Y1: Mechanics Flashcards
What is a scalar quantity
A value with magnitude, but no direction
What are some examples of scalar quantities
- Length/distance
- Speed
- Mass
- Temperature
- Energy
What is a vector quantity
A value with both magnitude and direction
What are some examples of vector quantaties
- Displacement
- Velocity
- Force (eg. Weight)
- Acceleration
- Momentum
How do you resolve the horizontal component of a vector
Vx = VCosθ
How do you resolve the vertical component of a vector
Vy = VSinθ
What is a free body diagram
Shows the forces acting on an object, but not the forces it exerts on others
How do you know if a system is in equilibrium
- Forces on the free body diagram will form a closed vector triangle
- Both the vertical and horizontal components will have a sum of 0
What is a moment
The turning effect of a force about a pivot
What is the equation for a moment
M=FCosθs
FCosθ: force acting perpendicular to the pivoting rod
s: distance between the force and the pivot
What is the principle of moments
When balanced, the total clockwise moments must be equal to the total anticlockwise moments
What is a couple
A pair of forces acting in opposite directions about a pivot
What is torque
the moment of a couple
What is the equation for torque
𝛕=FdCosθ
FCosθ: force acting perpendicular to the pivoting rod
d: distance between the two forces
What is the centre of mass of an object
The single point where all the weight can be considered to act through, when the object is in any orientation
What is speed
How fast something is moving, in no given direction
What is displacement (s)
How far an object travels from it’s starting point in a given direction (meters)
What is velocity (u/v)
The rate of change of an objects displacement (speed with a direction (ms^-1)
What is acceleration (a)
The rate of change of an objects velocity (ms-2)
What are the 5 SUVAT equations
v = u + at
s = 1/2(v+u)t
s = vt - 1/2(at^2)
s = ut + 1/2(at^2)
v^2 = u^2 + 2as
How is velocity shown on a displacement-time graph
Gradient
How is acceleration shown on a displacement-time graph
Rate of change of gradient (i.e. if straight line, a=0)
How is displacement shown on a velocity-time graph
Area under the line
How is acceleration shown on a velocity-time graph
Gradient (if line is curved, shows none-linear acceleration)
How is velocity shown on an acceleration-time graph
Area under the line
What is Newton’s first law of motion
1) An object will remain in a constant state of motion unless acted upon by a resultant force
What is Newton’s second law of motion
2) The acceleration of an object is proportional to the force applied to it, and inversely proportional to it’s mass
(F=ma)
What is Newton’s third law of motion
3) Every force acting on an object has a resultant force of equal magnitude, acting in the opposite direction (same type of force, eg. electrostatic)
What is the value for acceleration due to gravity (g) on earth
9.81ms^-2
What is the Law of inertia
Larger masses require a larger force to be moved, so all objects fall at the same rate.
F = weight of an object in free fall
F = W
ma = mg
a = g
∴ acceleration of all objects, regardless of mass, is 9.81ms^-2
What are the SUVAT equations for objects in free fall (u=0)
v = gt
s = vt/2
s = 1/2(gt^2)
v^2 = 2gs
What is a projectile
An object with an initial velocity left to move freely under gravity
What is always true about the horizontal velocity of a porjectile
It remains constant, as there is no horizontal force
(only force is W, acting down)
What is the relationship between drag and velocity
Drag ∝ v^2
What is the terminal velocity of an object
The maximum velocity of an object, when the resistive force (friction) is equal to the driving force
What is momentum
The product of mass and velocity (kg ms^-1)
What is the equation for momentum
ⲣ = mv
What is the principle of linear momentum
When there are no external forces acting on a system, momentum is always conserved
m1u1 + m2u2 = m1v1 + m2v2
What is an elastic collision
When kinetic energy is conserved
1/2(mu^2) = 1/2(mv^2)
What is an inelastic collision
When kinetic energy isn’t conserved and some is converted into other forms (eg. dissipates as sound)
However, momentum is also still conserved
How is force related to momentum
F=ma, and a=Δv/t
∴ F = Δ(mv)/t
Force is the change in momentum per second
What is impulse
The product of force and time, which is equal to the change in momentum
F = Δ(mv)/t
∴ Ft = mv -mu
How is impulse shown on a force-time graph
Area under the line
How do safety features in transport design reduce the impact force
F = Δ(mv)/t
∴ F ∝ 1/t
Safety features increase the time of impact during a crash, with measures such as crumple zones, seat belts and air bags.
What is work done
The amount of energy transferred to cause movement (J)
What is the equation for work done
W = FsCosθ
FCosθ: The component of the force acting in the direction of movement
s: Distance move
What is power
The rate of doing work/rate of energy transfer (W)
What is the equation for power
P = ΔW/Δt
How is power related to velocity
W = FsCosθ, and P = ΔW/Δt
∴ P = (FsCosθ)/Δt
Also: v = s/Δt
∴ P = FvCosθ
What is the principle of the conservation of energy
Energy cannot be created or destroyed. Energy can be transferred between stores, but the total energy in the system will remain constant
What is efficiency
A measure of how well energy is transferred between stores
What is the equation for efficiency
Efficiency = Useful output / total input (x100 for %)
What is the equation for kinetic energy
1/2(mv^2)
What is the equation for gravitational potential energy
mgh
What is the equation for elastic potential energy
1/2(kΔL^2)
How does work done relate to the conservation of energy
Work done is the change in energy to cause movement
eg. mgh = FsCosθ + 1/2(mv^2)
