PHYS1002 - Lecture notes 1-30 PDF

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PHYS1002 Week 1 Static equilibrium no change between reactants and products the object is not moving in any way. Vector sum of forces on the body must be zero Vector sum of torques on the body must be zero Week 2 When doing buoyancy calculations, remember: Immersed an object submerged fully immersed...

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PHYS1002 Week 1 Static equilibrium = no change between reactants and products / the object is not moving in any way. - Vector sum of forces on the body must be zero - Vector sum of torques on the body must be zero

Week 2 When doing buoyancy calculations, remember: - Immersed = an object on/in water; submerged = fully immersed. - Buoyant force only acts on the submerged part of the object. Density = m/V Buoyancy = ability or tendency of an object to float in a fluid, which can be a liquid or a gas. The buoyant force only depends on the submerged volume. Buoyant force = weight of the volume of water displaced = the volume that overflows; only depends on the submerged volume Pressure = At rest = While afloat = The pressure in a fluid increases with depth (p = gd). Archimedes’ principle = when an object is immersed in a fluid, there is an upward buoyant force equal to the weight of the volume of fluid displaced by the object. The principle applies to either full or partial immersion.

Use the concepts of density, buoyancy and pressure

Explain phenomena associated with fluids at rest and flotation Explain variations in pressure with depth Use Archimedes’ principle

Week 3 Distance = total path length travelled; no direction. Displacement = length and direction of a straight line drawn from start to finish. Average speed = distance/time; no direction. Average velocity = displacement/time; has direction. Acceleration = rate at which velocity changes with time. A free falling object = one that’s only influenced by the force of gravity = acceleration is always g. Instantaneous measurements are made at a particular instant of time. Average measurements are made over a time interval. If Fa = Vector a, Fb = Vector b; then net force = Fa+Fb = Vector a + Vector b.

One dimension = distance, speed. Two dimensions = displacement, velocity. When analysing 2D motion, the horizontal and vertical components are independent of each other.

Describe motion using displacement, velocity, acceleration and free fall acceleration

Differentiate between average and instantaneous measurements Manipulate vectors describing physical situations

Explain motion in one and two dimensions and do associated calculations

Week 4 There’s acceleration when a satellite moves in a circle as its direction is constantly changing; its velocity is always tangent to the circle orbit of the earth. The reason why it stays circling in orbit is due to the fact that two separate accelerations are acting on it – centripetal (provided by gravity) (pushing it to the middle of the circle) and tangential (provided by momentum) (pushing it forward). The two accelerations are acting perpendicular to one another, thus the overall acceleration magnitude can be found using Pythagoras. Mass of the object does not depend on location, but weight does. An object in orbit is in a free fall, since the only force acting on the object is the gravitational attraction of the Earth, AND… Because it’s in free fall, we can calculate the apparent weight of the object by: wapp = w + may = mg + may Since it’s in free fall, the ay = -g , and therefore, wapp = 0 = weightlessness.

Explain the motion of satellites

Explain mass and weight in the context of orbiting objects

Week 5 Force = a push or a pull that changes the velocity of an object. It’s a vector, thus has a direction and magnitude. Two or more forces acting on the same object can be added by using the rules of vector addition. Force can be contact (e.g. push/pull, tension in rope, friction) or long-range (e.g. gravity, electromagnetic, weak). Net force = vector sum of all the forces acting on an object. Mass = quantity of matter in a body regardless of forces. Point of mass = point in space where the entire mass of the object has been concentrated as it seems. Force can be physical contact (e.g. push/pull, tension in rope, friction, normal) or field through empty space (e.g. gravity). - Gravitational force = force that attracts any two objects with mass. - Weight = force exerted on a body by gravity = mg. - Contact force = force that acts at a point of contact between two objects. - Normal force = if one pushes against a planar surface, the planar surface pushes back with a force perpendicular to that surface. - Frictional force = resistance to motion of one object moving relative to another; always parallel to the surface, and always opposes the direction of motion. - Tension = force that is transmitted through a rope/string/wire when pulled by forces acting from opposite sides; directed over the length of wire and pulls energy equally on the bodies at the ends. First Law = every object in a state of uniform motion will remain in that state of motion unless an external force acts on it. Also known as the law of inertia. Second Law = force equals to mass times acceleration. This law actually

Understand and be able to use the following concepts: - force - net force - mass - particle (or point mass) Describe the following different forces and use them where appropriate: - gravitational force - weight - contact force - normal force - frictional force - string force (tension)

Understand and apply Newton's three laws of motion

implies the first law, since when there’s no force, the acceleration is zero. Third Law = for every action there is an equal and opposite reaction. Implies conservation of momentum. It follows that forces always occur in pairs (e.g. bottle resting on a table has the gravitational force + normal force of the table acting on it). It’s important to remember that even though all forces are paired, the action and the reaction forces are NOT exerted on the same object. When two forces are acting on the same object, they aren’t considered to be an action-reaction pair. Free body diagram = diagram showing all the forces acting on a body. 1. Draw a dot representing the centre of mass of the body. 2. Draw each force acting on the body as an arrow originating at the dot. 3. Draw the net force vector.

