Mechanics/ biomechanics - unit 1 deck 4 Flashcards
Define pressure
This is the force exerted per unit area on a surface
==> Pressure is a measure of the distribution of a force over an area.
By definition what angle does pressure act to a surface ?
By definition it acts at 90 degrees to a surface
What is the dervived SI unit for pressure ?
The pascal (Pa)
State the equation for calculating pressure
P = F / A
- P = pressure
- F = the applied force (normal to the surface)
- A = the application area
As the magnitude of the force applied over a constant area is increased what happens to the pressure ?
The pressure increases
As the size of the area increases and the applied force stays constant what happens to the pressure ?
It decreases
Appreciate this example:
Imagine what happens when someone wearing high-heeled shoes stands on your foot compared to the same person wearing flat-heeled shoes (Figure 21). The high-heeled shoe is much more painful and is more likely to cause an injury. This is because the pressure is so much greater due to the much smaller area over which part of the person’s weight is applied
In reality how is pressure usually distributed in the human body ?
No it is concentrated on bony prominences
e.g. in the foot the pressure is concentrated in the heel, 1st and 5th metatarsals
What can excessive pressure over sustained periods of time lead to ?
Pressure (bed) sores
==> it is important that pressure is distributed evenly
How is pressure distributed evenly in orthoaedics and rehabilitation to reduce the risk of complications such as pressure sores?
This is achieved by soft materials to equalise pressure distribution, by spreading the pressure over large areas and by avoiding loading bony prominences
e.g. pressure distribution of over the pads of orthotic braces and in the sockets of lower extremity prostheses.
It is also important not to have excessive pressures on the bone in contact with joint replacements.
Do SAQ 5 pg. 9, forces unit, mechanics binder
Define what is meant by the term static equilibrium
This is when an object which is static with no resultant force (or moment) acting on it
remember by static we mean not accelerating, the body may be moving with a constant linear &/or angular velocity
What is the first condition of static equilibrium?
That the sum (Σ) of all the external forces (F) acting on an object is zero.
Therefore for a rectangular reference frame with x, y, and z axes:
- ΣFx = 0, the sum of all the external forces acting on the x-axis
- ΣFy = 0, the sum of all the external forces acting on the y-axis
- ΣFz = 0, the sum of all the external forces acting on the z-axis
What is the specific name given to static equilibrium along straight-lines?
Translational equilibrium
Appreciae this:
A body will not accelerate if all the forces that are acting upon it are balanced. If the forces are not balanced then it will accelerate under the action of the resultant force.
What does this symbol mean - Σ?
‘Sum of’
Which of newtons laws forms the basis for the analysis of forces acting on static systems ?
Newtons 3rd law - the law of reaction
State newtons 3rd law
To every action there is an equal and opposite reaction
e.g. consider 2 objects; the force exerted by the first object on the second must be equal to that exerted by the second object on the first. For example, if you press both your index fingers together the force exerted by the left index finger on the right index finger is the same as that exerted by the right index
Another example is standing on a floor; if the floor did not exert an upward force equal to your weight then you would fall through it!
When more than one force is acting on a body it is often desirable to know the net or resultant force. As already explained, when the resultant force is zero then the body is in static equilibrium. However, when several forces are acting on a body in static equilibrium there may be an unknown force that we wish to know.
What can be done to calculate this unknown force?
Found graphically or by resolving (the 2 methods for solving vectors)
Do the worked examples pg. 11&12, forces unit, mechanics binder
What is the perferred method for finding the unknown force ?
To resolve the forces, rather than graphically adding forces
Why is it preferrable to add forces by resolving ?
Because when trying to add forces graphically if one force is much smaller than the others then the diagram will become very tiny and difficult to draw accurately to scale. Acute angles are also difficult to represent accurately graphically
Do SAQ 7, pg. 13, forces unit, mechanics binder
To find the sum of two forces what is done ?
They are both resolved (into there horizontal and vertical components) and their horizontal and vertical components are added together, the resultant force can then be found using trigonometry to find its magnitude and direction
How is a force resolved into its horizontal and vertical components
Refer to pg. 13 forces unit, mechanics binder
- Horizontal component = Fcosθ
- Vertical component = Fsinθ
Think sin = sun
Note the horizontal component is always the line which forms the angle you use to the resultant line
Do SAQ 8, pg. 14&15, forces unit, mechanics binder
What is a free body diagram and what does it show?
- A free body diagram is often a useful tool for visualising and then solving quite complex mechanical problems.
- In a free body diagram all external forces (and moments) acting on a body are shown.
- These external forces include those due to gravity, friction forces and reaction forces.
Define what an external force is
These are forces which act on a body from outside it. They are transmitted through a body by means of internal forces
What can complex systems be broken down into to help calculate problems
They can be broken down in their component parts (i.e. a number of rigid bodies) and the interactions between these can then be found.
e.g. to calculate the force acting at the hip joint during gait, the ground reaction force acting on the foot may be measured using a force platform. The lower limb can then be broken down into three component segments; foot, leg and thigh, which are treated as rigid bodies. The forces acting at the intersection of these components (i.e. the joints) can the be calculated.
