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Unformatted text preview: Dynamics: Newton’s Laws of Motion
Chapter Outline GENERAL PHYSICS Force
PHY 302K
Newton’s First Law
Mass Chapter 4: Dynamics: Newton’s Laws of Motion Newton’s Second Law
Newton’s Third Law Maxim Tsoi Weight – the Force of Gravity; and the Normal Force
Solving Problems with Newton’s Laws
Physics Department,
The University of Texas at Austin Problem Involving Friction http://www.ph.utexas.edu/~tsoi/302K.htm
302K  Ch.4 The Concept of Force The Concept of Force Forces are what cause any change in the velocity of an object Examples of forces • An external force acts on an object object accelerates Fundamental forces in nature: • Several forces act simultaneously on an object object accelerates • Gravitational forces only if the net force acting on it is not equal to zero between objects Net (total) force is the vector sum of all forces acting on the object • Electromagnetic forces
between electric charges • Net force acting on an object is zero the acceleration of the classical physics 302K  Ch.4 • Nuclear forces between object is zero and its velocity remains constant subatomic particles • Velocity of an object is constant the object is said to be in • Weak forces that arise in equilibrium certain radioactive decay
processes 302K  Ch.4 302K  Ch.4 The Concept of Force Newton’s First Law Measuring the strength of a force Law of inertia convenient to use deformation of a spring to measure force • Calibrate the spring by applying vertical force F1 (1.00 cm) to a
spring scale • A moving object can be observed from different reference frames
If an object does not interact with other objects, it is possible • Applying different force F2 whose magnitude
is twice that of F1 pointer shows 2.00 cm
• Both forces the sum of the effects of the
individual forces
• Applying forces in
different directions the resulting
force is the vector
sum of the two
forces to identify a reference frame in which the object has zero
acceleration
• Such a reference frame is called an inertial frame of reference
• Any reference frame that moves with constant velocity relative to an inertial
frame is itself an inertial frame (e.g., relative to the distant stars)
In the absence of external forces, when viewed from an inertial
reference frame, an object at rest remains at rest and an object
in motion continues in motion with a constant velocity
• The natural state of matter is to resist changes in its motion inertia Must use the rules of vector addition to obtain the net force on an object !
302K  Ch.4 302K  Ch.4 1 Newton’s Second Law Mass
Mass vs Weight What happens to an object that has a nonzero net force acting on it? • Mass property of an object that specifies how much When viewed from an inertial reference frame, the acceleration of resistance an object exhibits to changes in its velocity
The greater the mass of an object, the less that object
accelerates under the action of a given applied force an object is directly proportional to the net force acting on it and
inversely proportional to its mass m1 a2 m 2 a1 F ma • The SI unit of mass is kilogram
• Mass is a scalar quantity
• Weight magnitude of the gravitational force exerted • Three component equations: on the object (e.g., 180 lb on the Earth vs 30 lb on the Moon) Fx ma x • Mass is an inherent property of an object and is
independent of the object’s surroundings and of the F y ma y F z ma z method used to measure it 302K  Ch.4 302K  Ch.4 Newton’s Second Law The Gravitational Force and Weight Unit of Force Gravitational Force • The SI unit of force is newton defined as the force that, when
acting on an object of mass 1 kg, produces an acceleration of 1 m/s2 1 N 1 kg m/s 2 • Gravitational force attractive force exerted by the Earth
• Weight magnitude of the gravitational force F ma Fg mg Fg mg At a given location ratio of weights = ratio of masses
• 1000 kg palette of bricks (9800 N) 1 N less at the top of the Empire State Building 302K  Ch.4 302K  Ch.4 Newton’s Third Law The Laws of Motion Action and Reaction • Newton’s 1st law: • If two objects interact, the force F12 exerted by object 1 on
object 2 is equal in magnitude and opposite in direction to the
force F21 exerted by object 2 on object 1 F12 F21
• Forces always occur in pairs (single isolated force cannot exist)
• The action force is equal in magnitude to the reaction force and
opposite in direction In the absence of external forces, when viewed from an inertial
reference frame, an object at rest remains at rest and an object in
motion continues in motion with a constant velocity
• Newton’s 2nd law:
When viewed from an inertial reference frame, the acceleration of an
object is directly proportional to the net force acting on it and inversely proportional to its mass F ma • Newton’s 3rd law:
If two objects interact, the force F12 exerted by object 1 on object 2 is
equal in magnitude and opposite in direction to the force F21 exerted by object 2 on object 1
F F
12 302K  Ch.4 21 302K  Ch.4 2 Some Applications of Newton’s Laws Some Applications of Newton’s Laws Assumptions Freebody diagram n
• Interested only in external forces that act on an object
• Objects can be modeled as particles
• No friction (frictionless surfaces)
• Light or negligible mass mass can be ignored
• A rope is pulling on the object exerts a force T, where T is
tension in the rope
• Neglect the mass of ropes, strings, or cables involved magnitude of force is the same at all points along a rope Fg 302K  Ch.4 302K  Ch.4 Some Applications of Newton’s Laws Some Applications of Newton’s Laws
Objects experiencing a net force Objects in equilibrium • Object (particle) experiences acceleration nonzero net force acting on the object • Acceleration of an object (particle) is zero • Find the acceleration of a crate pulled to the right particle is in equilibrium on a frictionless horizontal surface • Suspended lamp gravitational force • Forces: T acts through the rope, the gravitational and the upward force T exerted by the force, and the normal force chain F no forces in x direction F x ma x 0 F y T Fg 0 F T Fg v xf y x T ma x n Fg ma y 0
T v xi t
m ax T
m n Fg T x f xi v xi t 1 t 2
2
m NOTE n is not always equal to Fg!
Example 4.1 302K  Ch.4 302K  Ch.4 Forces of Friction Forces of Friction
Empirical laws of friction Resistance to motion from interaction with surroundings
Very important in everyday life allow us to walk, run; cars to move summarize experimental observations • Let’s drag a trash can across a real surface
by applying F • Static friction can have values: normal force’s magnitude counteracting force is the force of static
friction fs (F=fs)
• Large F can slips; F=fs,max at the verge of • On the verge of slipping:
• Kinetic friction is: slipping
• When trash can is in motion force of
kinetic friction fk
• To a good approximation both fs,max and fk
are proportional to n
Details of friction are complex (at the atomic level
involves electrical interactions between atoms)
302K  Ch.4 f s sn coefficient of static friction • F is small trash can remains stationary f s sn f k k n coefficient of kinetic friction (can vary with
speed)
• k and s depend on the nature of surfaces in
contact
• Direction of the friction force is parallel to
the surface and opposite to the actual or
impending motion
302K  Ch.4 Example 4.8 3 SUMMARY
Dynamics: Newton’s Laws of Motion
• Newton’s 1st law: In the absence of external forces, when viewed from an
inertial reference frame, an object at rest remains at rest
and an object in motion continues in motion with a constant
velocity • Newton’s 2nd law: When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it
F ma
and inversely proportional to its mass • Newton’s 3rd law: If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the
F12 F21
force F21 exerted by object 2 on object 1
• Gravitational force: Fg mg • Force of static friction:
• Force of kinetic friction: f s sn
f k k n 302K  Ch.4 4 ...
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