Mechanics/ biomechanics - unit 1 deck 4

Question 1

Define pressure

Answer 1

This is the force exerted per unit area on a surface

==> Pressure is a measure of the distribution of a force over an area.

Question 2

By definition what angle does pressure act to a surface ?

Answer 2

By definition it acts at 90 degrees to a surface

Question 3

What is the dervived SI unit for pressure ?

Answer 3

The pascal (Pa)

Question 4

State the equation for calculating pressure

Answer 4

P = F / A

• P = pressure
• F = the applied force (normal to the surface)
• A = the application area

Question 5

As the magnitude of the force applied over a constant area is increased what happens to the pressure ?

Answer 5

The pressure increases

Question 6

As the size of the area increases and the applied force stays constant what happens to the pressure ?

Answer 6

It decreases

Question 7

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

Question 8

In reality how is pressure usually distributed in the human body ?

Answer 8

No it is concentrated on bony prominences

e.g. in the foot the pressure is concentrated in the heel, 1st and 5th metatarsals

Question 9

What can excessive pressure over sustained periods of time lead to ?

Answer 9

Pressure (bed) sores

==> it is important that pressure is distributed evenly

Question 10

How is pressure distributed evenly in orthoaedics and rehabilitation to reduce the risk of complications such as pressure sores?

Answer 10

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.

Question 11

Do SAQ 5 pg. 9, forces unit, mechanics binder

Question 12

Define what is meant by the term static equilibrium

Answer 12

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

Question 13

What is the first condition of static equilibrium?

Answer 13

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

Question 14

What is the specific name given to static equilibrium along straight-lines?

Answer 14

Translational equilibrium

Question 15

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.

Question 16

What does this symbol mean - Σ?

Answer 16

‘Sum of’

Question 17

Which of newtons laws forms the basis for the analysis of forces acting on static systems ?

Answer 17

Newtons 3rd law - the law of reaction

Question 18

State newtons 3rd law

Answer 18

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!

Question 19

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?

Answer 19

Found graphically or by resolving (the 2 methods for solving vectors)

Question 20

Do the worked examples pg. 11&12, forces unit, mechanics binder

Question 21

What is the perferred method for finding the unknown force ?

Answer 21

To resolve the forces, rather than graphically adding forces

Question 22

Why is it preferrable to add forces by resolving ?

Answer 22

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

Question 23

Do SAQ 7, pg. 13, forces unit, mechanics binder

Question 24

To find the sum of two forces what is done ?

Answer 24

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

Question 25

How is a force resolved into its horizontal and vertical components

Answer 25

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

Question 26

Do SAQ 8, pg. 14&15, forces unit, mechanics binder

Question 27

What is a free body diagram and what does it show?

Answer 27

• 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.

Question 28

Define what an external force is

Answer 28

These are forces which act on a body from outside it. They are transmitted through a body by means of internal forces

Question 29

What can complex systems be broken down into to help calculate problems

Answer 29

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

Question 30

What is the section of mechanics which looks at how forces produce and change motion of bodies called?

Answer 30

Kinetics or sometimes dynamics

Question 31

Give an example of the use of kinetics in orthopaedics

Answer 31

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

Question 32

What two laws govern motion due to forces?

Answer 32

Newtons laws of motion; the laws of inertia and acceleration

Question 33

Define what a force is

Answer 33

A force is that which changes the motion of a body

Question 34

State newtons 1st law; the law of inertia

Answer 34

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

Question 35

Define what a bodies inertia is and what inertia is represented by

Answer 35

• A bodies inertia is its reluctance to accelerate (or decelerate)
• A bodies inertia is represented by its mass

Question 36

Give an example of inertia

Answer 36

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)

Question 37

State Newtons 2nd law; the law of acceleration

Answer 37

The acceleration of a body is proportional to the applied force and inversely proportional to its mass

Question 38

State the equation used to calculate acceleration in relation to force and mass

Answer 38

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)

Question 39

DO SAQ 11, pg. 17, forces unit, mechanics binder

Question 40

Define what is meant by dynamic equilibrium

Answer 40

This is when the sum of all the external forces is not equal to zero then there is a resultant force

Question 41

In dynamic equilibrium what is the sum of all the external forces acting on the body equal to and what can therefore be calculated ?

Answer 41

The sum of is equal to the resultant force ==> allowing newtons second law to be applied and acceleration can then be calculated

Question 42

State the difference between dynamic and static equilibrium

Answer 42

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; ΣF_x = 0, ΣF_y = 0, ΣF_z = 0

Dynamic equilibrium; ΣF_x = ma_x, ΣF_y = ma_y, ΣF_z = ma_z

Question 43

Do the worked example pg. 18&19, forces unit, mechanics binder

Answer 43

It is key to remember for this one that the line which forms to the angle to the resultant force is your horizontal component

Question 44

What is momentum and what 2 key factors does it incorporate?

Answer 44

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.

Question 45

What is momentum the product of?

Answer 45

Mass (remember inertia represented by mass) and the velocity of the body

Question 46

What type of quantity is momentum ?

Answer 46

It is a vector quantity

Question 47

What direction does momentum act ?

Answer 47

It acts through the body in the direction of motion

Question 48

State the equation for momentum

Answer 48

p = mv

• p = momentum
• m = body’s mass
• v = body’s velocity

Question 49

What are the units of momentum?

Answer 49

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

Question 50

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?

Answer 50

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

Question 51

State the equation for calculating the rate of change of momentum

Answer 51

F = mv - mu / t

• F = applied force
• m = body’s mass
• u = unitial velocity
• v = final velocity
• t = time taken

Question 52

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

Answer 52

• F = applied force
• m = body’s mass
• u = initial velocity
• v = final velocity
• t = time taken

Question 53

Go through the worked example on pg. 21, forces unit, mechanics binder

Answer 53

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

Question 54

Do SAQ 13, pg. 21, forces unit, mechanics binder

Question 55

State the principle of conservation of momentum

Answer 55

In a closed or isolated system a number of bodies can interact by colliding and the total momentum in the system will remain constant

Question 56

Do worked example pg.21&22, forces unit, mechanics binder

Answer 56

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