Transcript Ch. 7 Circular Motion and Gravitation

Circular Motion and Gravitation
Circular Motion
Any object rotating around an axis of rotation is said
to be in circular motion
Objects in circular motion are always accelerating
because the direction of the velocity is constantly
changing.
Examples of Circular
Motion
Satellites orbiting
the earth are in
circular motion
The pods on the ride are
always accelerating.
The force of kinetic friction is what
keeps the race car drivers on the
track.
Gravitation
Gravitational force is exerted by all objects on each
other
Satellites remain in orbit because they are falling
towards the earth at the same rate the earth is
falling away from them
Examples of
Gravitational Force
Gravity is pulling these
skydivers and this jumper
towards earth
Tides
Tides are caused by gravitational force. On the side
of the earth closest to the moon, it pulls the water
more than the earth. The water on the far side of
the earth is pulled less.
Kepler’s First Law of Planetary
Motion
Law One: Planets travel in elliptical orbits around
the sun.
Kepler’s Second Law
Law Two: An imaginary line drawn from the sun to
any planet sweeps out equal areas in equal times.
Planets travel faster when they are closer to the
sun.
Kepler’s Third Law
Law Three:
Speed and Period of Objects in
Circular Orbit
m stands for the mass of the central object
T represents the orbital period
Weightlessness
Apparent weightlessness can be experienced in
elevators.
If you are falling at free fall acceleration, there is no
normal force, which makes you feel weightless.
True weightlessness is only experienced in deep
space far from any object with significant mass.
Examples of
Weightlessness
When you are in
elevator going down,
you feel lighter
because the floor,
which provides the
normal force, is
falling away from
you.
These astronauts are so far away from
Earth’s gravitational field, they are
experiencing almost true weightlessness
Torque
Torque is a force rotating an object around an axis.
When referring to torque, lever arm is not the length
of the arm itself. It is the distance horizontally to
the axis and is equal to dsinq where d is the length
of the arm itself.
A force is being applied to
this lever to change the tire.
The farther out on the lever
you hold, the easier it is to
remove the lug nuts.
Simple Machines
Simple machines make it easier to accomplish tasks
by reducing the force required, although the
amount of work is equal to or greater.
Six kinds of simple machines are
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Levers
Inclined Planes
Wheel and Axle
Wedges
Screws
Pulleys
Levers
Levers rotate around a fulcrum. The closer the
fulcrum is to the object being lifted (and longer
the lever arm where force goes in) the easier it is
to lift.
Inclined Planes
Inclined planes reduce the amount of force required
to lift an object by lengthening the distance it
travels.
In this example,
people in
wheelchairs
have to travel a
farther distance
to get to the
same height as
the steps
Wheel and Axle
Wheel and axle is basically a
lever that turns in a circle.
Wheel and axle can be thought
of as “torque multipliers.”
The knob gives
a larger surface
area to grab and
turns a smaller
lever internally
A crank turns
which raises
the bucket
Wedges
Wedges are made up of two inclined planes put
together.
They are used primarily for cutting, like scissors or
axes, but can also be used to hold things in place,
like a door stop.
Axes split wood by
forcing it farther
and farther apart.
Screws
Screws are inclined planes wrapped around a rod.
They convert rotational force (torque) to a force
traveling in a straight line.
Pulleys
Pulleys distribute the force evenly along all sections
of the rope, which reduces the force required to lift
heavy objects.
Mechanical Advantage
Mechanical advantage is a measure of how much a
machine multiplies the force put into it.
Efficiency
Efficiency is a measure of how well a machine
converts work. An ideal machine would have a
100% efficiency rating, but real machines are less
than that due to friction and other forces.
Circular Motion Example
Problem
A 1.58 x 102 kg biker rounds a circular turn with a
radius of 15.0 m. The coefficient of kinetic friction
is .51. How fast can the biker go and still make the
turn?
m = 1.58 x 102 kg r = 15.0 m μk = .51
fn = mg = (1.58 x 102)(9.81 m/s2) = 1.55 x 103 N
fk = fn μk = (1.55 x 103 N)(.51) = 7.9 x 102 N
fk = fc = mvt2/r
=
=
8.7 m/s
Torque Example Problem
If the torque required to loosen a bolt is 75 N•m
using a wrench that is .40 m at an angle of 38°,
what is the force the must be applied?
 = 75 N•m d = .40 m q = 38° f = ?
 = fdsinq
f = /dsinq = (75 N•m)/(.40msin38° ) = 3.0 x 102 N
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