1- The first one is called scalar product or dot product because the result of the product is a

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1 Summary of the laws Vector 1- Vector addition a). Pythagorean Theorem R A B A 2 & 2 B 1 Tan (B/A ) To calculate the magnitude A+B & A-B with angle degree 2 2 A B A B 2AB COS 2 2 A B A B 2AB COS B). Analytical Method or called Component's Method To calculate the components and magnitude of vector for example the components of vector A are Ax = A Cos θ and Ay = A sin θ To calculate the magnitude of vector for example magnitude vector A and direction 1 angle We use the equation 2 2 A A x A y and Tan ( A /A ) y x 2- Product of Vectors There are two kinds of vector product: 1- The first one is called scalar product or dot product because the result of the product is a scalar quantity. A. B= A B COSθ 2- The second is called vector product or cross product because the result is a vector perpendicular to the plane of the two vectors A x B= A B Sinθ 3-Unit Vector Notation a) Unit Vector notation addition If A&B are two vectors, where A = axi + ayj + azk& B = bxi + byj + bzk Then the: 1- To find A+B and A B A+B= (ax +bx)i + (ay +by)j + (az +bz)k & A B= (ax bx)i + (ay by)j + (az bz)k b) Product Unit Notation Vector If A & B are two vectors, where A = Axi + Ayj + Azk &B = Bxi + Byj + Bzk Then, their Scalar Product is defined as: A B = AxBx + AyBy + AzBz Where 1

2 Newton's laws 1- Force a) Adding Forces Forces are vectors (They have both magnitude and direction) and so add as follows: Adding Forces In one dimension: Adding Forces In two dimensions F=F1+F2 a)the angle between them is 90. b) The angle between them is or 90. 2

3 Newton s First Law An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless an external unbalance force is acting on it. 2- Weight Weight (W) or Force due to Gravity is how our MASS (m) is effected by gravity (g). W mg 4. Calculate the Friction Force and Normal Force a) Without angle and constant speed Notes If the surface is smooth, the friction force, Ff= 0 5. Newton s Second Law Force equals mass times acceleration. F = ma Net Force The net force is the vector sum of all the forces acting on a body. Fnet F F1 F2 F3 F ma (a)acceleration: a measurement of how quickly an object is changing speed. a = F net m 3

4 Notes 1- Friction Force Ff= µk. FN & FN =m. g 2-The acceleration (a) a = F net m = F a F f m 6. Newton s Third Law For every action there is an equal and opposite reaction. 7.Coefficients of friction Coefficient of friction is the ratio between friction force and normal force. Symbol is the Greek letter mu (μ) μ= F f / F N The coefficient of friction has no units. Notes 1- Friction Force = Coefficient of friction Normal Force Ffriction = Fnormal 4

5 work and ene0rgy 1- Work: Is the physical quantity which is equal to the product of force and distance The unit of work is a joule (J) 1.1 Calculate work done on an object: Without angle a) with apply force The equation used to calculate the work (W) in this case it: W= F. d b) Also with friction force The equation used to calculate the work (W) in this case it: W= -Ff. d But F friction = F normal so you can write this equation (1) W= -( F normal )d But F normal = m g so you can write this equation(2) W= -( mg)d With angle In this case, the work done given by W = F. d cos 2. Kinetic Energy Kinetic Energy is: the energy of a particle due to its motion K.E = ½ mv 2 & V = 2k m The unit of kinetic Energy is a joule (J) 3. Work and Kinetic Energy When work is done on a system and the only change in the system is in its speed, the work done by the net force equals the change in kinetic energy of the system. So W = Kf - K And also W =½ mvf 2 ½ m v But W= -Ff. d,,,,, If vf = 0 From equation (4) you can calculate the friction force. Ff = 1 2 mv02 d

6 3- Potential energy (U) Potential energy is the stored energy of an object. The formula for potential energy (U) due to gravity is U = m.g.h P.E. (U) = mass x height x gravity The unit of Potential Energy is a joule (J) 5. Conservation of Energy 1-The law of conservation of mechanical energy states: Energy cannot be created or destroyed, only transformed 2-Potential energy and Kinetic Energy are mechanical Energy In this figure below. When a pendulum swings the point which has the highest potential energy is (1), and the highest kinetic energy is (3) K o + U o = Kf + Uf K= U vf = 2g(h0 hf) Power Power is: is the rate of doing work. It is the amount of energy consumed per unit time P = W t = F.d t = F.V 7- Calculate the fat consumed C = W t And the rate (t) = supplies energy x efficiency rate The mechanics of non-viscous fluids 6