Firstly the forces at the ankle, then the forces acting at the knee and finally at the hip joint
What is the section of mechanics which looks at how forces produce and change motion of bodies called?
Kinetics or sometimes dynamics
Give an example of the use of kinetics in orthopaedics
e.g. in calculating the loadings on a hip prostheses during walking. During walking the body segments are moving relative to the ground and each other. Forces (and moments) are produced as a result of the body segments’ masses and their accelerations. The calculated forces (and moments) can then be used to determine the design requirements of hip prostheses
What two laws govern motion due to forces?
Newtons laws of motion; the laws of inertia and acceleration
Define what a force is
A force is that which changes the motion of a body
State newtons 1st law; the law of inertia
Every body remains at rest or moving at constant velocity unless acted upon by a resultant force
In other words, if a body is at rest or moving with a constant velocity the forces acting upon it must be balanced; it is in static equilibrium. However if a resultant force acts on the body then its velocity will change
Basically, the law of inertia is saying that a body has a certain reluctance to accelerate (or decelerate) which is its inertia. A bodies inertia
Define what a bodies inertia is and what inertia is represented by
- A bodies inertia is its reluctance to accelerate (or decelerate)
- A bodies inertia is represented by its mass
Give an example of inertia
e.g. when driving, as you accelerate you feel yourself being pressed against the seat backrest, this is due to your bodies reluctance to accelerate. Similarly when decelerating you will feel yourself moving forward, this is again due to your bodies reluctance to decelerate (change its velocity)
State Newtons 2nd law; the law of acceleration
The acceleration of a body is proportional to the applied force and inversely proportional to its mass
State the equation used to calculate acceleration in relation to force and mass
a = F / m
- a = the body’s acceleration
- F = the applied force
- m = the body’s mass
The more familiar equation is the equation used to calculate force;
F = ma (easier to just remember this one)
DO SAQ 11, pg. 17, forces unit, mechanics binder
Define what is meant by dynamic equilibrium
This is when the sum of all the external forces is not equal to zero then there is a resultant force
In dynamic equilibrium what is the sum of all the external forces acting on the body equal to and what can therefore be calculated ?
The sum of is equal to the resultant force ==> allowing newtons second law to be applied and acceleration can then be calculated
State the difference between dynamic and static equilibrium
In static equilibrium the sum of all the external forces acting on a body must be equal to zero, whereas in dynamic equilibrium the sum of all the external forces is not equal to zero so there is a resultant force
In 3- dimensions
Static equilibrium; ΣFx = 0, ΣFy = 0, ΣFz = 0
Dynamic equilibrium; ΣFx = max, ΣFy = may, ΣFz = maz
Do the worked example pg. 18&19, forces unit, mechanics binder
It is key to remember for this one that the line which forms to the angle to the resultant force is your horizontal component
What is momentum and what 2 key factors does it incorporate?
It is an expression of the body’s persistence to continue in its present state of motion.
It incorporates a body’s resistance to change its motion (inertia) and its velocity.
What is momentum the product of?
Mass (remember inertia represented by mass) and the velocity of the body
What type of quantity is momentum ?
It is a vector quantity
What direction does momentum act ?
It acts through the body in the direction of motion
State the equation for momentum
p = mv
- p = momentum
- m = body’s mass
- v = body’s velocity
What are the units of momentum?
kg m s-1 (kilogram meters per second) or N s (newton second)
1 kg m s-1 ≡ 1 N s
1 N ≡ kg m s-2
≡ means equivalent to
Momentum is incorporated in a more formal expression of Newtons II law, the law of acceleration which is also called the law of momentum, what does the law of momentum state?
The rate of change of linear momentum is proportional to the applied force
For reference:
law of acceleration = the acceleration of a body is proportional to the applied froce and inversely proportional to its mass
State the equation for calculating the rate of change of momentum
F = mv - mu / t
- F = applied force
- m = body’s mass
- u = unitial velocity
- v = final velocity
- t = time taken
Appreciate the relationship of momentum and acceleration through this equation explanation:
F = mv - mu / t (recall p = mv is momentum so this is trying to prove that the rate of change of momentum is proportional to the applied force just like acceleration is)
==> F = m (v - u / t)
and since a = v - u / t (same as change in velocity over time = acceleration)
==> you can state F = ma
- F = applied force
- m = body’s mass
- u = initial velocity
- v = final velocity
- t = time taken
Go through the worked example on pg. 21, forces unit, mechanics binder
The force in this example is given a negative value cause it is a decelerating force so is acting in the opposite direction of the momentum of the lorry
Think of it going along an x axis the lorry is travelling in the +ve x direction and the breaking force is applied along the -ve x direction
Do SAQ 13, pg. 21, forces unit, mechanics binder
State the principle of conservation of momentum
In a closed or isolated system a number of bodies can interact by colliding and the total momentum in the system will remain constant
Do worked example pg.21&22, forces unit, mechanics binder
It is important to remember that a moment is a vector so it has a magnitude and direction so you need to define one of the directions as negative e.g. if two body’s collide then one of them will be travelling in the positive x direction and one will be travelling in the negative
Also important to remember that in closed/ isolated systems the total momentum will remain constant so you can make the momentum before = to the momentum after
