Physics: Principal Systems of Units & Laws of Motion - PDF

Ch 1 Principal system of units Physics is an experimental science. science of measurements. Measurements should be accurate and reproducible. To ensure accuracy and reproducibility, units are made. Measurements of quantity is expressed by a number and unit. Physical quantities: 1-...

Ch 1 Principal system of units Physics is an experimental science. science of measurements. Measurements should be accurate and reproducible. To ensure accuracy and reproducibility, units are made. Measurements of quantity is expressed by a number and unit. Physical quantities: 1- Basic (fundamental) quantities Length , Mass, Time Electric current - ampere (A) Luminous intensity - candela (cd) Temperature - Kelvin (K) Amount of substance-mole (mol) 2- Derived quantities combination of basic quantities velocity = Distance/Time Force = (mass) (acceleration) = (mass) (velocity)/(time) energy (E) = force x distance Standards: to measure any quantity, standard must be defined Durable and stable chemical structure 1- Standard of length & unit -The distance between two lines on a platinum–iridium bar (1 meter) - Wavelength of orange-red light of krypton lamp 1 m = 1650763.73  k ( of krypton lamp = 605 nm) 1 m = The distance traveled by light in vacuum during a time of 1/299 792458 second. 2- Standard of mass & unit Mass of a cylinder of platinum-iridium designated as one kilogram, kept under controlled conditions [39mm dia and 39mm h]. 3- Standard of time The time between successive appearance of the sun „solar day‟ 1 sec = (1/60) (1/60) (1/24) of a mean solar day. The time it took the sun to move and back to the same point „tropical year‟ 1sec = 1 / 31556925.974 of tropical year (tropical year = 365.24 days) 1sec = time required for 9192631770 oscillations of radiation emitted by cesium atoms Systems of units Unit System Length Mass Time CGS Centimeter Gram second cm gm sec MKS (SI) Meter Kilogram second m kg sec fbs (British) Foot Pound second ft lb sec units must be the same on both sides of an equation. Basic units and derived units. Multiplies and submultiples (fractions) of metric units Prefixes correspond to powers of 10 Each prefix has a specific name and abbreviation Units Conversion - convert units from one system to another - convert within a system - Units can be treated as algebraic quantities that can cancel or multiply each other. 1 mile = 1 609 m = 1.609 km 1m = 39.37 in. = 3.281 ft 1 ft = 0.304 8 m = 30.48 cm 1 in = 0.025 4 m = 2.54 cm Conversion factor A conversion factor is a rearranged form of the equality used to convert one unit to the other by simple multiplication. conversion factor is equal to 1. Dimensions : The dimension of a physical quantity specifies the nature of the quantity. distance, time, energy,... Dimension of length [L] Dimension of mass [M] Dimension of time [T] Examples A circle of diameter d, its area A =  d2,  is non-dimensional the dimension of A is [L2] F = m. a, [F] = [M] [LT-2] = [M LT-2]. CGS unit: 1 dyne = 1 gm. cm / s2 , MKS unit: 1 Newton = 1 Kg. m / s2 N = (1000 gm x 100 cm) / s2 = 10 5 gm cm / s2 = 105 dyne Dimensional analysis 1- Verification/check of physical equations 2- Derive relations betn. physical quantities 3- Determine dimensions of constants - Dimensions can be treated as algebraic quantities. - Terms on both sides of an equation must have the same dimensions. - Quantities can be added or subtracted only if they have the same dimensions. 1- Verification/check of physical equations v = v0 + a t [L] / [T] = [L] /[T ] + ([L] / [T2 ]). [T] v = v0 x + a t not correct 1 X  Vot  at 2 correct 2 2- Derive relations betn. physical quantities Simple pendulum Periodic time T Length of thread L Acc. due to grav. g T  La T  gb T =CLa gb [T] = [ L ] a. [ L T-2 ] b [L 0 M 0 T 1] = [ L a+b ]. [ T -2b ] 0 = a+b and 1 = -2 b b = -1/2 and a = 1/2 T = C ( L/g)1/2 3- Determine dimensions of constants The general law of gravity: [M].[L ].[T-2 ] = G [M2 ]. [L-2 ] G = [M]. [L]. [T -2 ] / [M2 ]. [L-2 ] = [M -1 ].[L3 ].[T-2 1- The displacement of a particle moving under uniform acceleration is some function of the elapsed time and the acceleration. Suppose we write this displacement s = kam t n , where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can this analysis give the value of k? 2- The period T of a simple pendulum is measured in time units and is L described by T = 2π where L is the length of the pendulum and g is the g freefall acceleration in units of length divided by the square of time. Show that this equation is dimensionally correct. GMm 3- Newton‟s law of universal gravitation is represented by F = Here F is r2 the gravitational force, M and m are masses, and r is a length. Force has the SI unitskg.m s2 n What are the SI units of the proportionality constant G?  Ch 2 The laws of motion The concept of force Force is what cause any change in motion of an object. A force is a push or a pull on an object.  