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Mechanics (Scalars & Vectors A scalar has only a magnitude (size)…
Mechanics
Scalars & Vectors
A scalar has only a magnitude (size) whereas a vector has both a magnitude and a direction.
Examples of Scalars
distance, area, volume, speed, time, mass, energy, power, temperature, electric potential
Examples of Vectors
displacement, velocity, acceleration, force, momentum, electric field strength, magnetic field strength
Conditions for Equilibrium
An object is in equilibrium if:
The resultant force acting on the object is zero.
The sum of the moments acting on an object must be zero.
Triangle of forces
When an object is in equilibrium the forces acting on it will form a closed triangle.
Momentum
The momentum (p) of an object is found by multiplying the objects mass (m) in kilograms (kg) by it’s velocity in metres per second (ms-1).
Impulse
If we multiply the force acting on an object by the time it is acting for this is called the impulse of a force.
Impulse is a vector and its unit is the kilogram metre per second (kgms-1) or the newton second (Ns).
Conservation
The principle of conservation of momentum when two objects interact the total momentum remains the same provided no external forces are acting.
Elastic and Inelastic Collisions
Elastic collisions are those in which kinetic energy is conserved. You have the same total mount of kinetic energy at the start and end of the collision.
Inelastic collisions are when you do not have the same amount of kinetic energy at the end as you had at the start. Some of the kinetic energy has been dissipated to the surroundings.
Newton’s Laws of Motion
1) Newton’s first law
An object continues in a state of rest or uniform motion in a straight line unless acted on by a resultant force.
2) Newton’s second law
The rate of change of momentum of an object is directly proportional to the resultant force applied and is in the direction of the resultant force.
3) Newton’s third law
When two objects interact they exert equal and opposite forces on each other.
Work, Energy & Power
W = Work done
F = Force
s = Displacement
θ = angle between the direction of motion of the object and the direction of the force in degrees (ᵒ)
P = Power
ΔW = Work done
Δt = time
P = Power
F = Resultant force
v = Velocity
Moments
The moment of a force about a turning point is the force multiplied by the perpendicular distance to the force from the turning point.
Moment = F d
The principle of moments.
"When an object is in equilibrium the sum of the anticlockwise moments about a turning point must be equal to the sum of the clockwise moments.”
Couples
A couple is two equal forces which act in opposite directs on an object but not through the same point so they produce a turning effect.
The moment (or torque) of a couple is calculated by multiplying the size of one of the force (F) by the perpendicular distance between the two forces (s).
Motion along a straight line
v = velocity in metres per second (ms⁻¹)
Δs = change in displacement in metres (m)
Δt = change in time in seconds (s)
a = acceleration in metres per second per second (ms⁻²)
S
U
V
A
T
Conservation of Energy
ΔEₚ = change in gravitational potential energy in joules (J)
m = mass in kilograms (kg)
g = gravitational field strength in newtons per kilogram ( N kg⁻¹)
Δh = change in height in metres (m)
Ek = kinetic energy in joules (J)
m = mass in kilograms (kg)
v = velocity in metres per second (ms⁻¹)
