Physics Chp. 10 Projectile and Satellite Motion

Escape Speed Human-kind has achieved this: 1. The first probe to escape the solar system was launched from Earth in ??? with a speed of only ??? 1a. The escape was accomplished by directing the probe into the path of ??? 1b.It was ??? around Jupiter's ??? field, ??? up speed in the process 1c. This increase in speed ??? the sun's escape speed at the ??? of Jupiter 1d. In 1984, ??? passed the orbit of ??? and continues outward away from our solar system through interstellar space.

1. 1972,15 km/s. 1a. Jupiter. 1b. sling-shotted, gravitational, picking 1c. exceeded, distance 1d. Pioneer 10, Jupiter

Fast-Moving Projectiles—Satellites 1. If you throw a ball at any speed, ??? ??? it will have fallen ??? below where it would have been without ???. 2. Using our value of g = 9.8 m/s^2, as a projectile moves horizontally, it will drop a distance of ~???. Distance determined with d = ½ gt^2 3. The faster the horizontal component, the less ??? the ??? of travel

1. 1s later, 5m, gravity 2. 5m per second 3. pronounced, curve

Circular Satellite Orbits 1. The ISS orbits at ??? above Earth's surface. 1a. Acceleration toward Earth is somewhat less than ??? because of its distance. 1b .This acceleration is ??? sensed by the astronauts; relative to the station, they experience ??? because they are in a state of ??? ??? - with no ??? force.

1. 360km 1a. 1g 1b. not, zero g, free fall, support

Circular Satellite Orbits 1. Communication satellites are located in orbit ??? ??? radii from Earth's ???, so that their period is ??? 1a. They orbit the ??? of the Earth and are always above the ??? place this way. 1b. The moon is ??? away, and has a ??? period

1. 6.5 Earth, center, 24 hours. 1a. plane, same 1b. farther, 27.3-day

Escape Speed For example: 1. The escape speed from the sun (at the surface) is ??? 2. At a distance ??? that of Earth's orbit, the escape speed from the sun is ??? 2a.So, escape speed from a body of mass depends on ??? as well.

1. 620 km/s. 2. equaling, 42.2 km/s 2a. distance

Fast-Moving Projectiles—Satellites 1. Satellite motion was understood by ??? ???, who reasoned that the Moon was simply a ??? circling Earth under the attraction of ??? 2. fig 10.19, p. 179: The greater the ??? with which a stone is projected, the ??? it goes before it falls to the Earth. We may therefore suppose the velocity to be so increased, that it would describe an arc of 1, 2, 5, 10, 100, 1000 miles before it arrived at the Earth, till at last, ??? the limits of the Earth, it should pass into space without ???

1. Isaac Newton, projectile, gravity 2. velocity, farther, exceeding, touching

Kepler's Laws of Planetary Motion 1. Newton's law of gravitation was preceded by ??? ??? laws of planetary motion. 2. We will be looking at three discoveries Kepler made regarding the motion of planetary bodies. 3. Kepler worked in an early observatory in ??? (before telescopes were invented around ????).

1. Johannes Kepler's 3. Denmark,1604

Kepler's Laws of Planetary Motion 1. Kepler's First Law - The path of each planet around the ??? is an ??? with the Sun as one ??? 2. The previous scientific belief was that all planets orbit the sun in perfectly ??? orbits. 3. Kepler was able to show, instead, that planets followed an ???- shaped orbit.

1. Sun, ellipse, focus. 2. circular 3. ellipse

Kepler's Laws of Planetary Motion 1. Using large brass, protractor-like instruments called quadrants, Kepler and his astronomer partner, ???, measured the position of planets over the course of ??? 1a. They were so accurate that their measurements are ??? valid today. 2. After Brahe died, Kepler converted these measurements to values that would be obtained by a stationary observer outside of the ??? ???

1. Tycho Brahe, 20 years. 1b still 2. solar system.

Energy Conservation and Satellite Motion 1. An elliptical orbit, a component of force exists ??? the direction of the satellite's ??? This component changes the ??? and, thus, the ??? 1b. The ??? component changes only the direction.

1. along, motion, speed, KE. 1b. perpendicular

Energy Conservation and Satellite Motion 1. Once the satellite gains ??? and moves against this component, its ??? and KE decrease. This decrease continues to the ??? 2. Once past the apogee, the satellite moves in the ??? direction as the component, and the ??? and KE ??? 2a.This cycle continues until the satellie whips past the ??? and ??? the cycle 2b. In this way, we can really consider this planet's orbit to be the ??? of a projectile!

