Engr. Rizaldo FuentesEngr. Rizaldo Fuentes

Physics is the scientific study of matter and energy and how they interact with each other.

The METRIC SYSTEM is a modern system, with all measurements based on the decimal system.

The ENGLISH SYSTEM is more ancient, and it has it's roots from the then more common measurements.

Quantity Unit Name Symbol

length meter m

mass kilogram kg

time second s

electrical current ampere A

temperature kelvin K

amount of substance

mole mol

luminous intensity candela cd

The mathematical quantities that are used to describe the motion of objects.

described by a magnitude (or

numerical value) alone.

SCALAR

described by both a magnitude and a

direction.

VECTOR

A little turtle is placed at the origin of an xy-grid drawn on a large sheet of paper. Each grid box is 1.o cm by 1.0 cm. The turtle walks around for a while and finally ends up at point (24,10). Determine the displacement of the turtle from the origin at the point.

Answer: 26 cm angle 23 degrees above x-axis

Galileo believed that when you slide a perfectly smooth object on a frictionless floor the object would travel forever.

Law of InertiaLaw of Inertia

“An object will remain at rest or move with constant velocity when there is no net force acting on it.”

Law of AccelerationLaw of Acceleration

“When the net force acting on an object is not zero, the object will accelerate at the direction of the exerted force.”

The acceleration is directly proportional to the net force and inversely proportional to the mass.

F=ma

Law of ReactionLaw of Reaction

“When one object applies a force on a second object, the second object applies a force on the first that has an equal magnitude but opposite direction.”

When you kick the wall, the wall kicks you back with equal force. As a result you will get hurt.

shows the quantity

MASS

shows the size of the gravity

WEIGHT

Your mass doesn't change when you go to the Moon, but your weight does.

W = weight of the objectm = mass of the objectg = acceleration due to gravity

W mg

29.81 m/s 232.1 ft/s

A 900kg car is going 20 m/s along a level road. How large a constant retarding force is required to stop it in a distance of 30 m?

Answer: 6 kN

FRICTION

Friction is defined as the limited amount of resistance to sliding between the surface of two bodies in contact. Friction acts parallel to the contacting surfaces.

Static friction – friction on stationary body.Dynamic friction – friction on bodies in motion.

WP

F

NR

F N

F

N R tan

ProblemProblemA 1600 N block is in contact with a plane inclined at 30 degrees. A force P parallel to the plane and acting up the plane is applied to the body. The coefficient of friction is 0.20. Find (a)the value of P to just cause the motion to impend up the plane, (b)the value of P to just prevent the motion down the plane, (c)the magnitude and direction of frictional force if P = 900N.

Answer : a. 1077.128 N Answer : a. 1077.128 N

b. 522.871 N b. 522.871 N c. 100 N, down the planec. 100 N, down the plane

Law of Universal Gravitation

1 2G 2

mmF G

r

11 2 2G 6.67x10 Nm / kg

The Earth’s radius is about 6370 km. An object that has a mass of 20kg is taken to a height of 160 km above the Earth’s surface. How much does the object weigh at this height?

Answer: 0.19 kN

The radius of the Earth is about 6370 km, while that of Mars is about 3440 km. If an object weighs 200N on Earth, what would it weigh and what would be the acceleration due to gravity on Mars? The mass of Mars is 0.11 that of Earth.

Answer: 75 N, 3.7 m/s^2

CENTRIPETAL FORCE / CENTRIFUGAL FORCE

The centripetal force is a realreal force on the body towards the center of rotation.

The centrifugal force is an apparent apparent force on the body directed away from the center of rotation.

ccp fF F

2 2

cp cfWV mv

F Fgr r

2

cv

ar

A 200 g object is tied to the end of a cord and whirled in a horizontal circle of radius 1.2 m at a constant 3 rev/s. Assume that the cord is horizontal. Determine the acceleration of the object.

Answer: 426 m/s^2

CENTRIFUGAL FORCE

r

Fcf

If there is no force other than friction:

cff rictionF F

cfF

FRICTIONF

W F d

transfer of energyWORK

ability of an object to do work for

whatever reason.

application of a force over a

distance

ENERGY

energy of position

Potential Energy

energy available because of the object's motion

PE mgh 21KE mV

2

Kinetic Energy

A uniform rectangular marble slab is 3.4m long and 2 m wide. It has a mass of 180kg. If it is originally lying on the flat ground, how much work is needed to stand it on end?

Answer: 3 kJ

A 0.50 kg ball falls past a window that is 1.5 m in vertical length. How much did the KE of the ball increase as it fell past the window? If its speed was 3 m/s at the top of the window, what was its speed at the bottom?

Answer: 7.4 J and 6.2 m/s

“In any closed system, the total amount of energy remains constant regardless of any process which takes place.”

