Mechanics: Unit 2 Forces (class) Flashcards
What are the two effects of force?
- change the state of motion of a body
2. deform a body
What is the SI unit of force?
the newton (N)
What is one newton equal to?
1kg m/s2
What is statics?
forces acting on bodies which are at rest or moving with constant velocity ie. not accelerating
Which type of body cannot be deformed?
rigid body
What is the difference between mass and weight?
mass is the amount of matter in a body whereas weight is the force of gravity on a body
How do we calculate weight?
mass (kg) x gravity (m/s2)
What unit do we use to measure weight?
a newton
What is gravity?
the acceleration due to an attraction between masses depending on the size of the mass and the distance
Which of mass and weight remains constant?
mass
What is pressure?
force per unit area
What is the derived SI unit for pressure?
a pascal (Pa)
What is a pascal equal to?
1N/m2
What is density?
mass per unit of volume
What symbol is used for density?
ρ - the greek letter rho
What is density measured in?
kg/m3
What is the density of water?
1000kg/m3
give an equation that links gravity, height, pressure and density
P = p g h pressure = density x gravity x height
What is the difference between P and p?
P is pressure
p is density
What is friction?
a force between surfaces that opposes motion
What do we measure friction in?
newtons
What is friction
a) dependent on?
b) independent of?
a) roughness of the surface and size of force
b) apparent contact area
What is friction force equal to?
μ (friction coefficient) x normal force
What is the friction coefficient?
the measure of the maximum friction force between two surfaces
What are the 3 types of friction?
static
sliding
rolling
What is static equilibrium?
a body which is static with no resultant force acting on it
Where will a rigid, symmetrical body with uniform density have its centre of mass?
its geometric centre
Where is the body’s centre of gravity?
at same point as centre of mass but only exists in a gravitational field
Which has more friction a rough or smooth surface?
a rough one
What is the maximum friction force dependent on?
surface texture
lubrication
magnitude of force pressing them together
What is the coefficient of static friction equal to?
the ratio of maximum friction force to the normal force
Which friction is greater static or sliding?
static: its more energy to start something than to keep it moving
How does rolling friction arise?
the normal force deforms the two surfaces
What effect does lubrication have on rolling friction?
does not lower it
- may reduce wear
how do we calculate max force before something moves?
max force = friction coefficient x weight
why does it help to lift an object a bit while you push it?
it lowers the force acting normally and reduce the friction force
why does an object that can slide down a slope not do so when carefully placed?
the object wont slide down the slope because the coefficient of static friction is greater than sliding friction
is pressure evenly distributed in a human?
no it is concentrated on bony prominences
What is the first condition of static equilibrium?
the sum of all external forces (F) acting on a body is zero
What is Newtons third law?
for every action there is an equal and opposite reaction
Can an accelerating body be in static equilibrium?
no it must be stationary or moving at constant velocity
What are free body diagrams used for?
illustrate the external forces acting on the body
What is an external force?
give 3 examples
a force that acts on the body from outside it
eg. those due to gravity, friction forces and reaction forces
what is kinetics?
how forces produce and change the motion of bodies
What is Newton’s first law?
the law of inertia: a body will remain at rest or constant velocity unless acted upon by a resultant force
What is Newton’s second law?
the law of acceleration: the acceleration of a body is proportional to the applied force and inversely proportional to its mass
What is the sum of all external forces in dynamic equilibirum?
does not equal zero
equal to a resultant force
resultant force equal to the mass x acceleration
What is momentum and how do we calculate it?
a body’s persistence to continue in its present state of motion
mass x velocity
What symbol do we use for momentum
p
What units do we use for momentum?
kg m s-1
What is the conservation of momentum?
A body will continue to move with constant momentum unless an external force acts to change that momentum
so
when multiple bodies with different momentums interact , the total momentum will be the same before and after the collision
In which type of collision is kinetic energy conserved?
elastic
What is the moment of a force?
its tendency to produce a rotation
What is another word for a moment?
torque
What is a moment of a force equal to?
force x moment arm
What units do we use for a moment?
Newton metres (Nm)
How do we know which direction of rotation in a moment is positive or negative ?
right hand grip rule
grab any axis (x,y,z) with thumb pointing up
the direction your fingers point in is the positive moment
Why is it easier to move a wheelchair with a larger diameter handrim than one with a small diameter handrim?
(wheels are the same)
when the moment arm is increased the force required is decreased
What is the sum of all forces in static rotational equilibrium?
equal to zero
When calculating a moment, if we pick a point what are the forces acting through that point?
does not produce a moment through that point
What is mechanical advantage?
ratio of lever arms
How do you calculate mechanical advantage?
effort distance/ resistance distance
Whats the problem with using moments in animal bodies?
indeterminate because there are so many unknown values when considering all the muscles that cross a joint and calculating each ones force
How can we solve inderminate problems ?
reduction or optimisation methods
What does a high mechanical advantage mean?
effort force is less than resistance force ie. something is easy to do
What is a lever?
a rigid bar pivotting on a fulcrum
acted on by effort and resistance forces
Wow do we calculate MA for levers?
force-fulcrum distance (df) / resistance-fulcrum distance (dr)
What does a high MA mean?
effort force is lower than resistance force
In humans what relationship tends to exist in the lever system around muscles?
force disadvantage because muscle insertion is closer to the fulcrum than the resistance so a lot of muscle effort is produced
What is a first class lever?
fulcrum located between effort and resistance
What is a second class lever?
resistance between effort and fulcrum
What is a third class lever?
effort located between fulcrum and resistance
What is a moment arm?
length of the line that passes through the centre of rotation and is perpendicular to the line of action of the force
What is a mechanical disadvantage?
what is it represented by?
when the effort force is more than the resistance force
MA of less than 1
What type of MA exists for
a) a first class lever?
b) a second class lever?
c) a third class lever?
a) MA or MD
b) MA
c) MD
Give an example of
a) a first class lever
b) a second class lever
c) a third class lever
a) see saw
b) wheelbarrow
c) fishing rod
Which force is much bigger than the other two: external force, joint force or muscle force?
joint force
Why are forces acting through the lumbar spine so large?
