Mechanics and Materials Flashcards
Horizontal and Vertical motion of a projectile
-Horizontal and vertical motion are independent.
-Gravitational force only acts vertically, so projectiles only experience acceleration due to gravity in vertical direction (down)
In absence of resistive forces:
-Horizontal motion: no force horizontally, no acceleration so constant velocity = Vcosθ
-Vertical motion: constant force due to weight, uniform acceleration down (g) = Vsinθ
difference between a scalar and a vector
vector has magnitude and direction, scalar has only magnitude
examples of scalars
speed, mass, time, energy, power
examples of vectors
displacement, velocity, acceleration, force, weight
adding perpendicular vectors by calculation
- draw vectors as a right angled triangle and use pythagoras to find magnitude of resultant vector
- use SOHCAHTOA for the angle
adding vectors by scale drawing
- write down scale
- draw vectors to correct length and angle to each other “tip to tail”
- add the resultant vector line and measure length (convert with scale) and angle of resultant vector
conditions for equilibrium of two or three coplanar forces acting at a point
total resultant force equals zero OR if vectors representing forces are added together they will form a closed triangle
two conditions for a body to remain in equilibrium
- resultant force = 0
- resultant moment about any force is zero
- stationary or travelling at constant velocity
moment
force x perpendicular distance from the point to the line of action of the force
principle of moments
in equilibrium, the sum of the clockwise moments about a point = sum of anticlockwise moments
definition of a couple
a pair of equal and opposite coplanar forces - only rotational motion occurs
definition of the moment of a couple
one force x perpendicular distance between the lines of actions of the two forces
definition of centre of mass
point in a body through which weight appears to act - object will balance if supported at its COM
stability
if the centre of mass of an object lies outside its base it will topple over
how size affects COM
the wider the base, the lower its COM
contact force
force exerted between two objects when they are in contact with each other (reaction force)
tension/tensile force
force applied to an object that acts to stretch it
stable equilibrium
when a body is displaced then released it will return to its equilibrium position
displacement
distance in a given direction
velocity
rate of change of displacement
acceleration
rate of change of velocity
accelerates / decelerates definition
accelerates - velocity increases with time
decelerates - velocity decreases with time
displacement and velocity time graph
uniform acceleration - gradient increasing, directly proportional
non uniform acceleration - curve upwards = increasing gradient
gradient of displacement and velocity time graphs
gradient of a s-t graph = velocity
gradient of a v-t graph = acceleration