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Chapters 4, 5 Force and Laws of Motion. What causes motion? That’s the wrong question! The ancient Greek philosopher Aristotle believed that forces - pushes and pulls - caused motion The Aristotelian view prevailed for some 2000 years - PowerPoint PPT Presentation
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Chapters 4, 5
Force and Laws of Motion
What causes motion?
• That’s the wrong question!
• The ancient Greek philosopher Aristotle believed that forces - pushes and pulls - caused motion
• The Aristotelian view prevailed for some 2000 years
• Galileo first discovered the correct relation between force and motion
• Force causes not motion itself but change in motion
Aristotle(384 BC – 322 BC)
Galileo Galilei(1564 – 1642)
Newtonian mechanics
• Describes motion and interaction of objects
• Applicable for speeds much slower than the speed of light
• Applicable on scales much greater than the atomic scale
• Applicable for inertial reference frames – frames that don’t accelerate themselves
Sir Isaac Newton(1643 – 1727)
Force
• What is a force?
• Colloquial understanding of a force – a push or a pull
• Forces can have different nature
• Forces are vectors
• Several forces can act on a single object at a time – they will add as vectors
Force superposition
• Forces applied to the same object are adding as vectors – superposition
• The net force – a vector sum of all the forces applied to the same object
Newton’s First Law
• If the net force on the body is zero, the body’s acceleration is zero
00 aFnet
Newton’s Second Law
• If the net force on the body is not zero, the body’s acceleration is not zero
• Acceleration of the body is directly proportional to the net force on the body
• The coefficient of proportionality is equal to the mass (the amount of substance) of the object
00 aFnet
mFa net
netFam
Newton’s Second Law
• SI unit of force kg*m/s2 = N (Newton)
• Newton’s Second Law can be applied to all the components separately
• To solve problems with Newton’s Second Law we need to consider a free-body diagram
• If the system consists of more than one body, only external forces acting on the system have to be considered
• Forces acting between the bodies of the system are internal and are not considered
Newton’s Third Law
• When two bodies interact with each other, they exert forces on each other
• The forces that interacting bodies exert on each other, are equal in magnitude and opposite in direction
2112 FF
Forces of different origins
• Gravitational force
• Normal force
• Tension force
• Frictional force (friction)
• Drag force
• Spring force
Gravity force (a bit of Ch. 8)
• Any two (or more) massive bodies attract each other
• Gravitational force (Newton's law of gravitation)
• Gravitational constant G = 6.67*10 –11 N*m2/kg2 = 6.67*10 –11 m3/(kg*s2) – universal constant
rrmmGF ˆ221
Gravity force at the surface of the Earth
g = 9.8 m/s2
jR
mmGrrmmGF
Earth
CrateEarthCrate
ˆˆ22
21
jmgjmR
GmF CrateCrateEarth
EarthCrate
ˆˆ2
Gravity force at the surface of the Earth
• The apple is attracted by the Earth
• According to the Newton’s Third Law, the Earth should be attracted by the apple with the force of the same magnitude
jR
mmGr
rmmGF
Earth
AppleEarthEarth
ˆˆ22
21
jm
Rmm
Ga
Earth
Earth
AppleEarth
Earthˆ
2
j
mm
RGm
Earth
Apple
Earth
Earth ˆ2
j
mm
gEarth
Apple ˆ
Weight
• Weight (W) of a body is a force that the body exerts on a support as a result of gravity pull from the Earth
• Weight at the surface of the Earth: W = mg
• While the mass of a body is a constant, the weight may change under different circumstances
Tension force
• A weightless cord (string, rope, etc.) attached to the object can pull the object
• The force of the pull is tension ( T )
• The tension is pointing away from the body
Free-body diagrams
Chapter 4Problem 56
Your engineering firm is asked to specify the maximum load for the elevators in a new building. Each elevator has mass 490 kg when empty and maximum acceleration 2.24 m/s2. The elevator cables can withstand a maximum tension of 19.5 kN before breaking. For safety, you need to ensure that the tension never exceeds two-thirds of that value. What do you specify for the maximum load? How many 70-kg people is that?
