Mechanics Flashcards
Newtons 1st Law
A body will remain at rest or continue at uniform velocity, unless acted upon by a resultant force
Newtons 2nd Law
The acceleration experienced by a body is parallel and directly proportional to the resultant force acting upon it
F=ma
F = (mu-mv)/t
Newtons 3rd Law
When two bodies interact, they exert forces upon each other which are equal in magnitude, but opposite in direction
Resultant force
Only required for acceleration
Any body moving at a constant velocity does not have a resultant force acting
What is Mass
A measure of a body’s inertia - its resistance to a change in velocity
What do bodies with more mass have
Greater inertia
Require more force to change their velocity
What is Weight
Force of attraction that acts on a body - owing to the body having mass and being in a gravitational field
W=mg
What is the Centre of Mass and where does it lie
A single point at which the body’s mass can be thought to be concentrated
Lays where all lines of symmetry cross
CoM practical
Suspend the body from a position near its edge
Allow it to come to rest
Draw a line vertically down - using plumb line to guide
Suspend the body from another point
Allow it to come to rest - vertical line straight down
CoM lays where lines cross
When body is in rest - it’s in equilibrium - weight must act through CoM - gives rise to a zero moment
Free fall
Motion of a body through a drag producing medium without a drag producing device
Resultant force accelerating body (the weight) stays the same - accelerates uniformly - use dynamic equations
Forces acting when a body falls through the air on earth
Calculate resultant force
Weight and drag
F=ma
W-D=ma
a=(W-D)/m = mg/m - D/m
a = g - D/m
Free fall assumption
Drag can be ignored as drag force up isn’t same order of magnitude as weight force
Times it can’t be ignored:
Body’s mass is very small in relation to surface area
Body is falling at a considerable velocity
Free fall ignoring drag working out
a = (W-R) / m
a = W/m
W = mg
a = mg/m
a=g
Driving force acting on a body of a certain shape in a given fluid
Body accelerates
Velocity increases
Drag force increases
Resultant force decreases
Acceleration decreases
Eventually drag force = driving force
Zero resultant force - zero acceleration - constant maximum speed attained - Terminal speed
Terminal speed
Maximum speed attained by a body during free fall, when it’s weight is balanced by the drag force acting upon it
Principle of moments
For a system in equilibrium
Components in every plane are balanced
Sum of clockwise moments = sum of anti-clockwise moments
Support force
Acts where a body is in contact with a surface
Bodies balanced horizontally on a pivot - support force always acts upwards
Bodies in equilibrium - support force up must equal all forces acting down
Supports force acts at the pivot in a single support - has no moment
Two pivots = two support forces - moments about one pivot means you must take into account the moment of the support force from the second pivot - value of support force at each pivot is determined by where CoM lies
Only way to get system in rotation without translational motion
Apply a pair of forces about the pivot point - acting in the same plane but opposing directions
How to get system in rotation with translational motion
Single force about a pivot point - unbalanced force in horizontal plane
Couple
Pair of forces which give rise to a resultant moment but no resultant force
Moment of a couple = torque
Triangle of forces
Triangle that represents magnitudes and directions of three forces whose resultant is zero
Density
Mass per unit volume
Measure mass
Scales
Measure volume
Liquid - measuring cylinder
Regular shaped solids - sides using ruler/vernier callipers/micrometer - calculate volume
Irregular shapes solids - displacement can
Pressure
Normal force exerted per unit area
F / A
Pressure in a liquid
At any given depth below the surface of a liquid - pressure is determined by weight of the water above that must be supported
Greater depth - more weight of water - greater pressure
Same depth - greater density - greater weight of water - greater pressure
Pressure in a liquid at a given depth formula
Pressure - density x g x depth
Archimedes Principle
Upthrust exerted on a body is equal to the weight of the liquid displaced by the body
Upthrust = density x g x submerged depth x surface area
Upthrust
Occurs whenever a body is immersed within a fluid
Results from the pressure difference that exists between the top and bottom of the fluid
What is instantaneous speed
Speed of an object over a very short interval of time
How to find instantaneous speed at a specific time
Draw a tangent at the gradient
What is acceleration when the gradient of a velocity of a time graph is constant and positive
Constant Acceleration
What is acceleration when the gradient of a velocity of a time graph is constant and negative
Constant deceleration
What is acceleration when the gradient of a velocity of a time graph is zero
Zero acceleration
What is acceleration when the gradient of a velocity of a time graph is a curve
Acceleration is changing
What is the area under a velocity-time graph
Displacement
What is the area under a velocity-time graph
Displacement
What is thinking distance
Distance travelled between the moment when you first see a reason to stop, to the moment when you use the brake
What is braking distance
The distance travelled from the time the brake is applied until the vehicle stops
What is stopping distance
Total distance travelled from when the driver first sees a reason to stop, to when the vehicle stops
Thinking distance formula
Speed x reaction time
When is an object said to be in free fall
When an object is accelerating under gravity, with no other force acting on it
What is the value for free fall
g
Equation for force parallel to the slope
W x sin theta
mg x sin theta
Equation for force perpendicular to the slope
W x cos theta
mg x cos theta
What is normal contact force equal to
mg x cos theta
Define Drag
A frictional force that opposes the motion of the object
What affects drag
Speed
Shape
Roughness
Texture
What is pressure at the base equal to
Weight of the column divided by A
What is pressure directly proportional to
height
What does pressure not depend on
Cross sectional area
Upthrust at the top surface of an object
height x density x gravity x area
h is the submerged depth
Force at the bottom surface of an object
(h + x) x density x gravity x Area
x is height of object
h is the submerged depth
When will an object sink
If upthrust is less than the weight of the object
When will an object float
upthrust = weight
What is momentum
Mass x velocity
What is the principle of conservation of momentum
For a system of interacting objects, the total momentum in a specified direction remains constant, as long as no external forces act on the system
Describe perfectly elastic collisions
Momentum is conserved
Total energy is conserved
Total kinetic energy is conserved
Describe inelastic collisions
Momentum is conserved
Total energy is conserved
Total kinetic energy is conserved
What is net force directly proportional to
Rate of change of momentum
Newtons second law
Newtons second law
F = (k (constant) x change in momentum) / change in time
When do we use F=ma
When the mass of the object remains constant during the period of acceleration
What happens to momentum because of Newtons 3rd Law
Net change is 0 therefore it always conserved
What is the impulse of a force
The change in momentum
Impulse equation
F x change in time = change in momentum
What is the area under a force time graph
Impulse
Resolving momentum in the horizontal plane
total initial momentum = total final momentum
m1v0 = m1v1cos(theta) = m2v2cos(theta)
Resolving momentum in the vertical plane
total initial momentum = total final momentum
m1v0 = m1v1sin (theta) = m2v2sin(theta)