Conservation of EnergyConservation of Energy

energy in = energy out

A 1200 kg car is coasting down a 30 degrees hill. At a time when the car’s speed is 12 m/s the driver applies the brakes. What constant force F (parallel to the road) must result if the car is to stop after travelling 100m?

Answer: 6.7 kN

rate of doing work or changing energy.

The unit of power is the watt, W which is the J/s.

W EP

t t

A 0.25hp motor is used to lift a load at the rate of 5.0 cm/s. How great a load can if lift at this constant speed?

Answer: 381 kg

MOMENTUMMOMENTUM

To stop the object, it is necessary to apply a force against its motion for a given period

of time.

The object is moving and is going to be

hard to stop.

IMPULSEIMPULSEmomentum is changed

p m V

calculated by multiplying the mass

and velocity of an object.

MOMENTUMMOMENTUM

change in momentum

IMPULSEIMPULSE

p m V

I F t

The total linear momentum of a system of colliding bodies, with no external forces acting, remains constant.

Conservation of MomentumConservation of Momentum

momentum before = momentum after

A 16g mass is moving in the (+)x-direction at 30 cm/s while a 4g mass is moving in the (–)x direction at 50 cm/s. They collide head on and stick together. Find their velocity after the collision.

Answer: 0.14 m/s in the (+) x direction

Two balls of equal mass approach the coordinate origin, one moving downward along the (+)y-axis at 2 m/s and the other moving to the right along (–)x-axis at 3 m/s. After they collide, one ball moves out to the right along the (+)x-axis at 1.2 m/s. Find the scalar x and y velocity components of the other ball.

Answer: Vx = 1.8 m/s, Vy = - 2 m/s

A 15g bullet is fired horizontally into a 3kg block of wood suspended by a long cord. The bullet sticks in the block. Compute the speed of the bullet if the impact causes the block to swing 10 cm above its initial level.

Answer: 0.28 km/s

there is no loss of kinetic energy in

the collision

Elastic Collision

part of the kinetic energy is changed to some other form

of energy in the collision

Inelastic Collision

2 2 2 21 1 2 2 1 1 2 2

1 1 1 1m u m u m v m v

2 2 2 2

a variable number with no units, with limits from zero to one

2A 2B

1B 1A

V Ve

V V

Coefficient of RestitutionCoefficient of Restitution

2

1

he

h

A 1.0 kg ball moving at 12 m/s collides head on with a 2 kg ball moving in the opposite direction at 24 m/s. Determine the motion of the each after impact if the collision is perfectly elastic.

Answer: V1 = - 36 m/s, V2 = 0

A motion, which repeat itself over and over again after a regular interval of time.

Revolution of earth around the sun

Motion of hour hand of a clock

The fixed interval of time after which the motion is repeated

Revolution of earth around the

sunone year

Motion of hour hand of a clock 12 - hour

Motion in which a body moves back and forth repeatedly about a fixed point in a definite interval of time.

Motion of the pendulum of a wall clock

Motion of a load attached to a spring, when it is pulled and then released

an object is made to vibrate with an initial application of force and then allowed to

vibrate freely

Free Vibratory Free Vibratory MotionMotion

when a force is applied to an object at regular intervals which causes to move back

and forth

Forced Vibratory Forced Vibratory MotionMotion

the least interval of time after which the periodic motion repeats itself

Time Period

Frequency the number of periodic motions executed by body per second

seconds (s)

Hertz (Hz)

particle moves back and forth repeatedly about a mean position under a restoring force

special type of periodic motion

Restoring force α Displacement

F = restoring forcex = displacement of the particlek = force constant (Newton/meter)

F kx

Restoring force α Displacement

When a 400g mass is hung at the end of a vertical spring, the spring stretches 35 cm. What is the spring constant of the spring, and how much further will it stretch if an additional 400g mass is hung from it?

Answer: 11 N/m, 0.7 m

eKE PE constant

Energy Interchange

2 2 2o

1 1 1mv kx kx

2 2 2

Acceleration of the restoring force

Time period of motion

ka x

m

mT 2

k

A 200g mass vibrates horizontally without friction at the end of a horizontal spring for which k =7 N/m. The mass is displaced 5 cm from equilibrium and released. Finda.Maximum speedb.Acceleration at maximum speedc.period

Answer: 0.3 m/s, 0, 1.06 sec

frictionlesspivot

masslessrod

amplitude

massivebobequilibrium

position

bob’strajectory

the pendulum swings back and

forth with periodic motion against the

pivot point

Time period of motion mT 2

k

Spring Factor

mgk

L

LT 2

g

m = mass of the bobL = length of the simple pendulum

When a mass is hung on a spring, the spring stretches 6 cm. Determine its period of vibration if it is then pulled down a little and released.

