1

Summary of the laws

Vector

1- Vector addition

a). Pythagorean Theorem

&

To calculate the magnitude A+B & A-B with angle degree

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

angle We use the equation and

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= (axbx)i + (ayby)j + (azbz)k

2-To find the magnitude of A+B and A B

22 BABAR )B/A (1Tan

COSABBABA 222 COSABBABA 222

22

yx AAA ) /AA( xy1Tan

222 )()()( zzyyxx bababaBA

222 )()()( zzyyxx bababaBA

2

3- magnitude of vector in Unit Vector Notation

If A is vectoring, where A = axi + ayj + azk Then the: To find magnitude of vector A we

use the equation

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: AB = AxBx + AyBy + AzBz

Where

_______________________________________________________________________________

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: F=F1+F2

Adding Forces In two dimensions

a)The angle between them is 90°.

222

zyx aaaA

3

b) The angle between them is or 90°.

2- 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).

mgW

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

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.

321net FFFFF

aF m

(a)Acceleration: a measurement of how quickly an object is changing speed. a =𝐹𝑛𝑒𝑡

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= Ff / FN

The coefficient of friction has no units.

Notes

1- Friction Force = Coefficient of friction Normal Force

Ffriction = Fnormal

5

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 -----------1

But Ffriction = Fnormal so you can write this equation (1)

W= -(Fnormal)d ---------2

But Fnormal= m g so you can write this equation(2)

W= -(mg)d ---------3

No angle With angle

1- Friction Force

Ff= µk . FN & FN =m . g

2-The acceleration (a)

𝑎 =𝐹𝑛𝑒𝑡

𝑚=

𝐹𝑎 − 𝐹𝑓

𝑚

Fx = F cos θ

Fy = FSin θ

1- Friction Force

Ff= µk . FN & FN=mg Fy

F

2-The acceleration (a)

𝑎 =𝐹𝑛𝑒𝑡

𝑚=

𝐹𝑥 − 𝐹𝑓

𝑚

6

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 mv2 & 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 - K0 ------------1

And also W =½ mvf2 ½ m v0

2 ------------2 But W= -Ff . d

So -Ff . d=½ mvf2 ½ m v0

2 ------------3

𝐹f =1

2𝑚𝑣02

𝑑 ------------4 If vf = 0

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

2-Potential energy and Kinetic Energy are mechanical Energy

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)

Ko + Uo = Kf + Uf---------- 1

K= U----------2

vf = √𝟐𝒈(𝒉0 − 𝒉f) -------- 3

6- 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 = 𝑊𝑡

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

•

• 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

𝚫𝐓 & ΔV= Q . 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 = 𝜋𝑟2 Q = 𝜋𝑟2.v where (r) radius

Also to calculate the speed (v) 𝑣 =𝐐

𝜋𝑟2

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

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

𝑣1 =𝑟2

2 v2

𝑟21

& 𝑣2 =𝑟2

1 v1

𝑟22

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 (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 𝑃𝐵=𝑃𝑎𝑡𝑚 + ρ𝑔𝑑

where 𝑃𝑎𝑡𝑚 = 1.013×105 Pa & 𝑔=10 m/s2

To calculate the different pressure between two point ∆𝑃= ρ𝑔𝑑

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:

t

QI

10

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 & 𝑅 =

𝑉

𝐼

3-Resistance (R)

A Resistance is : a component of a circuit that resists the flow of electrical current.

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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)

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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+ .

2- 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+ .

4- 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.

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14

15

16

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.

So The distance a current can travel without amplification is characterized by the Space

parameter

According to our model the axoplasm resistance R is proportional to length L of the axon

segment, and the leakage resistance R is proportion to 1/L

Thus, there is some distance for which the rsistance R and R are equal. So using equation

(1) and (2)

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______________________________________________________________________________

Nernst equation

Equilibrium occurs when the potential energy of on ion with charge q ,

q(ViV), 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 10 -23 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 )

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Problem 1 Find the equilibrium potential for Cl- Ion of charge q= 1.6 x 10-19 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 =273K (Kelvin), and Boltzmann

constant (KB )= 1.38 x 10 -23 J. K -1 .

Answer

we apply the Nernst equation q(Vi V) = KBT ln (C / Ci )

Given q= -1.6 x 10 -19 C, KB = 1.38 x 10 -23 J. K -1 ,T=273+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 10-19 (Vi V) = 1.38 x 10 -23 x 310 ln (105 / 5 )

1.6 x 10-19 (Vi V) = 0.427 x 10-20 x ln (105 / 5)

081.0)V (V

10^-19 x 1.6-

3.044 x ^-20 10 x 0.427)V (V

10^-19 x 1.6-

) 5 / (105ln x ^-20 10 x 0.427)V (V

i

i

i

So equilibrium potential (Vi V)=- 0.081 volt

______________________________________________________________

Problem 2

The equilibrium potential of an ion of charge q= 1.6 x 10-19 C, at 30C in particular axon is 80 x

10-3 Volt. If the concentration of the ion outside the cell is 105 mol. m-3 knowing that zero Celsius

Temperature 0C =273K (Kelvin), and Boltzmann constant (KB )= 1.38 x 10 -23 J. K -1 .what is the

ion concentration inside the axon ?