Be able to draw free body diagrams and solve problems using Newton’s Laws

Week 6 All types of friction act as to oppose the motion. - Static friction = applies to stationery objects; acts to prevent motion. - Kinetic friction = applies to moving objects. - Rolling friction = applies to objects that have very little contact with the surface (i.e. a wheel).  measures the strength of friction – it’s a property of both surfaces. This measure doesn’t depend on the size of the surfaces, only their properties. This value is largest with static friction > kinetic friction > rolling friction (for example, it’s harder to get a stationery object to move up a hill rather than a moving one; wheels have the least friction – rolling friction). Changing the magnitude of the push force will also change the friction force (directly proportional). Eventually, the static friction force can be overcome – at some point the friction force gave up. The maximum magnitude to which the static friction force can grow to is give by: F s=❑ s N This is a scalar equation, as the forces aren’t on the same axis (N vertical, and Fs is horizontal). Once the box starts to slide, static friction is replaced by kinetic friction: F k =❑k N Kinetic friction doesn’t depend on speed if the object is pushed with constant speed. When accelerating, there’s a net force (the two forces don’t cancel each other out). When an object is moving round in a circle with uniform motion, a force is applied, pulling it towards the centre = centripetal force. The magnitude of this force can be determined using the second law.

Describe the different types of frictional forces: - static frictional force - kinetic frictional force - coefficient of (static or kinetic) friction

Apply the different types of frictional forces in appropriate situations

Discuss the concept of centripetal acceleration and identify the forces that supply this acceleration

Week 7 Centre of mass = a unique point in an object/system to represent the system’s response to external forces. The concept is that of an average of the masses factored by their distances from a reference point.

Angular velocity = angular displacement through which the particle moves each second. Constant for a particle moving in uniform circular motion.

Angular position = angle from the positive x-axis, indicating the position of a particle in the circle with a fixed radius. Angular displacement = angle through which an object moves on a circular path = distance the particle had travelled along a circular path. Tangential velocity = component of motion along the edge of a circle whose direction at any given point on the circle is always along the tangent to that point. If motion is uniform and object takes time t to execute motion, then it has tangential velocity. Arc length/tangential displacement = distance the particle has travelled along a circular path. Centripetal acceleration = when acceleration points towards centre. Torque = rotational equivalent of force = measures the effectiveness of a force causing an object to rotate about a pivot. Rotational axis = Point of application = location at which the force is applied to a body. Line of action = line through the point at which the force is applied in the same direction as the vector of the force. For an object to be in static equilibrium: - No net force - No net torque

Linear momentum = product of an object’s mass and its velocity. Total linear momentum = vector sum of individual momenta. Conservation of linear momentum = total momentum before interaction equals total momentum after = momentum is conserved. Internal forces = forces between objects within the system; cause energy transformations within the system but don’t change the system’s total energy. External forces = forces from agents outside the system. Conservation of linear momentum expresses the fact that a body or a system of bodies retains its total momentum, the product of mass and vector velocity, unless an external force is applied to it. This law can consequently be explained from Newton’s second law = the rate of change of linear momentum of a body is equal to the net external force applied to it.

Understand and be able to use the concept of centre of mass and be able to estimate or calculate the position of this, in 1 and 2 dimensions, for simple objects or collections of particles Understand and be able to use the following concepts: angular velocity, angular displacement, tangential velocity, arc length or tangential displacement

Understand the following concepts: Torque, rotation axis, point of application of a force and line of action of a force Apply these concepts to find the torque of a force about an axis of rotation Calculate necessary values of forces for equilibrium conditions, using the fact that, for equilibrium, the sum of forces and the sum of torques are both zero Understand the concepts of linear momentum, total linear momentum, conservation of linear momentum, internal force, and external force

Understand the law of conservation of linear momentum for a system of particles Apply Newton's second law of motion to a system

