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 & B 1 Tan (B/A ) To calculate the magnitude A+B & A-B with angle degree A B A B AB COS A B A B AB 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 A A and x A y Tan ( A /Ax ) y - 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 - 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 = a x i + a y j + a z k& B = b x i + b y j + b z k Then the: 1- To find A+B and A B A+B= (a x +b x )i + (a y +b y )j + (a z +b z )k & A B= (a x b x )i + (a y b y )j + (a z b z )k -To find the magnitude of A+B and A B A B ( ax bx ) ( ay by ) ( az bz ) A B ( ax bx ) ( ay by ) ( az bz 1 )

2 3- magnitude of vector in Unit Vector Notation If A is vectoring, where A = a x i + a y j + a z k Then the: To find magnitude of vector A we use the equation b) Product Unit Notation Vector A If A & B are two vectors, where A = A x i + A y j + A z k &B = B x i + B y j + B z k Then, their Scalar Product is defined as: AB = A x B x + A y B y + A z B z Where a x a y a z 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 a)the angle between them is 90. F=F1+F

3 b) The angle between them is or 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. 3- 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 3

4 b) With angle 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 F F3 F ma (a)acceleration: a measurement of how quickly an object is changing speed. a = F net 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 F friction = F normal 4

5 No angle With angle 1- Friction Force Ff= µ k. FN & FN =m. g Fx = F cos θ Fy = FSin θ 1- Friction Force Ff= µ k. FN & FN=mg Fy -The acceleration (a) a = F net m = F a F f m -The acceleration (a) a = F net m = F x F f m work and ene0rgy 1- Work: Is the physical quantity which is equal to the product of force and distance 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() W= -(mg)d

6 With angle In this case, the work done given by W = F. d cos. Kinetic Energy Kinetic Energy is: the energy of a particle due to its motion K.E = ½ mv & V = k 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 ½ m v But W= -Ff. d So -Ff. d=½ mvf ½ m v If vf = 0 Ff = 1 mv0 d From equation (3&4) you can calculate the friction force. 4- 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 -Potential energy and Kinetic Energy are mechanical Energy 6

7 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 = g(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 1- Density The density of a fluid is defined as mass per unit volume. ρ=m/v -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 Q = πr.v where (r) radius Also to calculate the speed (v) v = Q πr 7

8 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 A in the same time interval. Therefore, A1 v1 = A v = 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 = r v r 1 & v = r 1 v 1 r 4-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". If you want calculate Pressure (P) Notes The pressure PB at a depth (d) below the surface of a liquid open to the atmosphere is greater than atmospheric pressure (P atm) by an amount ρgd : so where P atm = Pa & g=10 m/s P B=Patm + ρgd To calculate the different pressure between two point P= ρgd 8

9 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 Definition of the current: - 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 I Q t V = I. R & I = V R & R = V I 3-Resistance (R) A Resistance is : a component of a circuit that resists the flow of electrical current. 9

10 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 - 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 0 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) 10

11 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 In most neurons K +, and organic anions (such as those found in proteins and amino acids) are present at higher concentrations inside the cell than outside. 5- In contrast Na + and Cl - are usually present at higher concentrations outside the cell. This means there are stable concentration gradients across the membrane for all of the most abundant ion types. The electrical properties of neurons can be described in terms of electrical circuits. To understand the behavior of this circuit, we need to know the behavior of the basic components of electrical circuit such as resistor and capacitor. 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. 11

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17 Problem 1 Find the equilibrium potential for Cl - Ion of charge q= 1.6 x C, at 37C 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 0C =73K (Kelvin), and Boltzmann constant (KB )= 1.38 x 10-3 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 10-3 J. K -1,T=73+37=310K,C = 105 mol. m -3 and Ci = 5 mol. m -3. we want equilibrium potential (Vi V)? q(vi V) = KBT ln (C / Ci ) 1.6 x (Vi V) = 1.38 x 10-3 x 310 ln (105 / 5 ) 1.6 x (Vi V) = 0.47 x 10-0 x ln (105 / 5) (V (V (V i i i V V V ) ) ) 0.47 x 10 ^-0 x ln (105 / 5 ) -1.6 x 10^ x 10 ^-0 x x 10^ So equilibrium potential (Vi V)= volt 17

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19 Quiz on nerve conduction 1- Choose the correct answer 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 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 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 Narrow gaps in the myelin sheath between Schwann cells are called a-axon b- Dendrites c- nodes of Ranvier. d-synapses The distance a current can travel without amplification is characterized by the a-resistance b- Space parameter c-capacitance d- Length 19

20 -In a particular axon the equilibrium potential at 37 o C is 80X10-3 volt for Cl - Ion of charge q= x10-19 coulomb.the concentration of the ion outside the cell is 110 mol/m 3.knowing that 0 o C=73 o K and Boltzmann constant KB=1.38X10-3 J /K. What is the concentration of the ion inside the cell? 3- Myelinated segment of axon has a radius of (0.00m) and a length of 0.01m If (Cm) Capacitance per unit area = 10 - F/m. Find the Membrane capacitance(c)? 4-The k + concentration inside an axon is 165 mol. m -3 and outside it is 8 mol. m -3. Find the equilibrium potential of an ion of charge q= 1.6 x C, at 37C in particular axon? knowing that zero Celsius Temperature 0C =73K (Kelvin), and Boltzmann constant (KB )= 1.38 x 10-3 J. K A meylinated segment of axon of radius.5 X10-6 m and length of X10 - m. The specific resistance of the axoplazm ρ = Ωm.Find the axon resistance (R ) to flow of information? 6- Find the space parameter λ of an axon radius 0.4X10-6 m,axoplazm resistivity ρ=ωm and resistance of unit area of membrane R m =40Ωm 0