Biomechanics Exam 2

State Newton's laws of motion.

1st: an object will not change its motion unless a force acts on it.

2nd: the force on an object is equal to its mass times its acceleration.

3rd: when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

Newton's 1st law

An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force

Newton's 2nd law

Force = mass x acceleration

acceleration of an object is directly proportional to the net external force applied, and it is indirectly proportional to its mass

Newton's 3rd law

For every action there is an equal and opposite reaction

When we exert a force on the foot, the earth's mass is too large to allow our foot to move away from our body. Therefore, what must the body be doing in relation to the foot in order for us to move?

The force of the Earth as well as the foot coming in contact with the Earth causes body's center of gravity to go in the opposite direction of the foot. This pushes the body up and forward with the help of internal muscles.

- if push on ground, earth doesn't move away from you, so you are forced to move away from your foot

Friction depends on what 2 factors? (do not just give the pieces of the equation above; define the pieces of the equation for this answer)

Force = Ft x CFr

- Normal force and coefficient of friction

- Normal force: amount of force pushing two things together

- coefficient of friction: number representing texture and hardness of two surfaces involved (sandpaper vs glass)

Normal Force

amount of force pushing two things together

Coefficient of Friction

number representing texture and tion: hardness of two surfaces involved (sandpaper vs glass) (0.0-1.0)

What does it mean if the coefficient of friction for 2 surfaces is equal to 0.0? What if it is equal to 1.0?

Coefficient of frictions is percentage of normal force:

- = 0.0 means any force at will will make object slide (wet ice)

- = 1.0 means that force applied needs to be equal to weight of object needs to be applied to make object slide (concrete)

The coefficient of friction for a synovial joint is 0.001. Why is this important?

Synovial joint friction is very close to 0.0, so it is very easy to make the joint move and does not require a lot of force

- If coefficient of friction is high in joint then there is lots of friction and can cause damage to joint and make it harder to move

How can friction be both resistive and motive during running?

When you push on ground friction resists foot from sliding away from you so resistive in that way

- because the leg resists the foot from moving away from you, you move away from the foot (moving forward and upward) making it motive

(Ex: lacking resistance makes it hard to move anywhere like on ice)

In terms of friction, why is it often easier to pull rather than push an object?

We tend to pull things instead of pushing because of how the body is built, if we push an object we end up pushing from above and force goes downward (this increases normal force)

- Pulling an object increases upward force so normal force is decreased

How is it possible to lie on a bed of nails without injury?

P= F/A -> (force/area)

- when you have a lot of nails you increase the area

- when you increase area you decrease pressure b/c pressure is being evenly distributed among all tiny nail heads

If a person weighs 600N and the surface area of the bottom of both feet combined is 200cm^2, what is the pressure? What is the pressure if the person stands on only one foot?

Pressure = Force/Area

P=600/200= 3 N/cm^2

P=600/100= 6 N/cm^2 (b/c half of two feet (200) equals 100)

Why are spike heeled shoes not as effective as snowshoes for walking on snow without sinking?

P=F/A

Snow shoes increase the surface area and decrease pressure, spike heels have small surface area and increase pressure

(Pressure is what is changing when surface area changes. Area does not change force, it changes the pressure)

Explain the difference between stress and strain. Also, explain how they are used in the calculation of Young's Modulus and discuss the interpretation of that Modulus value.

- Stress: amount of force applied to given area (when you're stressed it's because of outside forces being applied to your brain... like class)

- Strain: reaction to amount of stress applied (change in length) (When you have a lot of stress in your classes you strain your mind when studying)

- if we plot stress and strain, we get young's modulus

- Young's modules: Steeper slope=Stiffer [Steep = Stiff: SS] materials

: less steep slope=more pliant materials)

What is the stress on the Achilles tendon if 4700 N of force are applied and the cross sectional area of the Achilles is 90 mm2?

Stress = F/A ->(Force/Area)

4700/90= 52.22 N/mm^2

Explain viscoelasticity and its relationship to loading rate.