Impulse of a force = the change in momentum caused by that force. Average force = constant force that has the same duration and the same area under the force curve as the real force. . Impulse-momentum theorem = states that an impulse delivered to an object causes the object’s momentum to change. Elastic collision = a collision in which both momentum and kinetic energy are conserved (e.g. a rubber ball thrown on the floor). Inelastic collision = a collision in which the momentum is conserved, but a part of kinetic energy is converted to other forms of energy (e.g. car crash). This introduces recoil momentum =

of particles using the concept of linear momentum for a system of particles Understand the concepts of impulse, average force Apply the impulse-linear momentum theorem Understand the difference between an elastic and inelastic collision, and apply the relevant conservation laws in each case

Week 8 Kinetic energy = energy of motion. Translational kinetic energy = k.e. of an object moving along a line/path. Rotational kinetic energy = kinetic energy due to rotation. A rolling object undergoes both. Potential energy = energy stored in the system of interacting objects – it has the potential to be converted into other forms of energy. Work = process by which energy is transferred to or from a system by the application of mechanical forces. . Power = rate at which energy is transformed or at which work is done.

W = Fd

Describe the concepts of, kinetic energy, potential energy, work and power

Calculate the work done by the gravitational force Calculate the work done by a variable force Explain the difference between conservative and non-conservative (or dissipative) forces

Conservative forces = interaction forces that can store useful energy = gravity elastic forces. The work a conservative force does on an object in moving it from A to B is path independent – depends only on the end point of the motion. Nonconservative forces = energy is transformed/dissipated rather than stored = friction, air resistance. The work done in going from A to B depends on the path taken. Kinetic energy + potential energy = mechanical energy. Understand and apply the In an isolated system without friction, mechanical energy is conserved. principle of conservation of mechanical energy for an isolated system In an isolated system with friction, the total energy is conserved; friction Understand the converts work directly into thermal energy. relationship between work done by external forces, including frictional forces, and the change in energy of the system Use the above concepts and principles for calculations in appropriate situations

Week 9 Periodic motion = any type of repeated motion. Simple harmonic motion = periodic motion where the restoring force is proportional to the displacement = motion of constant amplitude. Period = time to complete one full cycle. Amplitude = object’s maximum displacement from equilibrium. Frequency = number of cycles per second. Phase = angular position of the particle on the circle. Angular frequency = radians per second. Frequency = cycles per second.

Describe and define periodic motion and simple harmonic motion (SHM) Use the period, amplitude and phase to describe SHM, and find the position, velocity and acceleration Distinguish frequency and angular frequency Describe restoring forces acting on a spring or simple pendulum

Week 10 Components of energy in SHM oscillate between kinetic (of the moving object attached to the spring) and potential (elastic potential energy of the spring). Total energy is conserved: F = -kx

The string force is given by Hooke’s law; in SHM, this is the linear restoring force = net force toward the equilibrium position that’s proportional to the distance from equilibrium. Pendulum = mass suspended from a pivot point by a light string/rod. At small angles, sinx = x.

Damped oscillation = an oscillation that runs down and stops. Amplitude decreases, but the period and the frequency remain the same + velocity decreases. . Caused by friction, and decreases exponentially. Faster decay = smaller time constant (time for amplitude to decay). When things vibrate at resonance frequency, there’s a huge rise in energy transfer. Supplied frequency to a natural frequency system = driving frequency of a system. Response curve = graph of amplitude vs driving frequency. Highest amplitude = lowest damping = highest time constant. Wave = organised disturbance that travels with a well-defined wave speed.

Explain the interchange of potential and kinetic energy in mechanical oscillations Use energy conservation in solving for parameters of an oscillating system Relate the force law (e.g. Hooke’s law for a spring) and the mass to the period in SHM Explain the motion of the simple pendulum; recognise the approximation used in deriving the smallamplitude formula for the period of a pendulum Explain the behaviour of a damped oscillator, including the effects of different degrees of damping Explain the phenomenon of resonance Sketch resonance diagrams (amplitude vs driving frequency) Explain the dependence on driving (forcing) frequency, natural frequency, and degree of damping Define, describe, and give

Mechanical waves = move through a medium; the medium’s “particle” doesn’t propagate with the wave, it only moves. Transverse = Particles in a medium move perpendicular to the direction in which the wave travels; e.g. light, radio. Longitudal = particles in the medium move parallel to the direction in which the wave travels; e.g. sound.

examples of wave motion Explain the critical difference between the motion of a wave and the motion of a particle in the medium as the wave passes Distinguish and describe transverse and longitudinal waves...