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Final

# Physics Final Review.docx

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School
University of Guelph
Department
Physics
Course
PHYS 1080
Professor
Mike Massa
Semester
Fall

Description
Physics Final Review: Mechanics: - Relationship between object’s motion (kinematics) and forces acting on it (newton’s laws) Displacement: velocity: acceleration: If a=0: v=v ond x=x + vot o - Displacement is - displacement is positive - Velocity is positive and positive constant - Velocity is increasing - Acceleration is positive - Acceleration is zero - Displacement is positive - Displacement is positive - Velocity is increasing - Velocity is positive and constant - Acceleration is positive - Acceleration is zero - Area under curve = displacement Gravity influences motion with constant vertical acceleration g= 9.8m/s , motion in the horizontal and vertical direction are independent of each other Pen swipe: swipe over θ gives cos, away gives sin; put pen over vector r and then rotate it from there to component of interest Relative velocity: - Motion occurs at constant velocity but total motion is due to contribution from 2 factors - Ex. Someone trying to swim directly across a river with a current - Usually contain 3 velocities: identify 2 and add to determine 3 (resultant) - Wind speed or water speed not likely resultant velocity - One velocity in normal conditions - Combine to give resultant or net motion Force: - Interaction between 2 bodies: an object and an agent - Something that causes an acceleration - A vector (magnitude and direction) - Without a force there is no acceleration 1 - Can be produced with or without contact - Types: gravitational, normal force, tension, friction, magnetic/electric Newton’s laws of motion: - An object in a state of uniform motion will remain doing so unless acted on by a non-zero resultant force - If a resultant force acting on an object leads to an acceleration in the direction of the force, the acceleration is proportional to the force and inversely proportional to the object’s mass - For every force there is an equal but opposite reaction force ⃗⃗⃗⃗⃗⃗⃗ object at rest remains at rest and object in motion remains in motion unless external force is applied Static equilibrium- net force is zero and object isn’t moving (v=0) Dynamic equilibrium- net force is zero and object moves with constant velocity Equilibrium ⃗⃗⃗⃗⃗⃗⃗ Free body diagrams- diagram that represents all forces acting on object - Don’t draw forces acting on other objects, caused by this object, internal forces, forces for “ma” term Static friction (objects that are NOT moving): - fswill match applied force - f doesn’t have a pre-defined value s - force of static friction can have value up to some maximum (just as object starts to move) - static friction will take whatever value is needed to ensure that the object obeys Newton’s Laws Kinetic friction (unbalanced forces): - fk=µ k - when drawing FBD line up x or y axis with direction of acceleration Torque- forces caused by rotation - measure of ability of a force to cause rotation of an object - depends on how hard we push (F), how far we are from pivot (R) 2 - generate a larger torque with either a larger force or by applying force at a larger distance from pivot - in order to keep things from rotating, applied torques must satisfy: Linear momentum: [kg•m/s] Conservation of momentum: - system with no external forces, total momentum remains constant - comes from Newton’s laws of motion - remember: total comes from a vector summation over all objects in system Momentum in 2-D: - is a vector quantity- can treat x,y components independently, conservation of momentum applies to each - Collision types: completely inelastic objects stick together, elastic energy is conserved Energy and work: - Kinetic - Gravitational potential - Food/chemical - Heat 2 2 - Units: Joule= kg•m /s - Work= force x distance - Work and energy are both scalar Work done by a conservative force is independent of path traveled by object the force is acting on; same no matter the path Work done by non-conservative force depends on path taken Kinetic and potential energy: K= ½ mv 2 Change in K = total work done on object: Potential Energy (gravity): U=mgy When height changes, you have a change in potential energy ** only the vertical displacement matters: ΔU=mgΔy 3 Conservation of energy: - Energy can be transferred from one form to another but the total energy of the system is conserved - E= Total mechanical energy - With only conservative forces (gravity, elasticity) only initial and final positions matter - When work is done on the system work done by friction depends on objects path Uniform Circular Motion: - Object moves in a circular motion