capacity to do work
- Gravitational potential energy: possessed by an object because of its position relative to a lower position
- Eg = FΔh = mgΔh
- Kinetic energy: energy due to the motion of an object
- Ek = FΔd = maΔd = ½mv² (derivation)
- Thermal energy: energy in which temperature
- temperature: measure of the average kinetic energy of the substance
- Law of Conservation of Energy and Efficiency
- When energy changes from one form to another, no energy is lost. (example problem)
- Efficiency = useful energy output / energy input (e.g. lightbulb - heat)
- Work:energy transferred to an object by an applied force over a measured distance (Joules = N x m)
- W = FΔd
- Power:rate of doing work or transforming energy (Watts = J / t)
- P = W/Δt= ΔE/Δt
Momentum and Collision
- p = mv
- J = Δp = FΔt =
- Conservation of momentum: momentum stays constant
- Collision
- Elastic collision
- Inelastic collision
Circular Motion
- Uniform circular motion: occurs when a body moves in a circular path with constant speed
- Centripetal Acceleration: ac = v² / r
- Centripetal Force: T = mac = mv² / r
- Newton’s Law of Universal Gravitation
- Fg = G x m1m2 / r²
- gravitational constant G = 6.67e-11 Nm²/kg²
Physics: Work & Energy problem set
1. How much work does a person do in pushing a box with a force of 10 N over a distance of 4.0 m in the direction of the force?
2. A person pushes a 10 kg box at a constant velocity over a distance of 4 m. The coefficient of kinetic friction between the box and the floor is 0.3. How much work does the person do in pushing the box?
3. How much work does the force of gravity do in pulling a 10 kg box down a 30º inclined plane of length 8.0 m? Note that sin 30 = cos 60 = 0.500 and cos 30 = sin 60 = 0.866.
4. How much work does a person do in pushing a box with a force of 20 N over a distance of 8.0 m in the direction of the force?
5. A worker does 500 J of work on a 10 kg box. If the box transfers 375 J of heat to the floor through the friction between the box and the floor, what is the velocity of the box after the work has been done on it?
6. A person on the street wants to throw an 8 kg book up to a person leaning out of a window 5 m above street level. With what velocity must the person throw the book so that it reaches the person in the window?
7. A forklift lifts a crate of mass 100 kg at a constant velocity to a height of 8 m over a time of 4 s. The forklift then holds the crate in place for 20 s.
How much power does the forklift exert in lifting the crate?
How much power does the forklift exert in holding the crate in place?
Answer key: 1. 40J 2. 120J 3. 400J 4. 160J 5. 5 m/s 6. 10 m/s 7. 2.0 kW; 0W