7 1- Density The density of a fluid is defined as mass per unit volume. ρ=m/v 2-Pressure (P): is the force applied perpendicular to the surface of an object per unit area (P=F/A) 3-The flow rate (Q): is The flow rate which is the volume ΔV of the fluid flowing past a point in a channel per unit time ΔT : Q = ΔV & ΔV= Q. ΔT ΔT Also the flow rate(q) : equals the cross-sectional area of the channel (A) times the velocity of the fluid (v). Q = A. v but A = πr 2 Q = πr 2.v where (r) radius Also to calculate the speed (v) v = Q πr 2 3-The Equation of Continuity When fluid moving with steady flow through a pipe of varying cross sectional area. The volume of fluid flowing through area A1 in a time interval T must equal the volume flowing through area A2 in the same time interval. Therefore, A1 v1 = A2 v2 = constant This expression is called the equation of continuity for fluids. This just means that the amount of fluid moving in any section of pipe must remain constant. The product of the cross-sectional area and the velocity of the fluid is constant: A v = constant v 1 = r2 2 v 2 r 2 1 & v 2 = r2 1 v 1 r Bernoulli's Equation It states that "the consequences of the principle that the work done on a fluid as it flows from one place to another is equal to the change in the mechanical energy". 7

8 If you want calculate Pressure (P2) Notes The pressure PB at a depth (d) below the surface of a liquid open to the atmosphere is greater than atmospheric pressure (Patm) by an amount ρgd : so where Patm = Pa & g=10 m/s 2 To calculate the different pressure between two point P= ρgd PB=Patm + ρgd Direct currents 1- Electric current: The electric current in a wire is the rate at which the charge moves in the wire. Electric current is the movement of negative charges (electrons) in a circuit. The unit of current is Ampere 2- Ohm s Law: For many conductors, current depends on: Voltage - more voltage, more current Current is proportional to voltage Resistance - more resistance, less current Current is inversely proportional to resistance V = I. R & I = V & R = V R I 3-Resistance (R) A Resistance is : a component of a circuit that resists the flow of electrical current. The unit of Resistance is Ohm 8

9 Nerve Conduction 1- What is nerve conduction study? These include nerve cells (or neurons). A nerve conduction study (NCS), also called a nerve conduction velocity (NCV) test--is a measurement of the speed of conduction of an electrical impulse through a nerve. NCS can determine nerve damage and destruction. A nerve conduction study (NCS) is a medical diagnostic test commonly used to evaluate the function, especially the ability of electrical conduction, of the motor and sensory nerves of the human body. Neurons are the basic functional units of the nervous system, and they generate electrical signals called action potentials, which allow them to quickly transmit information over long distances 2- Structure of nerve Cell Neurons are made up of a cell body, dendrites, and axons. Dendrites: -Receive inputs from other cells and conduct signals towards the cell body. -Receive information. Axons: -Axon: is the information which transmitted in the human body by electrical pulses in nerve fibers. axon has a very high resistance. Axon typically 1 to 20 micrometers in diameter. - send information. -Larger axons are enclosed by sheaths of myelin produced by Schwann cells. Narrow gaps in the myelin sheath between Schwann cells are called nodes of Ranvier. Nerves are cable-like bundles of axons. A neuron consists of a cell body that receives electrical messages from other neurons through contacts called synapses located on the dendrites or on the cell body. Myelinated neurons are covered in myelin sheaths (Schwann Cells). These increase the speed in which nerve impulses can be transmitted. Unmyelinated neurons don't have myelin so they pass impulses "slower" than the myelinated ones (They do not have node of Ranvier) 9

10 3-Nerve electric properties Axon is responsible for transforming signals between different points of the nervous system. In neurons and their surrounding fluid, the most abundant ions are: 1- Positively charged (cations): Sodium Na +, and potassium K Negatively charged (anions): Chloride Cl -, and organic anions 3- In a resting neuron (polarized), the membrane is much more permeable to K + than to Na +. A Resistance: is a component of a circuit that resists the flow of electrical current. The capacitance: is the ability of a component to store an electrical charge. 10

