Mechanics Definitions Flashcards
Any quantity which has both magnitude and direction is a
vector
Any quantity which has magnitude only is a
scaler
Parallelogram Law states: if two vectors are represented by two adjacent sides ab and ad of a parallelogram abcd then
the diagonal ac represents their resultant
a _____ has no components at right angles to itself
vector
_______ is the distance of a body, in a given direction, from a fixed point
displacement
speed in a given direction =
velocity
the rate of change of velocity =
acceleration
equations of motion =
V=+ _
s=_ +1/2 _^-
V^2= _^- + _ _ _
V=u + at
s= ut +1/2at^2
v^2= U^2 + 2as
a body has acceleration if it is either its _____ or its _____ is changing
speed or direction
ignoring air resistance/ in a vacuum, the acceleration of a falling body due to _____ is always the same
gravity
gravity always acts _____ towards ____ ____ __ ___ ____
downwards towards the centre of the earth
a body at its highest point has zero _____ but not zero ______
velocity but not acceleration //acceleration due to gravity still operates
Give an example of a scaler quantity
distance
time
mass
Give an example of a vector quantity
velocity
force
anything which changes , or tends to change, the motion of a body in magnitude or direction =
a force
an unbalanced force causes
motion
the force with which the earth attracts a body is called the
weight of the body
the mass of a body is
the amount of matter in it
the product of mass and velocity of a body=
momentum
Newtons first law motion
a body remains at rest or moving with uniform velocity unless an unbalanced force acts on it
Newtons second law motion
the rate of change of momentum is proportional to the force acting upon it AND takes place in the direction of said force
Newtons third law motion
to every action there is an equal and opposite reaction. //Action and reaction never happen on the same body//
equation for force
force = mass x acceleration
equation for weight
weight = mass x g
A newton is the force which gives ….
an acceleration of 1ms/2 to a mass of 1kg
the principle of conservation of momentum states
if no external force acts on a system of colliding bodies the total momentum of the bodies remains constant
impulse= change in momentum =
force x time
or
Ft = mv - mu
centre of gravity
the point at which the whole weight of the body appears to act is called its centre of gravity
the principle of stable design is to have
a low centre of gravity and a wide base
a lever is
a rigid body which is free to rotate about a fixed point called the fulcrum
the moment of a force about a point is
force x the perpendicular distance from the point to the line of action of the force
the principle of moments states
that when a body is in equilibrium the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about that point
the two conditions for equilibrium are
- the principle of momentum must apply
2. the vector sum of the forces in any direction is zero
the moment of a couple is the product of
one force x the perpendicular distance between them
work =
force x distance (moved in the direction of the force)
a joule is the work done
when a force of one newton moves its point of application 1m
potential energy is
is energy due to position or mechanical condition
equation for potential energy
Ep = mgh
Kinetic energy is
energy due to motion
equation for kinetic energy
Ek = 1/2 mv^2
the law of conservation states that
energy can neither be created nor destroyed; it simply changes from one form to another
power is the amount
of work done per second
1 watt =
1 joule s^-1
friction is a force which
opposes relative motion between two bodies in contact
lubricants
reduce friction
viscosity is
resistance to flow in fluids
a sphere falling through a fluid has three forces acting on it. List these three forces
- Its weight W acting downwards
- An upthrust U due to displaces liquid
- A frictional force F acting upwards
//W and U are constant. As the sphere begins to fall, it accelerates but, as its velocity increases, F also increases until U + F = W and the net force acting on the sphere is zero.
It now continues to fall with a uniform/ constant velocity known as terminal velocity
the mass of unit volume of a substance is called its
density
pressure=
force per unit area
the unit of pressure is the
pascal
1 Pa = 1Nm^2
pressure in a fluid depends on three things;
give equation
depth, density and acceleration due to gravity
P = pgh
Archimedes’ Principle:
A body partly or wholly immersed in a fluid experiences a upthrust equal to the weight of the fluid displaced
law of flotation:
A floating body displaces its own weight of fluid
the angular velocity is the rate of change of
angle in radians per second,
ω = θ/t
The periodic time equation
T= 2π/ω
Linear Velocity equation
arc/t = rθ/t = rω v = rω
Acceleration towards the centre of a circle equation
a = rω^2 or a = v^2/r
the force necessary to keep a body moving in a circle is a
centripetal force acting towards the centre of the circle.
F = mrω^2
or F = mv^2/r
The Law of gravitation;
the force of attraction between any two bodies is proportional to their masses and inversely proportional to the square of the distance between them
f ∝ (M1 M2)/d^2 ⇒ F = (GM1M2)/d^2
mg =GmM/d^2 ⇒ g/G = M/ d^2 or g = GM/d^2
Give Kepler’s Three laws of planetary motion
- The Planets move in elliptical orbits round the sun as one focus.
- The line joining the sun and the planet sweeps out equal areas in equal time intervals
- The square of the periodic time of a planet is proportional to the cube of its mean distance from the sun. // GmM/r^2 = mrω^2 = mr (4π^2/T^2) ⇒ T^2 = 4π^2r^2/GM//
Give Kepler’s Third Law mathematically
GmM/r^2 = mrω^2 = mr (4π^2/T^2) ⇒ T^2 = 4π^2r^2/GM
For the signal of a satellite to be transmitted from earth to said satellite and back the satellite must always be above the same point on the earth. i.e it mus have the same period as the earth - 24 hours. The satellite is said to be
geostationary or parking orbit
Hooke’s Law;
Provided a spring is not extended beyond its elastic limit, the extension is proportional to its load.
give the mathematical definition of simple harmonic motion ( S.H.M )
a = -ω^2s // the minus indicates that the body begins to retard as it passes through 0, the centre of its motion
when a particle is undergoing S.H.M its acceleration is
maximum when its displacement is maximum
Give an example where a body has acceleration but zero velocity
a body that has been thrown vertically upwards and is at its greatest height.
When does a body travelling at constant speed have an acceleration?
when it is changing direction
Why is it easier to turn a nut using a longer spanner rather than a shorter one?
The distance from the effort to the fulcrum is greater, giving a greater turning effect.
State the law of flotation
a floating body displaces its own weight of fluid.
A container contains 5kg of water. if the area of the base of the container in 0.5m ^2, what is the pressure on the base?
P = F/A = (5 x 9.8)/0.5 = 98 Pa
What is the relationship between the acceleration due to gravity, g and the distance from the centre of the earth?
g ∝ 1/d^2
A particle travels at constant speed of 10ms-1 in a circle of radius 2m. What is its angular velocity?
v = rω ⇒ ω = v/r = 10/2 =5 radians per second
The moon orbits the earth. What is the relationship between the period of the moon and the radius of its orbit?
T^2 ∝ R^3 (Kepler’s third Law)
