Relevant concepts: inertia and force a) Inertial reference
frame b) accelerated frame of the car - fictitious force
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Rolling friction
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Conical Pendulum (e.g. )
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Car traveling in a banked curve Design the curve with no
friction in equilibrium in the vertical direction. in uniform
circular motion in the horizontal direction a component of the
normal force supplies the centripetal force. The angle of bank is
Note: The banking angle is independent of the mass of the vehicle.
If the car rounds the curve at less than the design speed, friction
is necessary to keep it from sliding down the bank. If the car
rounds the curve at more than the design speed, friction is
necessary to keep it from sliding up the bank.
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Car traveling in a horizontal (Flat) Curve uniform circular
motion in the horizontal direction. in equilibrium in the vertical
direction. The force of static friction supplies the centripetal
force. The maximum speed at which the car can negotiate the curve
is: Note: this does not depend on the mass of the car. Section
6.1
Slide 8
Ferris Wheel Uniform circular motion with constant speed v
(controlled by the motor) Under gravity, the child feels apparent
weight differently at top and bottom Section 6.1
Slide 9
Ferris Wheel (2) At the bottom of the loop, the upward force
(the normal) experienced by the object is greater than its weight.
Section 6.1 At the top of the circle, the force exerted on the
object is less than its weight.
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Non-uniform Circular Motion Section 6.2 If the speed also
changes in magnitude there is non-zero tangential acceleration
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Vertical Circle with Non-Uniform Speed Section 6.2
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Lecture 4 Work and Energy
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Outline Work done by a constant force Projection and scalar
product of vectors Force that results in positive work. negative
work? forces that do no work? Work done by varying force with
displacement Work-energy theorem
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6.1 Work Done by a Constant Force
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Work, cont. W = F r cos A force does no work on the object if
the force does not move through a displacement. The work done by a
force on a moving object is zero when the force applied is
perpendicular to the displacement of its point of application.
Section 7.2
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6.1 Work Done by a Constant Force
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Example 1 Pulling a Suitcase-on-Wheels Find the work done if
the force is 45.0-N, the angle is 50.0 degrees, and the
displacement is 75.0 m.
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6.1 Work Done by a Constant Force
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Example 3 Accelerating a Crate The truck is accelerating at a
rate of +1.50 m/s 2. The mass of the crate is 120-kg and it does
not slip. The magnitude of the displacement is 65 m. What is the
total work done on the crate by all of the forces acting on
it?
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6.1 Work Done by a Constant Force The angle between the
displacement and the friction force is 0 degrees.
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Scalar Product of Two Vectors Section 7.3
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Scalar Product, cont The scalar product is commutative. The
scalar product obeys the distributive law of multiplication.
Section 7.3
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Dot Products of Unit Vectors Using component form with vectors:
In the special case where Section 7.3
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6.2 The Work-Energy Theorem and Kinetic Energy Consider a
constant net external force acting on an object. The object is
displaced a distance s, in the same direction as the net force. The
work is simply
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6.2 The Work-Energy Theorem and Kinetic Energy DEFINITION OF
KINETIC ENERGY The kinetic energy KE of and object with mass m and
speed v is given by
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6.2 The Work-Energy Theorem and Kinetic Energy THE WORK-ENERGY
THEOREM When a net external force does work on and object, the
kinetic energy of the object changes according to
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6.2 The Work-Energy Theorem and Kinetic Energy Example 4 Deep
Space 1 The mass of the space probe is 474-kg and its initial
velocity is 275 m/s. If the 56.0-mN force acts on the probe through
a displacement of 2.4210 9 m, what is its final speed?
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6.2 The Work-Energy Theorem and Kinetic Energy
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In this case the net force is
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6.2 The Work-Energy Theorem and Kinetic Energy Conceptual
Example 6 Work and Kinetic Energy A satellite is moving about the
earth in a circular orbit and an elliptical orbit. For these two
orbits, determine whether the kinetic energy of the satellite
changes during the motion. W0 W