11 D)- Space parameter Space parameter : indicate how far a current travels before most of it has leaked out through membrane. Thus a current pulse can travel much farther without amplification in myelinated nerve. = R m r 2 ρ Nernst equation Equilibrium occurs when the potential energy of on ion with charge q, q(vi V ), is equal to the work necessary to transfer it to the region of higher concentration. According to the model, this work is KBT ln (C / Ci ), where - KB (Boltzmann constant )= 1.38 x J K -1 - T is the Kelvin temperature - ln (C / Ci ) the nature logarithm of the concentration ratio -Where C is the concentration of the ion outside the cell and Ci is the ion concentration inside the axon show table The Nernst equation relates the potential difference across a membrane to the equilibrium ratio of ionic concentrations Hence the ion is in equilibrium if the concentrations satisfy the Nernst equation q(vi V ) = KBT ln (C / Ci ) (Vi V ) = K B T ln (C O / C i ) q 11

12 Problem 1 Find the equilibrium potential for Cl - Ion of charge q= 1.6 x C, at 37 C in particular axon? If the concentration of the ion outside the cell is 105 mol. m -3 and inside the axon is 5 mol. m -3.knowing that zero Celsius Temperature 0 C =273 K (Kelvin), and Boltzmann constant (KB )= 1.38 x J. K -1. Answer we apply the Nernst equation q(vi V ) = KBT ln (C / Ci ) Given {q= -1.6 x C, KB = 1.38 x J. K -1,T=273+37=310 K,C = 105 mol. m -3 and Ci = 5 mol. m -3. we want equilibrium potential (Vi V )? K B T ln (C O / C i ) (Vi V ) = (Vi V ) = q 1.38 x ln (105/ 5 ) 1.6 x So equilibrium potential (Vi V )= volt Problem 3 Find the equilibrium potential of an ion of charge q= 1.6 x C, at 37 C in particular axon. If the concentration of the ion outside the cell is 105 mol. m -3 and inside the axon is 20 mol. m -3.knowing that zero Celsius Temperature 0 C =273 K (Kelvin), and Boltzmann constant (KB )= 1.38 x J. K -1. Answer we apply the Nernst equation q(vi V ) = KBT ln (C / Ci ) Given {q= -1.6 x C, KB = 1.38 x J. K -1,T=273+37=310 K,C = 105 mol. m -3 and Ci = 20 mol. m -3. we want equilibrium potential (Vi V )? we want equilibrium potential (Vi V )? K B T ln (C O / C i ) (Vi V ) = (Vi V ) = q 1.38 x ln (105/ 20 ) 1.6 x So equilibrium potential (Vi V )= volt 12

13 Ch Ionizing Radiation What is the Ionizing Radiation? is radiation with enough energy so that during an interaction with an atom, it can remove tightly bound electrons from the orbit of an atom, causing the atom to become charged or ionized. It can interact with the atoms in tissue and causes cellular damage. Types of Ionizing Radiation 1- (α) Alpha particles are a radioactive process in which a particle with two neutrons and two protons is ejected from the nucleus of a radioactive atom. 2- (β)beta particles are essentially electrons emitted from the nucleus of a radioactive atom. 3- (γ)gamma rays) Gamma rays can be emitted from the nucleus of an atom during radioactive decay. 4- (χ) x rays X-rays are photons, like visible light, photons have enough energy to cause ionization. X- rays are produced when accelerated electrons interact with a target, then electron ejects an inner-shell electron. 4- (n) Neutrons: are particles found in the nucleus of atoms, thy have no net electric charge. 13

14 6.3 Radiation Quantities, Units 1- The absorbed dose D Is defined as the mean energy(dē) imparted to matter of mass dm: D = dē dm The SI unit for absorbed dose is 1 J/kg and its name is the gray (Gy). 2- Equivalent dose (HT) Equivalent dose is a physical quantity to measure the effect to a tissue or organ by different types and energies of radiation. DT, R is the absorbed dose delivered by radiation type R averaged over T a tissue or organ. wr is the radiation weighting factor for radiation type R. The SI unit of equivalent dose is J/kg and its name is the sievert (Sv) 3- Exposure X It is denned as the amount of ionization produced in a unit mass of dry air at standard temperature and pressure (STP). Exposure X is: the quotient of (dq )by (dm), where (dq) is the absolute value of the total charge of the ions of one sign produced in air when all the electrons and positrons liberated or created by photons in mass (dm) of air are completely stopped in air: x = dq dm The unit of exposure is coulomb per kilogram (C/kg). The unit used for exposure is the roentgen R, where 1 R = C/kg. In the SI system of units, roentgen is no longer used and the unit of exposure is simply C/kg of air. Summary 14