Answer we apply the Nernst equation q(Vi V) = KBT ln (C / Ci )

Given q= -1.6 x 10 -19 C., (Vi V)= 80 x 10-3 V , KB = 1.38 x 10 -23 J. K -1 ,T=273+30=303K and (concentration of the ion outside )C = 105 mol. m-3

we want ion concentration inside the axon) Ci = ?

q(Vi V) = KBT ln (C / Ci )

1.6 x 10-19 (80 x 10-3 )= 1.38 x 10 -23 x 303 ln (105 / Ci ) 1.28 x 10-20 = 0.418 x 10-20 x ln (105 / Ci )

1.28 = 0.418 x ln (105 / Ci ) ln (105 / Ci )= 1.28/ 0.418

ln (105 / Ci )=3.06 105 / Ci = e3.06 105/Ci = 21.32

so Ci = 105/21.327 Ci= 4.92 mol. m-3

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Problem 3

Find the equilibrium potential of an ion of charge q= 1.6 x 10-19 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 20 mol. m-3 .knowing

that zero Celsius Temperature 0C =273K (Kelvin), and Boltzmann constant (KB )= 1.38 x 10 -23

J. K -1 .

Answer

we apply the Nernst equation q(Vi V) = KBT ln (C / Ci )

Given q= -1.6 x 10 -19 C, KB = 1.38 x 10 -23 J. K -1 ,T=273+37=310K,C = 105 mol. m-3

and Ci = 20 mol. m-3 . we want equilibrium potential (Vi V)?

q(Vi V) = KBT ln (C / Ci )

1.6 x 10-19 (Vi V) = 1.38 x 10 -23 x 310 ln (105 / 20 )

1.6 x 10-19 (Vi V) = 0.427 x 10-20 x ln (105 / 20)

044.0)V (V

10^-19 x 1.6-

1.65 x ^-20 10 x 0.427)V (V

10^-19 x 1.6-

) 20 / (105ln x ^-20 10 x 0.427)V (V

i

i

i

So equilibrium potential Vi V = 0.044 Volt

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Exercise on nerve conduction

1- Choose the correct answer

1. ------- is responsible for transforming signals between different points of the nervous

system

Axon b- Schwann cells

c- nodes of Ranvier. d-synapses

2. --------- 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

3. 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+ .

4. 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+ .

5. A myelinated axon is surrounded by

a-Axon b- Schwann cells

c- nodes of Ranvier. d-synapses

6. 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

7. Narrow gaps in the myelin sheath between Schwann cells are called

a-Axon b- Dendrites

c- nodes of Ranvier. d-synapses

8. The distance a current can travel without amplification is characterized by the

a-Resistance b- Space parameter

c-Capacitance d- Length

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2-In a particular axon the equilibrium potential at 37oC is – 80X10-3volt for Cl- Ion of

charge q= - 1.6 x10-19coulomb.The concentration of the ion outside the cell is 110

mol/m3.knowing that 0 oC=273oK and Boltzmann constant KB=1.38X10-23 J /K.

What is the concentration of the ion inside the cell?

3- Myelinated segment of axon has a radius of (0.002m) and a length of 0.01m If (Cm)

Capacitance per unit area = 10-2 F/m2 . 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 10-19 C, at 37C in particular axon ?

knowing that zero Celsius Temperature 0C =273K (Kelvin), and Boltzmann constant

(KB )= 1.38 x 10 -23 J. K -1 .

5- A meylinated segment of axon of radius 2.5 X10-6m and length of 2 X10-2m. The specific

resistance of the axoplazm ρ = 2 Ωm .Find the axon resistance (R ) to flow of

information?

6- Find the space parameter λ of an axon radius 0.24X10-6m ,axoplazm resistivity

ρ=2Ωm and resistance of unit area of membrane Rm =40Ωm2

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Review Exercises (all chapters).

Q1: Choose the correct answer

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

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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

13. 100N 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

24

23. What are fluids?

a). Substances that flow b). Liquids, and gases

c). A&b 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 b).non-viscous

c). Incompressible d). both a and b

26. If every particle of fluid has irregular flow, then flow is said to be

a). laminar flow b). turbulent flow

c). fluid 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

25

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)

34 ------- is responsible for transforming signals between different points of the nervous

system

a.Axon b- Schwann cells

c- nodes of Ranvier. d-synapses

35.--------- 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+ .

37. 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+ .

38. A myelinated axon is surrounded by

a-Axon b- Schwann cells

c- nodes of Ranvier. d-synapses

26

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

_______________________________________________________________________________

Q2. Answer these questions

1- A lady of 50 kg mass climbs a mountain 3000 m high. Fat supplies mechanical

energy of 3.8x107 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?

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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 ?

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- A meylinated segment of axon of radius 2 µm's and length of 1Cm.The specific

resistance of the axoplazm ρ = 2 Ωm .Find the axon resistance (R ) to flow of

information .

6- The brain of a man is 0.6m above his heart level .The blood density ρ =1059.5

Kg/m3.What is the blood pressure difference between the brain and the heart?

7- Given |A|= 4, ӨA =100o and |B|=6 , ӨB =45o .Find the magnitude |A +B| ,A x B and

A . B

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8- 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/m2 and ( Rm) Resistance per unit area of

membrane =40 ohm m2. Find its

a). Membrane capacitance,

b) . Membrane leakage resistance

9- In a particular axon the equilibrium potential at 37oC is – 80X10-3volt for Cl-

Ion of charge q= - 1.6 x10-19coulomb.The concentration of the ion outside the

cell is 110 mol/m3.knowing that 0 oC=273oK and Boltzmann constant

KB=1.38X10-23 J /K.

What is the concentration of the ion inside the cell?

29

10- 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?

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11- A human femur will fracture if the compressional force is 340000N. 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?

12-Water with density ρ = 1000 kg/m3 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 4x105 pa. what is the pressure P2- at

the upper side?

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13. A man is pulling a bag of 20 Kg mass on a horizontal floor. The pulling force is

40 N inclined at 30° above the horizontal 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?

14- What is the current in a wire with a potential difference of 15 V across its ends and a

resistance of 3 ohms?

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