Answer: T = 0.49 s

Johannes Kepler Johannes Kepler (1571-(1571-1630)1630)

- He is a German Astronomer who formulated the Kepler’s law. The laws are applicable to any two bodies in space that interact through gravitation where the larger is called primary and smaller as the satellite or secondary.

First Law First Law “ A satellite will orbit around a primary body like Earth following an elliptical path.”

Second Law or Law of Second Law or Law of Areas Areas “ For equal intervals of time, a satellite will sweep out equal areas in the orbital plane, focused at the barycenter.”

Third Law or Harmonic Third Law or Harmonic LawLaw“ The square of the periodic time of orbit is proportional to the cube of the mean distance between the primary and the satellite.”

2

3a kT

DensityDensity

Density of a material is its Density of a material is its mass per unit volume:mass per unit volume:

mass of body m

volume of body V

Density of Water: 1000 kg/m3=1 g/cm3

Measuring DensityMeasuring DensityFor solidsFor solids

m 103g

V 127ml 100ml3.81 g/ml

Measuring DensityMeasuring DensityFor LiquidsFor Liquids

m 93g 43g

V 50m1 g/m

ll

Measuring DensityMeasuring DensityFor GasesFor Gases

m 110.2g 110g

V 50.0004 g/ml

00ml

Specific GravitySpecific GravityIt is the ratio of the density of the It is the ratio of the density of the substance to the density of some substance to the density of some standard substance.standard substance.

standard

spgr

Standard for solid and liquid:water (at 4°) 1000 kg/m3

Standard for gases:air 1.3 kg/m3

The mass of a calibrated flask is 25 g when empty, 75 g when filled with water, and 88 g when filled with glycerin. Find the specific gravity of glycerin.

Answer: 1.26

FLUID FLUID STATICSSTATICS

F

F

F

F

F

F

FF

For static fluids, the force exerted on any particle within the fluid is the same in all directions.

The pressure exerted by the fluid is perpendicular to the interior walls at every point.

Pascal’s PrinciplePascal’s Principle

Average PressureAverage Pressureforce acting normal to an area

Average pressurearea over which the force is distributed

FP

A

The SI unit for pressure is the Pascal (Pa), 1 Pa = 1 N/m2

Hydrostatic PressureHydrostatic PressureHydrostatic Pressure is due to a column of

fluid of height and mass density .h

h h

P gh

When a submarine dives to a depth of 120 m, to how large a total pressure is its exterior surface subjected? The density of seawater is about 1.03 g/cm^3.

Answer: 1.31 MPa

Pascal’s PrinciplePascal’s PrincipleWhen the pressure on any part of a confined When the pressure on any part of a confined fluid (liquid or gas) is change, the pressure on fluid (liquid or gas) is change, the pressure on every other part of the fluid is also changed every other part of the fluid is also changed by the same amount.by the same amount.

InputInputOutputOutputiFoF

Ai Ao

di

do

i o

i o

F F

A A

i i o oAd A d

i i o oFd F d

In a hydraulic press such as the one shown, The large piston has cross-sectional area A1 = 200 cm^2 and the small piston has cross-sectional area A2=5 cm^2. If a force of 250 N is applied to the small piston, find the force F1 on the large piston.

Answer: 10 kN

Archimedes’ PrincipleArchimedes’ PrincipleA body wholly or partly immersed in a A body wholly or partly immersed in a fluid is buoyed up by a force equal to the fluid is buoyed up by a force equal to the weight of the fluid it displaces. The weight of the fluid it displaces. The buoyant force can be considered to act buoyant force can be considered to act vertically upward through the center of vertically upward through the center of gravity of the displaced fluid.gravity of the displaced fluid.

W

FBBF weight of displaced fluid

Archimedes’ PrincipleArchimedes’ Principle

What must be the volume V of a 5kg balloon filled with helium (density of helium = 0.178 kg/m^3) if it is to lift a 30kg load? Use air density = 1.29 kg/m^3

Answer: 32 m^3

Energy EquationEnergy EquationThe energy of the flowing fluid per unit time passing The energy of the flowing fluid per unit time passing any upstream section is the same as the energy per any upstream section is the same as the energy per unit time passing any downstream section plus the unit time passing any downstream section plus the loss of head between two sections.loss of head between two sections.

Bernoulli’s Equation:

2 21 1 1 2 2 2

1 1

2 2 P v h g P v h g L

The pipe shown has a diameter of 16 cm at section 1 and 10 cm at section 2. At section 1 the pressure is 200kPa. Point 2 is 6m higher than point 1. When oil density 800 kg/m^3 flows at a rate of 0.030 m^3/s, find the pressure at point 2 if viscous effects are negligible.

Answer: 1.5 x 10^5 kPa