Chapter 10: Projectile and Satellite Motion (from Lecture Slide) Flashcards
Projectile
Any object that moves through the air or space under the influence of gravity, continuing in motion by its own inertia
Trajectory
The path of the projectile
Projectile motion are three examples of
1) An object thrown vertically upward
2) An object thrown upward at an angle to be horizontal
3) An object dropped from rest
Without gravity, a tossed object follows a
Straight line path
With gravity, the same object tossed at an angle follows a
Curved path
Projectile motion is a combination of
A horizontal component and a vertical component
Acceleration due to gravity only affects the
Y-axis motion (vertical velocity)
Projectile motion: Horizontal component
No horizontal force component equal to constant velocity
Projectile travels equal horizontal distances in
Equal time periods
Projectile motion: Vertical component
Affected by the acceleration due to gravity
Gravitational force is downward so projectiles accelerates
Downward
Slow down on the way and speeds up on the way
Down
Combining the horizontal and vertical components produces a
“Curved path” referred to as a parabola
Parabola
Curved path of a projectile that undergoes acceleration only in the vertical direction, while moving horizontally at a constant speed
- Consider a cannonball launched horizontally, gravity causes the cannonball to accelerate downward at a rate of 9.8 m/s^2
1) Y-component of velocity only points downward (only falls)
2) X-component of velocity remains constant
- Consider a cannonball launched upward at an angle to the horizontal
1) Horizontal velocity component same as before, remains constant
2) Vertical velocity component is different, the cannonball now rises before falling
The velocity of a typical projectile can be represented by horizontal and vertical components. Assuming negligible air resistance, the horizontal component along the path of the projectile
Remain the same
When no air resistance acts on a fast moving baseball moving in a parabolic path, its acceleration is
Downward
As the projectile rises toward its max height, it is
Slowing down
As it falls from its max height, the magnitude of the vertical velocity is
Increasing
The vertical velocity one second before reaching its peak is the same as
The vertical velocity one second after falling from its max height
Although different directions, magnitudes are
Equal
Assuming negligible air resistance, the vertical component along the path of the projectile
Changes throughout
Launch angle determines the range and maximum height that an object will
Experience after being launched
The same object being launched at the same speed but different
Angle
Maximum height occurs for a launch at
90 degrees
Maximum range occurs for launch at
45 degrees
Same range obtained from
Complementary angles
A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? Its horizontal acceleration?
g in the vertical, zero acceleration in the horizontal
Without air resistance, the time for a projectile to reach maximum height is
Halfway between when it was launched and when it descends to its initial height
In the presence of air resistance, the path of a high-speed projectile falls
Below the idealized parabola
With no air resistance: time up equal to
Times down
With no air resistance: 45 degrees gives
Max range
With air resistance: Time up is less than
Times down
With air resistance: Max range occurs at
Less from 25 degrees to 34 degrees
Downward resistance forces are greater on the way up than the way
Down, the net effect is to spend less than in the air
Satellite
A projectile that falls around Earth rather than onto it
Sufficient tangential velocity needed for
Orbit
With no air resistance to reduce speed
A satellite orbits Earth indefinitely
Satellite are an example of
A high speed projectile
A high speed is required to
Launch the satellite so that it may overcome Earth’s gravitational pull and enter maintain its orbit
The Moon does not crash into Earth because
Moon has a sufficient tangential speed
Planet would crash into the Sun, if it weren’t for
Their tangential velocities
A weightless astronauts in an orbiting satellite is
Like the satellite, pulled by Earth’s gravitation
Satellites are above Earth’s atmosphere where they are free of air drag that would
Reduce their tangential/ orbit speed
When a projectile is launched horizontally, its initial vertical velocity is
Zero
Projectile starts to fall immediately due to
Earth’s gravity
Reminder: Horizontal and vertical components of projectile motion are:
Independent and they do not affect each other