Increase (accelerate) or decrease the speed of an object  change the direction in which an object is moving. Forces do not always cause motion. The net force (T.F, R.F) on an object is the vector sum of all forces acting on that object. the net force = 0 object not accelerates (acc=0 & con. Velocity) the net force  0 object accelerates Balanced Force and unbalanced Force 1- Balanced forces Forces in equal and opposite directions. Do not cause a change in motion. 10 N 10 N Net force = 0 object at equilibrium Do not accelerate 2- Unbalanced Force cause an object to move, stop moving, or change direction. Net force 3N 10 N 20 N 10 N = 10 N 20 N 10 N 4N = 10 N 30 N 5N = 20 N 36o object is not at equilibrium accelerate forces in opposite directions combine by subtraction. forces in the same direction combine by addition.  Newton’s Laws of Motion 1st Law – An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force. 2nd Law – Force equals mass times acceleration. 3rd Law – For every action there is an equal and opposite reaction. Newton’s 1st law (law of inertia) In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity in a straight line. It deals only with objects that are not accelerating. No interaction between the object and environment (Isolated object). Isolated object is either at rest or moving with const velocity (in equilibrium). If objects in motion tend to stay in motion, why don‟t moving objects keep moving forever ? Things don‟t keep moving forever because there‟s almost always an unbalanced force acting upon them. A book sliding across a table slows down and stops because of the force of friction. If you throw a ball upwards it will eventually slow down and fall because of the force of gravity. Inertia of the object Objects tend to "keep on doing what they're doing.“ Inertia is the tendency of an object to resist changes in its state of motion (moving or at rest). Inertia is a property of an object that describes how much it will resist changes to the motion. More mass more inertia more force to start or stop small mass small inertia less force to start or stop The mass of an object is a quantitative measure of inertia. Types of Inertia: Inertia of Rest: The inability of a body to change by itself its state of rest. Examples: (i) Person sitting in a car falls backwards, when the car suddenly starts. It is because the lower portion in contact with the car comes in motion where as the upper part tries to remain at rest due to inertia of rest. (b) Inertia of Motion: The Inability of a body to change by itself its state of uniform motion. Examples: (i) When a moving car suddenly stops, the person sitting in the car falls forward because the lower portion of the body in contact with the car comes to rest whereas the upper part tends to remain in motion due to inertia of motion. (c) Inertia of Direction: The inability of a body to change by itself its direction of motion. Examples: (i) When a car moves round a curve the person sitting inside is thrown outwards in order to maintain his direction of motion due to inertia of motion. Mass and inertia Mass is the amount of matter in an object. Independent of the object‟s surroundings and of the method used to measure it. Mass units is kg or gm Inertia is a measure of how an object responds/resists to an external force. Mass is that property of an object that specifies how much inertia the object has.  12N 3 kg a = 4m/sec 2 m1 a2 12 N  6 kg a = 2m/sec 2 m2 a1 The greater the mass of an object, the less that object accelerates under the action of an applied force. Newton’s 2nd law [Force, Mass, and Acceleration ] 1st law of Newton explains what happens to an object (at rest or moves) when no forces act on it. 2nd law of Newton explains what happens to an object when the net force ≠ 0 (unbalanced). The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F = ma     F  F  ma, a m F  m a x x F  m a y y F  m a z z 10 N 5 kg a = 2 m/sec2 20 N 5 kg a = 4 m/sec2 a F 30 N 5 kg a = 6 m/sec2 12N 3 kg a = 4m/sec 2 1 a 12 N m 6 kg a = 2m/sec 2 Unit of force (N) The Newton (N) is defined as the force needed to cause a mass of a 1-kg to accelerate at 1 m/sec2. MKS unit: 1 Newton = 1 Kg. m / sec2 1 N = (1000 gm x 100 cm) / sec2 =10 5 gm cm / sec2 CGS unit: 1 dyne = 1 gm. cm / sec2 1N = 105 dyne  Using Newton‟s 2nd Law to Solve Problems 1. Identify all forces acting on the object -Pushes or Pulls -Frictional forces -Tension in a string -Gravitational Force (or weight = mg) - “Normal forces” (one object touching another). 2. Draw a “Freebody Diagram” -draw the object, show all forces acting on that object as vectors pointing in the correct direction. Show the direction of the acceleration. 3. Chose a coordinate system. 4. Translate the freebody diagram into an algebraic expression based on Newton‟s second law. A free-body-diagram is a diagram that represents the object and the forces that act on it. The Force of Gravity and Weight All objects are attracted to the Earth due to the force of gravity. The force of gravity (Fg ) is the attractive force exerted by the Earth on an object. Directed toward the center of the Earth. Fg magnitude is called the weight of the object. Ex: a freely falling object of mass (m) experiences an acceleration g acting toward the center of the Earth. Fg  mg g = 9.8 m / sec2 WEIGHT WEIGHT is a measure of the force of gravity on the mass of an object. measured in Newtons Newton’s 3rd Law - Action and Reaction Newton‟s 1st and 2nd laws of motion explain how the motion of a single object changes. Newton‟s 3rd law describes what happens when one object exerts a force on another object, interactions between them. “For every action there is an equal and opposite reaction.” “ For every force, there is an equal and opposite force”. action-reaction force pair.  