5 Ch 05 Circular Motion and Gravitation.pdf

(1) the partner hangs straight down and is stationary or when

(1) The path of the planets about the sun is elliptical in shape, with

(1)A lamp of mass m hangs from a spring scale that is

(2) An imaginary line drawn from the center of the sun to the

(2) cos sins

(2) the partner is swinging through the straight-down position?

(3) The ratio of the squares of the periods of any two planets is

(a) (b) (c) (d)

(a) It remains the same.

(a) less than mg (b) more than mg

(a) Where is the location of the stone in the vertical

(b) Determine the speed of the stone. 8.48 m/s

● A review of the relationship between v and ac.

● The velocity changes direction, not magnitude.

• Each stride is taken as one in a series of arcs:

A Car on a Banked

A Car on a Level

a circular path without depending on friction? 75

a component of the

a height of 598 km above the earth’s surface.

a r

A race-track has the shape of an inverted cone, as shown in

a rad

A rock is whirled on the end of a string in a horizontal circle of

a satellite in orbit.

A stone is tied to a string (length = 1.10 m) and

acceleration due to gravity on the Earth’s surface?

acceleration due to gravity, and

acceleration of g/3 in the case of an emergency.

acceleration that results is directly proportional to the net

accurate description of the motion of any planet and any satellite.

All forces on the car

allow for interesting

altitude equal to twice the radius of the Earth, 2RE, how would its speed v

an amusement park ride. Not only are the sensations the

An object is in uniform

and

and A or along the

and you have orbit.

anyone who has been temporarily suspended above the seat on

apparent

apparent

arc may be approximated as a straight line.

are extended as shown in Figure and the tension in the upper string is

are vertical, so no

arms downward, holding his partner. Is it harder for the man to hold his

around the earth, the gravitational

as the direction of the net force.

astronaut experiences a push

Astronauts merely feel weightless because there is no external contact force

Astronauts on the orbiting space station are weightless because...

Astronauts who are orbiting the Earth often experience

at 2.00 m/s 2. Find the tension in

at each turn for a speed of 34 m/s.

At what speed must the surface of

attached to the ceiling of an elevator. When the

attraction provides the centripetal force that keeps

away from the center of the turn. The

b. space is a vacuum and there is no gravity in a vacuum.

banked curve with friction, a frictional force acts on a fast car to oppose the tendency to

be generated.

be related to the Earth’s radius RE, and the magnitude g of the

c. space is a vacuum and there is no air resistance in a vacuum.

car will "want to" slide up the incline,

case when the tension in the string is maximum?

Cavendish balance

ceiling of an elevator as in Figure.

center of rotation and

center of the circle and continually changes direction as the object

center of the planet will sweep out equal areas in equal

center of the turn. If there is a friction

centripetal force and the car will "want

circular arc between

circular motion. At point

circular path. Does the

coefficient of static friction between tires and pavement is

component of the

component of the normal force will be less

component of the normal force. The vertical component of the normal

Conceptual Example :

Consider a satellite in a circular orbit around the Earth. If it were at an

constant speed on a circle that is parallel to the ground.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley

cos sin (2)sN mg N

cos sin / (1)s N N mv Rμ β β+ =

curve. For a bank angle of

d. the astronauts are far from Earth's surface at a location where

degrees. Suppose these turns were frictionless. At what speed

Determine the speed at which the

Determine the speed of the Hubble Space Telescope orbiting at

diagram above. This

different densities

different ways. First, the circle is horizontal and the

direction as the change in velocity.

direction.

distance d should a driver locate his car if he wishes to stay on

Distances from the

down to stop at the forty-fifth floor?

Downward

Drag

drain). Consider a circular curve of radius R = 200 m and bank angle

During free-fall, the elevator

elevator is stopped at the fortieth floor, the scale

elevator is stopping.

elevator to hang three sections lamp one below

enough for humans to notice.

equal to the ratio of the cubes of their average distances from

Escape velocity 11.2 km/s 2.38 km/s

Even within the earth itself,

Falling towards the Earth without colliding into it:

figure. On this surface the cars race in circles that are parallel

Find the centripetal acceleration

followed by the hip.

For a satellite in circular orbit

For any astronomical object:

For safety reasons an elevator stops with an

for the turn, videal . In this case, the

force and has a magnitude that is inversely proportional to

force balances the car’s weight.

Global Positioning System: hours24=T EGM

Gravitation applies elsewhere:

gravitation has a minimal effect.

Gravitational force falls off quickly

gravity varies

he could compute the mass of the earth!

horizontal component of the normal force

horizontal force can

horizontal plane because the weight of the plane is balanced

Ideal No Friction

If a car goes through a curve too fast, the car tends to slide out of the curve. For a

If either m1 or m2 are small, the force decreases quickly

In a circus, a man hangs upside down from a trapeze, legs bent over and

In the early 1600s, Johannes Kepler proposed three laws of planetary motion.

In uniform circular motion, the

increase in Fg.