From the same height, an increase or decrease in horizontal velocity will not affect the
Vertical component or the fall time of a projectile will take the same time to hit the ground
For an orbit, falling distance must match
Earth’s curvature
A satellite in a circular orbits speeds is:
Great enough to ensure that its falling distance matches Earth’s curvature
A satellite in a circular orbits speeds is constant:
Only direction changes
A satellite in a circular orbits speeds is not affect by gravity:
X-component and y-component independent
When you toss a projectile sideways, it curves as it falls. It will be an Earth’s satellite if the curve it follows
Matches the curved surface of Earth
In circular orbit, the speed of a satellite is
Not change by gravity and speed isn’t increased or decreased
The gravitational force is always perpendicular to
The direction of motion of the satellites
Changing direction of the satellite keep it following that
Curved path
A satellite in a circular orbits motion is perpendicular to
The force of gravity acting on it and provides a centripetal force (Fg = Fc)
With a speed of 8 km/s, the curved path of the satellite and the curve of Earth’s surface are:
Match all the way around the planet (8km)
When a satellite travels at a constant speed, the shape of its path is
A circle
The higher the orbit of a satellite (greater r)
The less its speed, the longer its path, and the longer its period
The period of an Earth’s satellite depends on the satellite’s
Radial distance from Earth
Launching a satellite into orbit requires control over
Speed and distance that carries it above the atmosphere
What happen if the projectile is given a horizontal speed somewhat greater than 8 km/s?
An elliptical orbit
Ellipse: A planet curve surrounding two focal points, such that for:
All points on the curve, the sum of the two distances to the focal points is a constant
A circle is
A special type of ellipse where the two focal points are the same
1) If initial speed exceeds that needed for
Circular orbit, the satellite overshoots a circular path and moves away from Earth
2) Satellites loses speed as
It gets futher, and then regains speed it as it falls back toward Earth
3) It rejoins its original path with the
Same speed it had initially
Satellites in elliptical orbit speed up when they are closer to
The Earth due to stronger gravitational force and slow down as they move away because gravitational force decreases with distance.
Johannes Kepler found the motion of planets was not
Circular, rather, it was elliptical and first law of planetary motion
White dwarf star is obliterated, sending its
Debris hurtling into space
Debris is critical for enriching surrounding space with
Heavier element
Kepler’s First Law of Planetary Motion: The path of the planet around the Sun is
An ellipse with the Sun at one focus
Kepler’s Second Law of Planetary Motion: The line from the Sun to any planet sweeps out:
Equal areas of space in equal time intervals
Kepler’s Third Law of Planetary Motion: The square of the orbital period (T) of a planet is
Directly proportional to the cube of the average distance of the planet from the Sun (for all planets)
Object in motion possesses KE due to its motion
KE dependent on mass and velocity
Object above Earth’s surface possesses PE by virtue of its position
PE dependent on mass, height, and g
Satellite in orbit possesses KE and PE
Sum of KE and PE is constant at all points in the orbit = Energy is conserved
Whether in circular or elliptical motion, there are no external force capable of
Altering the total energy
PE, KE, and speed in circular orbit: Distance between the satellite and center of the attracting body
Does not change
Height (h) of satellite above Earth
Does not change and PE is the same everywhere
No components of force acts along
The direction of motion and speed and KE remain constant
KE and PE vary in
Elliptical orbits
1) PE is greatest when the satellite is
Farthest away
2) PE is least when the satellite is
Closest
3) KE is least when PE is
The most and vice versa
4) At every point in the orbit are
Sum of KE and PE is the same
The conservation of energy applies to satellites in
Both circular and elliptical orbit
When the potential energy of a satellite decreases
Its kinetic energy corresponding increases
Minimum speed required to
Escape an object’s gravitational pull
If you throw something with a fast enough speed, the time required for it to
Slow to a stop becomes infinite.
When a projectile achives escape speed from Earth, it
Outruns the influence of Earth’s gravity but is never beyond it
Voyages to the Moon, Mars, and beyond begin with
Launch that exceed escape speed from Earth