Viscoelasticity: materials that have Young's modulus that changes due to loading rate (Ex: water)

- When walking slowly is easy and painless but jumping into water from high up is like hitting a rock (a higher loading rate changes the viscoelasticity)

How does loading rate affect the safety of exercise performance?

if something is viscoelastic, and its loading rate goes up, the material becomes stiffer, and if stiffer materials are more likely to rupture instead of strain at all (slope becomes steeper when stiff)

- when trying to progress weight very quickly without working up to heavier weight over time, ligaments can rupture because they are not ready for the weight change yet

Define centripetal and "centrifugal" forces.

Centripetal Force: (mass x velocity^2)/ radius

- any force that causes something to rotate around an axis

Centrifugal Force: linear inertia of the bodies involved

- not a force at all, actually linear inertia of object

Give the equation for determining how much centripetal force is needed to constrain an object in a circular path. According to the equation, what would be the most effective way for a person riding a bike on a wet surface to keep from slipping? Why? What would be the next best thing? Why?

- most affective way to keep from slipping, fastest way to change centripetal force is to change velocity (b/c its squared) (slow down speed)

- next best: practicality, increase radius of turn so it is not as sharp and less mass has to be changed as quickly (widen turn duh)

- ride the bike in a larger circle slower

What is the cause of the "centrifugal force" in the above example? What is the cause of the centripetal force?

- Centripetal force is caused from riding the bike in the circle

- Centrifugal force is caused from the vertical enertia (it is not caused by an outside force but the system itself)

What would happen in the above example if "centrifugal force" were greater than centripetal force needed?

Centripetal force is trying to keep you in the circle (Newton's 1st law, things don't want to go in circle they want to go in straight line)

- If centrifugal force is greater than centripital needed, you're body wont want to travel in circle anymore, something will have to change

- You would begin to move into a straight line

State Archimedes principle and then put it into your own words.

Density= mass/volume

Archimedes Principle: "a body submerged in a fluid will be buoyed up by a force that is equal to the magnitude to the weight of the displaced water"

(when you go in water the water will rise)

- Archimede's developed "the gold standard" a way to tell if gold was real

What happens if a body's weight is greater than the weight of the fluid it displaces, and what is this called? Is less than? Is equal to?

- If you weigh more than the fluid displaced, then you will sink

- when sinking you go in negative y direction so negative buoyancy

- if you weigh less, then you float, you go in the positive Y direction so positive buoyancy

- If equal you will hang out in the middle and that is called neutral buoyancy

(Think of scuba diving with weighted and air-filled vests depending on peoples buoyancies)

If the whole body is the system, of what type are muscle forces?

Muscles are both Internal and External forces

- internal forces can only change your shape

- external forces can change your state of motion

- if you jump off a diving board and flex your muscles will it change your state of motion? NO

What type of force is the only one that can cause motion of a system?

External forces can cause motion of system

- if you jump off a diving board and flex your muscles will it change your state of motion? NO

If the above answers are true, how does the body move (such as in walking)?

if muscle forces are internal, we use muscles to change shape of the body

- shape change is in the form of pushing on the ground

- when pushing on the ground external force is friction

- we use external force of friction to move by changing our internal shape with internal force

When a diver leaves the board, muscle forces can only serve to change her/his ________, because they are internal to the system.

SHAPE: when diver leaves a board muscles forces can only change the shape because they're internal

If a car goes from 0 km/hour to 40 km/hour in 4 seconds, what is the acceleration?

Don't change units into other units ****

Acceleration = (velocity 2 - velocity 1)/time

- a = (v2 -v1)/time

- a= (40-0)/4 = 40/4 = 10 km/hr/sec

Acceleration Equation

(velocity 2 - velocity 1)/time

Define "g" and then give its numeric value.

g = acceleration due to gravity (g does not equal gravity)

- g= 9.8 m/sec/sec

What does it mean if acceleration is equal to 0?

If a = 0, it doesn't mean you aren't moving, it means your velocity is not changing (doesn't mean velocity is 0)

Explain terminal velocity and how it is achieved.

terminal velocity = gonna fall at exact same rate the whole trip down

- achieved when air resistance rises to the rate that achieves the same weight as your body weight

How is acceleration related to force and mass? Relate the equation to the equation for centripetal force needed.