Interference Phenomena.

intervals of time. (The Law of Equal Areas)

is greater than the ideal (no friction)

is no longer vertical, so

is vertical. In the vertical case the maximum tension in

It is static friction , rather than kinetic friction, because the

it takes for the

Kepler was able to summarize the carefully collected data of his mentor - Tycho Brahe

Kepler's Three Laws (General Knowledge - Optional)

Kepler's three laws of planetary motion can be described as follows:

kg1098.5kgmN1067.6

maximum radius of 316 m and are steely banked at 31

maximum speed to rise

Mean density 5.515 3.342

Mean diameter 12,742 km 3,476 km

Meaning and Cause of WeightlessnessContact versus Non-Contact Forces

measurable distances as the angle allows the initial and final

Notice that r is the distance between the centers of the two objects, not

O it is released from its

object move along the

object to travel

of 78

of emergency stop.

of those sensations of weightlessness are also the same.

On a frictionless banked curve, the centripetal force is the horizontal

on Centripetal Acceleration

on earth?

on his feet equal to his weight

once around the

Once Cavendish had measured G,

or not!

orbiting astronauts are the same sensations experienced by

outer edge of the wheel is moving.

radius R with a constant period T. If the radius of the circle is

Ratio = 41.3/21.2 = 1.948

Rav = 6,374 km

reads mg. What does it read as the elevator slows

Recall Newton’s Second Law:

reduced to R/2, while the period remains T, what happens to

revolutionmin102.1

revolutions per minute on a tire-

Safe Driving: Any car has this max. speed independent of the mass.

same (for astronauts and roller coaster riders), but the causes

satellite is to remain in an orbit with a fixed radius.

sensations of weightlessness. These sensations experienced by

shown in blue in the

slide out of the curve; the force is directed down the bank (in the direction water would

sliding out means that

small portion of the motion such that the Δv

speed for the turn, videal , the horizontal

string, the normal force, or friction, among others.

than the required centripetal force, and the

The “weight” of an object is the total gravitational force

the 17 m guideline for a

The 4.00 kg block in the figure is attached to a vertical rod by means of

The Apparent Weight is surprising!

the apparent weight is zero.

The bobsled track contains turns

the car due to the road

the center of the circle; in the same

the center of the sun being located at one focus.

The Centripetal

the centripetal acceleration of the rock?

the centripetal acceleration.

The centripetal force coming only from tire friction.

The direction of the centripetal

The elevator accelerates upward

The force Fg due to the earth’s gravitational

the force of static

the general direction of the center of the

the horizontal

The horizontal

the mass. The direction of the acceleration is the same

The model airplane has a mass of 0.90 kg and moves at

The normal force on

the other (as shown). The lamp is also attached

The path of the airplane and the guideline lie in the same

The picture can't be displayed.

The picture can't be displayed.

the presence or absence of contact forces.

The principle of the

The problem may be treated by extracting a

the road it will oppose this relative

the space station move so that the

the string is 15.0 % larger than the tension that exists

the sun. (The Law of Harmonies)

The tangential velocity allows to remain in orbital

The turns at the Daytona International Speedway have a

The wheel of a car has a radius of

there are no external objects touching one's body and exerting a push or pull

This can be easily done in a lab

This force may be provided by the tension in a

This may allow the

Thrust

tires are not slipping with respect to the radial direction.

To be on the verge of

to keep an object moving on a circular path.

to the ceiling. Each section of the lamp weighs

to the ground. For a speed of 34.0 m/s, at what value of the

to" slide down the incline toward the

Two blocks are fastened to the

two strings. When the system rotates about the axis of the rod, the strings

universal gravitational constant

When a net external force acts on an object of mass m, the

when Fc vanishes.

when icy conditions are not obvious to drivers, who tend to drive at normal speeds.)

When the car moves without skidding around a curve, static

when the circle is horizontal.

whirled in a circle at the same constant speed in two

will act to pull the car down the incline, in

will be greater than the required

wings. Find the tension in

with maximum

with radii of 33 m and 24 m.

would the cars have to travel around them?

you achieve escape velocity.

β = 10° find the ratio of the maximum car speed vmax that

 Directly proportional to the masses involved.

 Eventually, Fg balances

 Fg always attractive.

 Inversely proportional to the square of the separation between the masses.

 Masses must be large to bring Fg to a size even close to humanly

 The centripetal force is the name given to the net force required

 The direction of the centripetal force always points toward the

 The slight attraction of the masses causes a nearly imperceptible

 Thus, in uniform circular motion there must be a net force to produce

 Use of the laser allows a point many meters away to move through

 We already defined “weight” as the attractive gravitational

 We can now broaden the definition:

 Weightless sensations exist when all contact forces are removed.

 Weightlessness has very little to do with weight and mostly to do with

 Weightlessness is only a sensation. It is not a reality.

 Weightlessness is simply a sensation experienced by an individual when

 There is Only one speed that a satellite can have if the

 v is independent of m. 46

 Weightlessness has very little to do with weight.

 Weightlessness is not a reality.

 Weightlessness is only a sensation.