The head, thorax and any external force such as holding a weight are segments that have small loads carried through the lumbar spine during flexion.
Since these segments are farther away from the fulcrum (at the vertebrae) than the resistance given by the muscles there must be a much larger load to balance them out.
What reduces loading of the lumbar spine?
increased intra-abdominal pressure
ligaments
erector spinae
What increases loading of the lumbar spine?
dynamic rather than static loading
loading in other planes
torsional loads
What equation describes the relationship between linear and angular velocity?
v = r ω
linear velocity = radius x angular velocity
What does tangential acceleration represent?
the linear acceleration directed at a tangent to the circle formed by the motion
What is tangential acceleration equal to when the body rotates with a constant angular velocity?
zero
How do we calculate tangential acceleration?
at = r α
tangential acceleration = radius x angular acceleration
Is there radial acceleration if something is spinning at a constant rate?
yes
Which type of angular acceleration acts to maintain the body on its circular path?
centripetal/radial acceleration
How do we calculate radial acceleration?
ar = v2/ r = r ω2
What is moment of inertia and what symbol represents it ?
A body’s internal resistance to rotation
I
What is moment of inertia dependent on?
the body’s mass and the distribution of that mass in relation to the axis of rotation
What affect does an increase in moment of inertia have on acceleration?
the more inertia the harder it is to accelerate
Does moment of inertia increase or decrease when the mass is distributed further from the axis of ration?
increase
What is moment of inertia equal to?
I = mk2
moment of inertia = mass x radius of gyration2
What symbol represents radius of gyration?
k
How do we calculate k for a solid ring or spoked wheel?
it is equal to the radius
How do we calculate k for a solid diskeg a fly wheel?
k2 = 1/2 r2
What symbol represents angular momentum?
L
What is L equal to?
L = I ω
angular momentum = moment of inertia x angular velocity
What are the SI units of angular momentum?
kg m2 rad s-1
If the radius of gyration decreases what happens to
a) angular momentum?
b) moment of inertia?
c) angular velocity?
a) remains constant due to conservation of movement
b) decreases because I = mk2
c) must increase
What assumptions do we make about link segment models?
- body segments are rigid
2. joints are frictionless
Give an example of a a) external b) internal c) inertial force acting on a segment.
a) weight, gravity, reaction forces
b) muscle contraction force, ligament force, joint friction
c) changes in state of motion ie acceleration
mass of segment x acceleration
What is a quasi static system?
when the change in state of motion is so small that we ignore it
What is anthropometry?
Estimation of body segment parameters
What body parameters can we calculate from body weight and height?
segment length
segment mass
centre of mass for a segment
radius of gyration of a segment
What is work?
when a force moves a body ie. force (N) X distance (m)
What are the units for work?
Joules (j)
What is power?
the rate of doing work ie. work done (j) / time taken (s)
What are the units for power?
Watts (W)
What is energy?
the capacity to do work
What are the units for energy?
joules (j) = Nm = kg m2 s-2
Which type of energy is possessed due to
a) motion?
b) position?
a) kinetic
b) potential
How do we calculate potential energy?
mg.h
mass x gravity x height
How do we calculate kinetic energy?
1/2 m v2
1/2 x mass x linear velocity squared
What are the units for radius of gyration?
metres
What does the symbol P stand for?
power
If two identical objects with masses of 1kg and 2kg fall from the same height at the same time which will hit the ground first?
PE = KE mgh = 1/2mv2
so v = √`2gh
ie. it is independent of the mass and they will hit the floor at the same time
What is conservation of energy?
energy can be redistributed or changed to another form but cannot be created or destroyed
How do we calculate rotational kinetic energy ?
KE = 1/2 I ω2
When calculating the KE of a spinning object which equations need to be used?
- work out the liner KE (1/2 m v2)
2. work out the rotational KE (1/2 I ω2)
In a force-distance graph what is the area under the curve equal to?
work done
How do we calculate elasticity?
N/m
On a velocity time graph when is
a) maximum velocity?
b) maximum acceleration?
a) acceleration –> deceleration
b) steepest part of the slope
What priniciple do accelerometers use?
newtons second law F=ma
we know force and mass so we can work out a
if a point on a wheel is moved further from the centre what happens to its tangential velocity?
it increases
firstly it will cover more distance and secondly an increase in radius will increase the tangential velocity
what is radius of gyration?
the radius from the axis of rotation to the centre of mass during rotatory motion
What represents a body’s inertia?
its mass
How can we calculate a moment involving angles?
moment = perpendicular force x l sin θ
If we have a lever system with a fulcrum, muscle and gravity what would be
a) the effort force?
b) the resistance force?
a) the muscle
b) gravity
Calculate the tangential linear acceleration of a wheelchair with a radius of 2cm moving at a constant angular velocity of 10 rad/s
tangential acceleration (at) = r α α is zero as it is moving at constant velocity so at = zero also
how can we relate friction to radial acceleration?
friction force = mass x radial acceleration
F = ma
Is pressure a vector or a scalar?
pressure is a scalar because although force is a vector quantity pressure has only a magnitude and not a direction
What are the two components we need to consider when thinking of angular acceleration?
- changes the magnitude of velocity
2. changes the direction
What is the symbol for
a) momentum?
b) angular momentum?
a) p
b) L
What are the units of energy?
joules
