Mechanics (Unit 2) Flashcards
Difference between a scalar and a vector
vector has magnitude (size) and direction, whereas scalar only has magnitude (size).
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
- use pythagoras’ theorem to find magnitude of resultant vector
- use trigonometry to calculate the angle of resultant vector (sin=o/h; cos=a/h; tan=o/a)
Adding vectors
by scale drawing
- write down scale eg 1cm=2N
- draw vectors to correct length and angle to each other “tip to tail”
- add the resultant vector line (from original tail to free tip)
- measure length and angle of resultant vector
- convert length into appropriate quantity (using scale) to find magnitude of resultant vector
Conditions for equilibrium of two or three coplanar forces acting at a point
total resultant force equals zero
or
if the vectors representing the forces are added together they will form a closed triangle.
Two conditions for a body to remain in equilibrium
- resultant force acting on body is zero
- resultant moment about any point is zero
object could be stationary OR travelling at constant velocity
Definition of a moment
force multiplied by the perpendicular distance between the line of action of the force and the pivot.
Units of moment
Nm
Principle of Moments
in equilibrium, the sum of the clockwise moments about a point equals the sum of the anticlockwise moments.
Definition of moment of a couple
(one) force multiplied by the 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
or
point in a body where the resultant moment is zero
Stable equilibrium
When a body is displaced then released, it will return to its equilibrium position
Unstable equilibrium
When a body is displaced then released, it will not return to its equilibrium position.
Displacement
distance in a given direction
Velocity
rate of change of displacement
or
change in displacement divided by the time taken
Acceleration
rate of change of velocity
or
change in velocity divided by the time taken
Gradient of displacement and velocity time graphs
Gradient of a displacement time graph = velocity
Gradient of a velocity time graph = acceleration
Area under velocity and acceleration time graphs
Area under a velocity time graph = displacement
Area under an acceleration time graph = velocity
Average velocity
total displacement divided by total time
Instantaneous velocity at a point
rate of change of displacement at that point
gradient at a point on a displacement time graph (need to draw a tangent to calculate gradient)
Conditions for an object falling at terminal velocity
- resultant force on object is zero (weight and drag forces are balanced)
- acceleration is zero (F=ma)
- object travels at a constant velocity
Factors affecting drag force on an object
- the shape of the object
- its speed
- the viscosity of the fluid/gas (measure of how easily fluid/gas flows past a surface)
Explain why an object reaches terminal velocity falling through air
- initially only force acting is weight, so object accelerates at g.
- drag force increases with increasing speed.
- therefore resultant force decreases.
- eventually drag force = weight, forces are balanced.
- so resultant force is zero.
- as F=ma, acceleration is zero so object falls at constant speed.
Horizontal and Vertical motion of a projectile
In absence of resistive forces
Horizontal motion: no force horizontally, no acceleration so constant velocity.
Vertical motion: constant force due to weight, constant acceleration (equal to g).
Newton’s Laws of motion
1st Law
An object will continue at rest or uniform velocity unless acted on by a resultant force
2nd Law
The acceleration of an object is proportional to resultant force acting on it, ie F=ma (providing mass is constant)
3rd Law
If object A exerts a force on a second object B, then object B will exert an equal and opposite force on object A.
Principle of conservation of energy
Energy is neither created or destroyed, only converted from one form to another
Energy conversions of an object falling in presence of resistive forces
loss in gpe = gain in ke + work done against resistance
work done typically appears as heat
Definition of work done
force multiplied by distance moved in the direction of the force
Units of work done
J
Power
rate at which energy transferred
or
energy transferred (work done) divided by time taken
Units of Power
W (Watts) or Js^-1
Resolving vectors into two perpendicular components
See sheet
Resolving components along, and perpendicular to, an inclined slope
See sheet
Displacement and Velocity time graphs for uniform acceleration
See sheet
Displacement and velocity time graphs for non-uniform acceleration
See sheet
Sketch time graphs for an object falling under gravity then reaching terminal velocity
See sheet
Sketch time graphs for a bouncing ball
See sheet
