Mechanics 2 Flashcards
definition of pressure
force per unit area
P=
F/A
P
pressure
F
force
A
area
unit for pressure
N/m cubed = pascals
if an object is immersed in a liquid
it will experience a pressure due to the liquid
what does the pressure in a liquid depend on 3
depth below the surface (h)
density of the liquid (p)
acceleration due to gravity (g)
h
depth below the surface
p
density of the liquid
g
acceleration due to gravity
explain atmospheric pressure
the earth is surrounded by gases. these gases are attracted to the earth by the pull of gravity. these gases therefore exert a force on the earth and all objects near the earth, This force puts a pressure on all the objects
the average value of atmospheric pressure at sea level
1 x 10 to the 5 Pa
Pa stands for
pascals
what is used to measure atmospheric pressure
a barometer
as you rise above sea level
atmospheric pressure decreases
what is the name of the experiment to show atmospheric pressure
the collapsing can experiment
experiment to show atmospheric pressure
put a small amount of water into a metal can and boil this water with a bunsen burner
as the can fills with steam the air is driven out of the can
turn off the burner and put a tightly fitting lid on the can
the steam condenses back to water leaving a partial vacuum in the can
the can is crushed as the outside atmospheric pressure is greater than the pressure inside the can
the bends - explain
the predominant gas in normal air is nitrogen. if diving deep below the water surface the very high pressure causes too much nitrogen to dissolve in the blood. if the diver returns to the surface to quickly this nitrogen can form bubbles in the blood. this blocks air getting to the brain. a slow and gradual return to the surface avoids this
is pressure a vector or a scalar quantity
a scalar quantity
density =
mass/volume
p =
m/v
archimedes principle
when an object is immersed in a fluid it will experience an upthrust equal in magnitude to the weight of the fluid displaced
law of floatation
when an object floats, the weight of the object equals the weight of the fluid displaced
what measures the density of a liquid
a hydrometer
what indicates the alcohol content of beer and wine
its density
what indicates the cream content of milk
its density
when an object is suspended below the surface of water
upthrust =
upward force on bottom - downward force on top
if the upthrust is greater than the weight
the object floats
if the upthrust is small than the weight
the object sinks
Boyle’s law
for a fixed mass of gas at a fixed temperature, the pressure of the gas is inversely proportional to the volume of gas
boyles law in maths
p ∝ 1/V
p = (boyles law)
k x 1/V
p x V =
k1
p1 x V1 =
p2 xV2
why can we say that p1 x V1 = p2 x V2
because pressure multiplied by volume is constant
when do you use p1 x V1 = p2 x V2
when you have 2 volumes and pressures or if it changed
Moment of a force
how much of a spin that a force will cause
definition of moment of a force
M = F x d
M
moment of a force
F
force
d
perpendicular distance from the line of action of the force to the axis
3 qualifications to be a couple
parallel but acting in opposite directions
equal in magnitude
do not meet ‘head on’
what does the moment of a couple tell you
how much of a spin the couple will cause (Torque)
Definition of moment of a couple
T = F x d
T
moment of a couple
F
force
d
perpendicular distance between the lines of action
unit of moment of a couple
Nm
Lever
a simple machine consisting of a rigid body which is free to rotate about a fixed point called an axis or fulcrum
what can a lever be used for
to amplify a force
Laws of equilibrium
a body is in equilibrium if
i) the vector sum of the forces in any direction on the body is zero
ii) the sum of the moment of the forces about any point on the body is zero
what does it mean if the the vector sum of the forces in any direction on the body is zero
the forces acting on the body combine together to give no motion or to give uniform motion. we take this to mean no motion
what does it mean that the sum of the moment of the forces about any point on the body is zero
the forces acting on the body result in no rotation or that body rotates uniformly. we take this as no rotation
where can you assume the centre of gravity of a metre stick
50cm in (half way)
equations if a body is in equilibrium
upward forces = downward forces
moment clockwise = moment anticlockwise
2 ways to measure angles
degrees
radians
angle in radians =
arc length / radius length
theta =
s/r
to convert from degrees to radians
360 º = 2 pi radians
w =
theta/t
w
angular velocity
theta
change in angular displacement
t
time taken for change
is angular velocity a vector or scalar quantity
vector
derive the relationship between angular and linear velocity
w = θ/t = s/rt = (1/r)(s/t) = v/r rw = v
Periodic time
the time taken to complete one full circular motion
full circular motion
θ = 2 π radians
(period) w =
2 π/T
T =
2 π/ w
how do objects moving with circular motion have a constant speed but continuously accelerate
because of their change in direction
which direction is acceleration in circular motion
towards the middle
name for acceleration in circular motion
centripetal acceleration
2 formula for centripetal acceleration
v squared over r
w squared r
what is centripetal force needed for?
to keep an object in circular motion
equations for centripetal force
F = mv squared / r F = m w squared r
definition of centripetal force
the force acting towards the centre of the circle for an object undergoing circular motion
questions with horizontal circular motion
ignore gravity
how to do questions with vertical circular motion
ON TOP
T + mg = mv squared / r
ON THE BOTTOM
T - mg = mv squared / r
Newton’s law of universal gravitation
any 2 point masses in the universe attract each other with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them
Newton’s law of universal gravitation in maths
F = Gm1m2 / d squared
F
force
G
gravitational constant
relationship between periodic time and radius of a satellite
T squared is proportional to R cubed
derive that T squared is proportional to R cubed
GMm/ r squared = m R w squared GM/r squared = R (2π/T) squared GM = R cubed (4π squared/T squared ) T squared = R cubed 4π squared/ GM T squared ∝ R cubed
Geostationary satellite
gives the illusion of being stationary above a particular point on the Earth. To an observer on Earth it always seems to be at the same place
3 things a satellite must have to be geostationary
orbit the earth in the equatorial plane
have the same rotational period as the earth (24h)
move in the same direction as the earth
what are geostationary satellites used for
communication satellites
is the radius of the earth the radius of a geostationary satellite?
no
to get the mathematical expression for the speed of a satellite
GMm/R squared = mv squared / R
some examples of SHM
weight vibrating on the end of a sping
pendulum bob swinging through a small angle
vibrating tuning fork
vibrating stretched string
Definition of Simple Harmonic Motion
The motion of an object whose acceleration is proportional to its displacement from a fixed point. The direction of acceleration is opposite to the direction of displacement
maths for SHM
a = -w squared s
a
acceleration
s
displacement
w
constant of proportionality
2 equations for T
T = 1/f T= 2pi/w
Hookes law (ALWAYS WORDS)
if an object is stretched or compressed the restoring force us directly proportional to the displacement if you stay within the elastic limit of the object
maths for hookes law
F is proportional to s
F=-ks
minus sign in hooke’s law means
the direction of the restoring force acts in the opposite direction to the displacement
maths for a system that obeys hooke’s law and moves with SHM
w squared = k/m
