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 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
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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
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Gravity force at the surface of the Earth
g = 9.8 m/s2
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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
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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
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
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)
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
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
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
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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.
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 5
Problem 28580 N; opposite to the motion of the
cabinet
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