Either force can be considered the action force or the reaction force. Action and reaction force pairs don‟t cancel because they act on different objects. Action-reaction pair of forces cannot act on same body; they act on different bodies. Forces of Friction When an object is in motion either on a surface or in a viscous medium such as air or water, there is resistance to the motion because the object interacts with its surroundings. We call such resistance a force of friction. The friction force arises from the nature of the two surfaces: because of their roughness, contact is made only at a few locations where peaks of the material touch. At these locations, the friction force arises in part because one peak physically blocks the motion of a peak from the opposing surface. Smooth surfaces produce less friction than rough surfaces. Forces of Friction Friction force is the force that resists the motion between two surfaces that touch. Friction force acts in a direction opposite to the direction of the object‟s motion. The friction force depends on: Roughness of the surfaces. Force pushing the surfaces together. Types of Friction 1. Static friction 2. Sliding (kinetic) friction (strongest) 3. Rolling friction 4. Fluid friction (weakest). Force of static friction fs F  fs F  f s max   s n  F  f s max F  fs fs  fk net force  F  f k Object at rest Static friction force Object accelerates, +x kinetic friction force if F is increased, fs also increases what if F  f k f s  s n µs is the coeff. of static friction. n is the normal force. f k  k n µK is the coeff. Of kinetic friction. f s  f s max   s n n is the normal force. F  f s max  s n  µs and µK are dimensionless constant, µs and µK depend on the nature of the surfaces. 0   s ,k  1 An Accelerating Hockey Puck A hockey puck having a mass of 0.30 kg slides on the horizontal, frictionless surface of an ice rink. Two forces act on the puck, as shown in Figure. The force F1 has a magnitude of 5.0 N, and the force F2 has a magnitude of 8.0 N. Determine both the magnitude and the direction of the puck’s acceleration. Solution The resultant force in the x direction is F = F1x + F2x = F1 cos −20° + F2 cos(60°) x F = (5.0 N)(0.940) + (8.0 N)(0.500) x = 8.7 N F = F1y + F2y = F1 sin −20° + F2 sin(60°) y F = 5.0 N −0.342 + 8.0 N 0.866 = 5.2 N y  xF8.7N ax = = = 29 m 2 m 0.3Kg s yF 5.2N ay = = = 17 m 2 m 0.3Kg s The acceleration has a magnitude of a= 292 + 172 = 34 m s2 its direction relative to the positive x axis is −1 ax −1 17 θ = tan = tan = 30 ay 29 A Traffic Light at Rest A traffic light weighing 125 N hangs from a cable tied to two other cables fastened to a support. The upper cables make angles of 37.0° and 53.0° with the horizontal. Find the tension in the three cables.  xF = −T1 cos37° + T2 cos53° = 0 (1) yF = T1 sin37° + T2 sin53° + −125N = 0 (2) cos37° T2 = T1 = 1.33T1 cos53° This value for T2 is substituted into (2) to yield T1 sin37 + 1.33T1 sin53 − 125 = 0 T1 = 75.1N T2 = 1.33T1 = 99.9N T3 = Fg = 125N In what situation does T1 = T2 ? The Sliding Hockey Puck A hockey puck on a frozen pond is given an initial speed of 20.0 m/s. If the puck always remains on the ice and slides 115 m before coming to rest, determine the coefficient of kinetic friction between the puck and ice. xF = fk = max (1) y F = n − mg = 0 (ay = 0) (2) from (2), n = mg Therefore, (1) becomes −μk n = −μk mg = max (fk = μk n) ax = −μk g 2 2 vxf = vxi + 2ax xf − xi , with xi = 0 and vxf = 0 2 2 vxi + 2ax xf = 0 vxi − 2μk g xf = 0 (20m s)2 μk = = 0.177 2(9.8m s2 )(115m) - A ball is held in a person’s hand. (a) Identify all the external forces acting on the ball and the reaction to each. (b) If the ball is dropped, what force is exerted on it while it is falling? Identify the reaction force in this case. (Neglect air resistance.) - If a car is traveling westward with a constant speed of 20 m/s, what is the resultant force acting on it? - A rubber ball is dropped onto the floor. What force causes the ball to bounce? - What is wrong with the statement, “Because the car is at rest, no forces are acting on it”? How would you correct this statement? - A force F applied to an object of mass m1 produces an acceleration of 3.00 m s 2. The same force applied to a second object of mass m2 produces an acceleration of 1.00m s2. (a) What is the value of the ratio m1 m2 ? (b) If m1 and m2 are combined, find their acceleration under the action of the force F. - A force of 10.0 N acts on a body of mass 2.00 kg. What are (a) the body’s acceleration, (b) its weight in newton, (c) its acceleration if the force is doubled?