15 Q1: Choose the correct answer Review Exercises (all chapters). 1. The acceleration of an object is equal to the net force acting on the object divided by its a) Wight b) Mass c) Volume d) Distance 2. Potential energy and kinetic energy are types of? a) Electrical Energy b) Magnetic Energy c) Heat Energy d) Mechanical Energy 3. Which of the following is an example of a vector quantity? a) Time b) weight c) Power d) Mass 4. Name the physical quantity which is equal to the product of force and distance a) Energy b) Pulling force c) Work d) Wight 5. Which of Newton's Laws of Motion states that objects at rest tend to stay at rest and objects in motion tend to stay in motion unless acted upon by an unbalanced force? a) Newton's first Law of Motion b) Newton's second Law of Motion c) Newton's Third Law of Motion d) None 6. The force perpendicular to the surface that pushes up on the object of concern. a) Friction force b) Pulling force c) Normal force d) Net force 7. When an unbalanced force acts on an object, the force a) Is cancelled by another force. b) Changes the motion of the object. c) Is equal to the weight of the object d) Does not change the motion of the object 8. Which of the following is a physical quantity that has a magnitude but no direction? a) Vector b) Resultant c) Scaler d) None 9.An opposing force caused by the interaction between two surfaces. a) Drag force b) Pulling force c) Normal force d) Friction force 10.Which of the following is an example of a scaler quantity? a) velocity b) Force c) Power d) acceleration 15

16 11. An object's resistance to change in motion is called a) Inertia b) Mass c) Motion d) Friction 12. When you use a boat paddle to push water backwards, the water exerts an opposite force pushing the boat forward. This is an example of: a) Newton's first Law of Motion b) Newton's second Law of Motion c) Newton's Third Law of Motion d) None N weight hanging DOWN from a rope. Vector or scalar? a) Scaler b) Vector c) Value d) None 14. State of rest or balance due to the equal action of opposing forces. a) Weight b) Gravity c) Friction d) Equilibrium 15. Which of the following is a physical quantity that has a magnitude and direction? a) Scaler b) Resultant c) Vector d) None 16. The coefficient of friction (µ) is the ratio between friction force and a) Pulling force b) Normal force c) Net force d) Mass 18. The law of conservation of energy states a) Energy cannot be created b) Energy cannot be destroyed c) Energy can only be transferred d) All of these 19. Potential energy and kinetic energy are types of? a) Electrical Energy b) Magnetic Energy c) Heat Energy d) Mechanical Energy 20. Which of the following is an example of a vector quantity? a) Time b) weight c) Power d) Mass 21. Name the physical quantity which is equal to the product of force and distance a) Energy b) Pulling force c) Work d) Wight 22. What is kinetic energy? a) When an object is in motion b) When an object is not in motion c) all of the above d) none of the above 16

17 23. What are fluids? a). Substances that flow c). A&b b). Liquids, and gases d). Non of the above 24. Bernoulli's principle states that, for streamline motion of an incompressible non-viscous fluid: A. pressure at any part + kinetic energy per unit volume = constant B. kinetic energy per unit volume + potential energy per unit volume = constant C. pressure at any part + potential energy per unit volume = constant D. pressure at any part + kinetic energy per unit volume + potential energy per unit volume = constant 25. If layers of fluid has frictional force between them then it is known as a).viscous c). Incompressible b).non-viscous d). both a and b 26. If every particle of fluid has irregular flow, then flow is said to be a). laminar flow c). fluid flow b). turbulent flow d). both a and b 27. According to Ohm's law, Resistance is equal to to voltage divided by: a). Potential difference b). conduction c). time d).current 28. What is a circuit? A. A pathway that electricity flows in. It has a load, wire, and a taco B. A pathway that protons flow in. It has a load, wire, and a power source. C. A pathway that electricity flows in. It has a load, wire, and a power source. D. A pathway that electricity flows in. It has a load and wire. 29. What is an Electric Current? A. An Electric Field B. An Ampere C. The flow of electric charge. 30. What is Ohm's Law? A. I=V/R B. R=V/I C. Power= Voltage Current D. A&B 17

18 31. A closed path that electric current follows A. Voltage B. Current C. Resistance D.Circuit 32. This is related to the force that causes electric charges to flow A. Voltage B. Current C. Resistance D. Circuit 33. What charge does an electron have? A. negative (-) B. positive (+) C. neutral or no charge (0) is responsible for transforming signals between different points of the nervous system a.axon b- Schwann cells c- nodes of Ranvier. d-synapses are covered in myelin sheaths (Schwann Cells). These increase the speed in which nerve impulses can be transmitted a).dendrites b- Schwann cells c- Unmyelinated neurons d- Myelinated neurons 36.In neurons and their surrounding fluid, ions Positively charged (cations) a- Chloride Cl -, and organic anions b- Chloride Cl +, and potassium K +. c- Chloride Cl +, and Sodium Na + d- Sodium Na +, and potassium K In neurons and their surrounding fluid, ions Negatively charged (anions): a- Chloride Cl -, and organic anions b- Chloride Cl +, and potassium K +. c- Chloride Cl +, and Sodium Na + d- Sodium Na +, and potassium K A myelinated axon is surrounded by a-axon b- Schwann cells c- nodes of Ranvier. d-synapses 18