at a uniform speed, the velocity is tangent to the circle - Must be an acceleration that has direction towards center of circular path Period (T)- time to travel circumference Frequency f=1/T Radians- units of measure of angular distance in θ direction 2π radians= 360⁰ Angular velocity (ω): ω=2π/T = 2πf Centripetal acceleration: v=rω, so a second expression for centripetal acceleration is: Centripetal force- force directed radially inward on an object moving in a circular path, source of centripetal force could be gravity, tension, friction, etc. RESULTANT FORCE - Don’t add as a contributing force in FBD Centrifugal force- radially outward from axis of rotation, a fictitious force arising from observations from a non-inertial frame of reference Position described by angle θ, distance displacement: Units: 2 Angular velocity (ω): [rad/s] Angular acceleration (α): [rad/s ] Convention: define positive direction to be counter clockwise 4 The effectiveness of force at causing rotation depends on: - Magnitude of force - Distance from pivot - Direction of force with respect to pivot The net torque acting on a system is the vector sum of all torques action on the system Rigid body equilibrium: Translational equilibrium: Rotational Equilibrium: Therefore a rigid body is in equilibrium if both Force of gravity acts at centre of mass- for objects of uniform density, simple shape, and centre of mass is at centre of object Using a pivot point- choose based on simplifying problem (fewer torques to consider)- forces point directly towards/away from pivot, forces acting at zero distance from pivot **for statics can choose pivot anywhere you want and can look at as many pivots as it takes Two ways to think about torque: The lever arm or momentum arm is perpendicular distance from the axis of rotation to the line of the force θ is the angle between force and line from pivot to point of force Rotational Kinetic Energy: Moment of inertia: - Depends on rotation axis - m far from axis large I - m close to axis  small I - for some extended body rigid objects there is often a simple expression for I such as: 5 Kinetic energy- of a spinning top- rotation axis is fixed: Kinetic energy of a flying frisbee (rotational and translational): For rolling need friction Disc vs. hoop: small I large v, small I in ½ Iω term means more of the input energy, mgh, can be used to increase v 6 If there is a net torque, the object will rotationally accelerate: ⃗ Conservation of angular momentum (L): , if no external torque is applied then angular momentum is conserved (L=constant) When you can’t use conservation of angular momentum: - when the external force is applied to the system, the system’s momentum, p is no longer conserved - when an external torque is applied to a system, the system’s angular momentum is no longer conserved Elasticity- no material is completely rigid: apply a force, it will deform, depending on type of material, some things may deform more readily than others, apply large enough force, eventually it will break Ways to deform: tension, compression, shear, torsion Tension and compression: Y= Young’s modulus [N/m =Pa] 2 2 Stress (σ) [N/m ] Strain (ε) [no units] Linear regime: when deformations are small Y is constant (but Y[tension] and Y[compression] may be different) Shear Deformation: G= shear modulus [N/m =Pa] 2 Non-linear response to stress (human bones): tension and compression applied at same time; starts off linear Torsional shear for a solid cylinder: torsional shear for a hollow cylinder: Scaling: set of arguments that can be used to suggest reasons behind some trends in living organisms such as upper limits to size, function of organs, strength, speed, intelligence, age Isometric= same geometry, different size When we compare 2 objects we assume that their linear dimensions (length, width, height) scale in same proportion 7 Use ratios: Define a length scale L, Area (heat flow, strength) ∝ L ; volume (mass, heat generation) ∝L 3 Fluid statics: - molecular motion of fluids atoms/molecules collide with container walls- results in force on walls Pressure- magnitude of normal force per unit area; same2in every direction, liquid exerts this pressure on any immersed surface; Units: N/m = Pa, atm=101.3 kPa Hydrostatic pressure- pressure in a fluid that depends on the depth; deeper greater P ΔP ρgh Absolute vs. Gauge pressure: - Atmospheric pressure around us is an absolute pressure - Gauge pressure is a measure of one absolute pressure relative to another absolute pressure - Reference pressure (P ) 1ypically the atmosphere so: - Gauge can be negative - U-tube manometers are used to measure pressure differences between 2 gas chambers Other units of pressure: mmHg, bar, cmH O 2 A
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