mechanics Flashcards
scalar quantities
- quantities that have magnitude (size), but not direction
- e.g. mass, energy, pressure, temp, power, speed, distance, time
vector quantities
- quantities that have both magnitude (size) and direction
- e.g. displacement, acceleration, velocity, force, momentum
an accelerating object can be moving at a constant speed ifโฆ
it is changing direction constantly
displacement
the shortest distance from one point to another in a particular direction
acceleration=
(final velocity - initial velocity) /time
- units : ms-2
- direction is the same as the direction of the change in velocity
distance-time graphs
- can only be +ve, line cannot go down
- the gradient at a point = the speed at that point
displacement-time graphs
- zero value (on x-axis): at starting point
- +ve value (above x-axis): at +ve side of starting point
- -ve value (below x-axis): at -ve side of starting point
- flat line: stationary
- ascending line: moving in +ve direction
- descending line: moving in -ve direction
- exponential increasing line: increasing velocity
- exponential decreasing line: decreasing velocity
- the gradient at a point = the velocity at that point
velocity-time graphs
- zero value (on x-axis): stationary
- flat line: constant velocity
- ascending line: accelerating in +ve direction
- descending line: accelerating in -ve direction
- exponential increasing line: increasing acceleration
- exponential decreasing line: decreasing acceleration
- the gradient at a point = the acceleration at that point
- area under graph = change in displacement
speed-time graphs
- can only be +ve
- area under graph = distance travelled
equations of motion
- s=0.5(u+v)t
- ๐ =ut + 0.5at^2
- v^2=๐ข^2+2๐๐
- average v = 0.5(u+v)
forces
- the application of a push or a pull to an object by another object
- vector quantity,
- units: newtons (N)
- types: weight, normal contact, drag, friction, magnetic, electrostatic, upthrust, thrust, lift and tension
force formulae
F=ma F=momentum/time P=F/a moment=F x perpendicular distance Ew = F x displacement
weight formula
W=mg
W=weight in N
m=mass in kg
g=gravitational field strength in Nkg-1 (9.8 on Earth)
normal contact force
-force as a result of 2 solid objects being in contact with each other
tension
- when a spring/string/wire is pulled by equal and opposite external forces at each end as shown, it is said to be subjected to a tension force, ๐
- this tension force usually causes the length of the spring/string wire to increase slightly.
- the increase in length = the extension
- the greater the tension force, the greater the extension
- T=weight=mg
force-extension graphs
- the steeper the graph, the greater the spring constant -> more rigid
- the shallower the graph, the greater the spring constant -> less rigid
- work done by this force = the area under the graph
material types
- copper wire stretches uniformly initially, but then suddenly stretches much more just before reaching the breaking point
- glass is very rigid and deforms only very slightly before breaking
- rubber stretches non-uniformly
deformation
- elastic deformation is reversed when the force is removed
- inelastic deformation is not fully reversed when the force is removed (permanent stretching)
- materials that undergo permanent stretching are ductile
elastic limit
-the point on the force-extension graph where the extension goes from being elastic to inelastic (when the line on the graph starts to flatten)
Hookeโs Law
F=kx
- F=force applied to the material/spring (N)
- x=extension of the material/spring (m)
- k=spring constant, a measure of the stiffness of a spring up to its elastic limit, high k->rigid (Nm-1)
factors affecting spring constant
- the greater the cross-sectional area, the greater the spring constant
- the longer the wire, the smaller the spring constant
combining springs
- if 2 springs are connected together in series, then it double the extension -> spring constant is = 0.5๐.
- if 2 springs are connected in parallel, then it will double the force -> spring constant = 2๐
momentum formula
p = mv
- p=momentum (kg/ms-1 or Ns)
- m=mass (kg)
- v=velocity (ms-1)
newtonโs first law
an object will remain at rest or move with constant velocity in a straight line unless acted upon by an unbalanced force
newtonโs second law
when a constant unbalanced force is applied to an object, the object will move with constant acceleration in the direction of the unbalanced force
newtonโs third law
to every action there is an equal and opposite reaction
gravitational field strengths
- the magnitude of the gravitational force acting per unit mass of an object in the field
- Earth: 10Nkg-1
- Moon: 1.6Nkg-1
- Jupiter: 26Nkg-1
acceleration of free-fall
an object falling freely due to gravity falls with an acceleration that is numerically equal to the gravitational field strength
factors affecting air resistance
- increasing speed of motion increases air resistance
- increasing cross-sectional area of the object, increases air resistance.
- turbulent air flow gives greater air resistance force compared to streamlined air flow
terminal velocity
- the speed at which air resistance = weight
- vertical forces acting upon an object are balanced
power formulae
- P=E/t
- P=work done/time
- P=F x velocity
kilowatt-hour
1kWh=3600kJ
stored and active energy
active:
- electrical
- heat (thermal energy)
- light
- kinetic
- sound
stored:
- chemical potential energy (stored in a battery/cell)
- gravitational potential energy (stored due to height)
- strain potential (energy stored in a stretched spring)
energy formulae
- % efficiency = (useful energy/stored energy) x100
- Ek = 0.5mv^2
- Ep = mgh
- total energy = Ep/Ek + work done against frictional force
conservation of momentum (working out velocity of object B after a collision)
- work out total momentum before the collision (momentum of object A + momentum of object B)
- this will also be the total momentum after the collision
- work out the total mass after the collision (mass of object A + mass of object B)
- work out velocity of object B using v=p/m
moment of a force about a point formula
T=Fd
- T=moment of a force (Nm)
- F=force (N)
- d=perpendicular distance from pivot to the line of action of the force (m)