19 39. A neuron consists of a cell body that receives electrical messages from other neurons through contacts called located on the dendrites or on the cell body. a-axon b- Schwann cells c- Schwann cells d-synapses 40. Narrow gaps in the myelin sheath between Schwann cells are called a-axon b- Dendrites c- nodes of Ranvier. d-synapses 41. The distance a current can travel without amplification is characterized by the a-resistance b- Space parameter c-capacitance d- Length 42. Is defined as the mean energy(dē) imparted to matter of mass dm. a-dose Equivalent b- Absorbed dose c-exposure d- Current 43.. is a physical quantity to measure the effect to a tissue or organ by different types and energies of radiation? a-dose Equivalent b- Absorbed dose c-exposure d- Current 44...It is denned as the amount of ionization produced in a unit mass of dry air at standard temperature and pressure (STP). a-dose Equivalent b- Absorbed dose c-exposure d- Current. 45. Measurements for "dose equivalent" a). Gray b). Sievert c). C/Kg c). joule 46. Which type of radiation is most penetrating a) Alpha b). Gamma c). Beta d). are equal 47. Which type of radiation is most penetrating a) Alpha b). Gamma c). Beta d). are equal 19

20 48. Measurements for "absorbed dose " a). Gray c). C/Kg b). Sievert c). joule 50. Measurements for "Exposure" a). Gray b). Sievert c). C/Kg c). joule Q2. Answer these questions 1- A lady of 50 kg mass climbs a mountain 3000 m high. Fat supplies mechanical energy of 3.8x10 7 joule per kilogram fat. The body of this lady converts fat in to mechanical energy with efficiency rate 25%. Find the work she did against gravitational forces in the climb How much fat she consumed in the climb? 2- A child drops down a ball from rest from the top of a building 20 m height. What is the speed of the ball when just stroked the ground? 3- A box of 30 Kg mass is pulled with constant speed on a horizontal rough surface. The force of friction is Fk = 60 N. What is the coefficient of friction µk? 20

21 4- A man of 80 kg mass is sitting on a chair and his feet is resting against the ground. His feet is experiencing 300 N force applied by the ground. Find the force applied on him by the chair. 5- The brain of a man is 0.6m above his heart level.the blood density ρ = Kg/m 3.What is the blood pressure difference between the brain and the heart? 6- Given A = 4, ӨA =100 o and B =6, ӨB =45 o.find the magnitude A +B,A x B and A. B 7- Myelinated segment of axon has a radius of (2 mm) and a length of 1 cm. If ( Cm) Capacitance per unit area = 5x10-5 F/m 2 and ( Rm) Resistance per unit area of membrane =40 ohm m 2. Find its a). Membrane capacitance, b). Membrane leakage resistance 21

22 8- A water pipe leading up to a hose has a radius of 2 cm. Water leaves the hose at a rate of 4 liters per minute. Find the velocity of the water in the pipe. The hose has a radius of 0.5 cm. What is the velocity of the water in the hose? 9- A human femur will fracture if the compressional force is N. A person of mass 68 kg lands on one leg. so that there is a compressional force on the femur, what acceleration will produce fracture? 10. A man is pulling a bag of 20 Kg mass on a horizontal floor. The pulling force is 40 N and the coefficient of friction between the bag and the floor is 0.1. a. What is the magnitude of the force of friction? b. What is the acceleration of the suit case? 22

23 11-Water with density ρ = 1000 kg/m 3 moves in a pipe of radius 6cm with a speed of 5 m/s. the pipe goes up at a height of 7m and its radius becomes 4 cm. Show figure a- Find the speed of the water at the upper side of the pipe? b- If the pressure P1 at the lower side is 4x10 5 pa. what is the pressure P2- at the upper side? 23

24 12- What is the current in a wire with a potential difference of 15 V across its ends and a resistance of 3 ohms? 14. Calculate the amount of exposure caused by gamma rays to an air mass of 7 kg if you know that the amount of charge produced 6 x10-2 Coulomb? 15. Calculate the equivalent dose for a person who is exposed to a dose of 1.2mG of neutron? Where the radiation weighting factor(wr) for gamma ray=10 24