Normal force
• When the body presses against the surface (support), the surface deforms and pushes on the body with a normal force (n) that is perpendicular to the surface
• The nature of the normal force – reaction of the molecules and atoms to the deformation of material
Normal force
• The normal force is not always equal to the gravitational force of the object
Free-body diagrams
Free-body diagrams
Chapter 5Problem 19
If the left-hand slope in the figure makes a 60° angle with the horizontal, and the right-hand slope makes a 20° angle, how should the masses compare if the objects are not to slide along the frictionless slopes?
Spring force
• Spring in the relaxed state
• Spring force (restoring force) acts to restore the relaxed state from a deformed state
Hooke’s law
• For relatively small deformations
• Spring force is proportional to the deformation and opposite in direction
• k – spring constant
• Spring force is a variable force
• Hooke’s law can be applied not to springs only, but to all elastic materials and objects
Robert Hooke(1635 – 1703)dkFs
Frictional force
• Friction ( f ) - resistance to the sliding attempt
• Direction of friction – opposite to the direction of attempted sliding (along the surface)
• The origin of friction – bonding between the sliding surfaces (microscopic cold-welding)
Static friction and kinetic friction
• Moving an object: static friction vs. kinetic
Friction coefficient
• Experiments show that friction is related to the magnitude of the normal force
• Coefficient of static friction μs
• Coefficient of kinetic friction μk
• Values of the friction coefficients depend on the combination of surfaces in contact and their conditions (experimentally determined)
nf ss max,
nf kk
Free-body diagrams
Free-body diagrams
Chapter 5Problem 30
Starting from rest, a skier slides 100 m down a 28° slope. How much longer does the run take if the coefficient of kinetic friction is 0.17 instead of 0?
Drag force
• Fluid – a substance that can flow (gases, liquids)
• If there is a relative motion between a fluid and a body in this fluid, the body experiences a resistance (drag)
• Drag force (R)R = ½DρAv2
• D - drag coefficient; ρ – fluid density; A – effective cross-sectional area of the body (area of a cross-section taken perpendicular to the velocity); v - speed
Terminal velocity
• When objects falls in air, the drag force points upward (resistance to motion)
• According to the Newton’s Second Law
ma = mg – R = mg – ½DρAv2
• As v grows, a decreases. At some point acceleration becomes zero, and the speed value riches maximum value – terminal speed
½DρAvt2 = mg
Terminal velocity
• Solving ½DρAvt2 = mg we obtain
ADmgvt 2
vt = 300 km/h
vt = 10 km/h
Centripetal force
• For an object in a uniform circular motion, the centripetal acceleration is
• According to the Newton’s Second Law, a force must cause this acceleration – centripetal force
• A centripetal force accelerates a body by changing the direction of the body’s velocity without changing the speed
Rvac
2
RmvmaF cc
2
Centripetal force
• Centripetal forces may have different origins
• Gravitation can be a centripetal force• Tension can be a centripetal force• Etc.
Centripetal force
• Centripetal forces may have different origins
• Gravitation can be a centripetal force• Tension can be a centripetal force• Etc.
Free-body diagram
Chapter 5Problem 25
You’re investigating a subway accident in which a train derailed while rounding an unbanked curve of radius 132 m, and you’re asked to estimate whether the train exceeded the 45-km/h speed limit for this curve. You interview a passenger who had been standing and holding onto a strap; she noticed that an unused strap was hanging at about a 15° angle to the vertical just before the accident. What do you conclude?
Answers to the even-numbered problems
Chapter 4
Problem 207.7 cm
Answers to the even-numbered problems
Chapter 4
Problem 26590 N
Answers to the even-numbered problems
Chapter 4
Problem 385.77 N; 72.3°
Answers to the even-numbered problems
Chapter 5
Problem 28580 N; opposite to the motion of the
cabinet
Answers to the even-numbered problems
Chapter 5
Problem 50110 m