- a=F/m equals F=m x a

- (CFN) centripetal force needed=(m x v^2)/r

--> means you're accelerating in a circle

- Newton's 2nd law

Friction=Ft x CFr

Define linear momentum and give the equation.

Momentum= mass x velocity --> momentum = m x v

- something's resistance to having its state of motion changed

Define linear impulse and give the equation.

Linear Impulse = F x time = change in momentum

- amount of force and time it would take to change something's momentum

What is the momentum of a 100kg system moving at 5m/sec? Show all work. Using F(t) = ∆M, what is the magnitude of force that would have to be applied to stop the motion of the system (i.e. momentum changes to 0) in 2 seconds? Show all work. How long would it take to stop the motion of the system (i.e. momentum changes to 0) by applying a force of 100 N? Use F(t) = ∆M. Show all work.

- 100 x 5 = 500 kgm/sec

- F(2sec) = delta M —> 500/2 = 250 N

- 5 sec to stop the object

Show how to go from this equation: F = ma, to this one: F(t) = ΔM

F=ma → F=m(v2-v1)/t → F=mv2 - mv1/t → F= M2-M1/t → F(t) = M2-M1

What is required to change momentum?

need a force and need time

What is the safest way to absorb shock? Why?

If something's momentum is being changed in short period of time it requires higher force

- safest way is to increase the time and that would decrease the force

Define conservation of linear momentum.

because of linear impulse, needed force and time to change momentum, if there is no external force, momentum will stay the same if no external forces (space)

If the total momentum of a system before a collision is 20, what will it be after the collision?

20 (no external forces changing momentum)

A body having a mass of 1kg and moving 2m/sec collides with a body that has a mass of 100kg and is moving 0m/sec. What is the total momentum of the system before the collision? What is it after? What is their final velocity? Which body is affected most? Why?

Body 1: 1 kg and moving at 2m/sec -> 2 kgm/sec

Body 2: 100 kg and moving at 0m/sec -> 0kgm/sec

Total: 2 kgm/sec

Momentum = m x v

After: after will still be 2 kgm/sec bc we don;t know anything else

Vf = Total momentum/total mass: 2kgm/sec/101kg = 0.0198 m/sec

- which body affected the most?: (Newton's 2nd law, if two bodies affected, smaller one usually affected the most):

- first object: accelerated most because went from 0- 2

If a barbell weighing 300 N is moved a distance of 3 m, how much work is performed? If the work takes place in 1 sec, what is the power? What is the power if it takes 0.5 sec for the work to take place?

Work = force x displacement = 900 N/m

- 900/1= 900

- 900/0.5= 1,800

Define gravitational potential energy and give the equation.

persons weight x 9.8 x height

What is the gravitational potential energy of a person having a weight of 80.02 N that is 3 meters above the ground?

multiple someone's weight by g

- 80.02 x 9.8 x 3 = 2355 N/m (no matte what form of energy it is N meters)

Define strain energy and give the equation.

SE=1/2kdeltax^2

- energy of deformation, deforming something and its tendency to want to come back is K, and multiple that by deformation

The spring constant for a certain shoe sole is 10^6 N/m. When the foot is planted during running, the sole deforms 0.003 m. What is the strain energy?

4.5 N/m (10^6 is very normal spring constant)

Define kinetic energy and give the equation.

1/2 mass x velocity^2 = kinet

- energy that something possesses because its in motion

What is the kinetic energy of a 5kg ball traveling at 60 m/sec?

- if you take 1/2 mass times squared velocity = 9000 N/m

In what situation is momentum of interest as opposed to KE, and vice versa?

- Want to know about momentum

- kinetic energy interested in if wanting to know its ability to do work on something

Stress

amount of force applied to a specific area

Strain

reaction to amount of stress applied (change in length

Young's Modulus

A measure of the stiffness of an elastic material and defined by stress/strain.

(can be viscoelastic when force applied changes stiffness of material... like water )