1. altitude, speed, apogee. 2. same, speed, increase. 2a. perigee, repeats 2b. trajectory

Projectile Motion 1. Projectile Definition: 2. Examples: cannonball shot from a cannon, a rock tossed from a catapult, a potato fired from a potato gun, a baseball hit by the batter, a satellite in orbit, etc. 3.They can be acted upon by ???, friction, etc. as well during flight, but ??? ??? applied force moving the object. 4. If we consider any projectile in the absence of gravity, the object would continue in its "projected" direction ???. Because of gravity, projectiles travel in a ??? ??? back towards the earth

1. any object that is "projected" by some means and continues in motion by its own inertia. 3. gravity, NO continually 4. indefinitely, curved trajectory

Energy Conservation and Satellite Motion 1. At all points along the orbit, except at the ??? and the perigee, there is a component of ??? force ??? to the direction of motion of the satellite. 1a. This component changes the ??? of the satellite 1b. Can be an ??? or decrease formula: (this component of force) x (distance moved) = ∆KE

1. apogee, gravitational, parallel 1a. speed 1b. increase

Kepler's Laws of Planetary Motion To visualize: 1. Equal ??? are swept out in equal intervals of ??? 2. Kepler was the first to coin the term ??? 3. However, he did not have a way to explain why the planets moved this way; he lacked a ??? ???

1. areas, time. 2. satellite. 3. conceptual model

Elliptical Orbits 1. In circular orbit the speed of a satellite is ???, but ??? varies in an elliptical orbit. 1a. For initial speed ??? than 8km/s, the satellite ??? a circular path and is pushed from the earth, against the force of ??? 1b. It ??? speed as the force of gravity applies a force ??? its ??? 1c. The speed it loses in receding is ??? as it falls back toward Earth, and it fully ??? its original path with the ??? speed it had initially. 1d. This repeats for each ??? the satellite undergoes. The satellite is like a ??? !!!

1. constant (if no resistance), speed 1a. greater, overshoots, away, gravity 1b. loses, opposite, velocity. 1c. regained, rejoins, same 1d. orbit projectile

Fast-Moving Projectiles—Satellites 1. If friction were present at this speed, the projectile would burn to a ??? 1a. Recall: fluid friction is dependent on ??? and ??? ??? 1b. This explains how falling stars occur as meteorites fall through the Earth's atmosphere and ??? ??? due to ??? 2.Space shuttles and space satellites are launched to altitudes of 150km or more to get above the atmosphere and to be nearly free from ??? ??? 2a.Even at this distance, ??? is still working on satellites nearly as strong as if it were on the ??? still.

1. crisp. 1a. speed, area of contact 1b. burn up, friction. 2. air resistance. 2a. gravity, surface

Kepler's Laws of Planetary Motion 1. Kepler's Second Law - The line from the Sun to any planet sweeps out ??? areas of space in equal ??? intervals. 2. Kepler found that planets moved ??? when they were nearer the ??? and slower when they are ??? away. 3. To find this, Kepler imagined taking the ??? ??? from the orbit of the planet when both far and near the sun over the course of a month. 3a.The area contained within this arc "slice" would be ??? for both measurements taken.

1. equal, time 2. faster, Sun, farther 3. arc segment 3a. equal

Projectile Motion: Let's consider comparing two golf balls launched at the same time. One is falling vertically, the other is launched horizontally. The strobe-light photograph shows the positions of each ball at the same time interval. 1. Although one golf ball is moving horizontally, the only accelerative force is the downward acting ??? - which acts ??? on both golf balls. 2. As they are projected, each gains downward velocity ???, hence the same relative vertical positions. 3. The trajectory of a projectile moving at a constant horizontal velocity that accelerates ONLY in the vertical direction will be ??? Again, only in these ideal conditions...

1. force of gravity, equally 2. at the same rate 3. parabolic

Projectiles Launched Horizontally 1. The downward motion of a horizontally launched projectile is the same as that of ??? 2. Ideal horizontal motion occurs as described by ??? - a constant velocity with ??? 3. Since gravity does not act ???, it does not retard the horizontal ??? 4. It now rolls of its own ??? and covers equal ??? in equal ??? intervals. Formula: ⧍x= vt

1. free fall. 2. Galileio, no acceleration 3. horizontally, velocity. 4. inertia, distances,

Elliptical Orbits 1. If a projectile just above the resistance of the atmosphere is given horizontal speed somewhat ??? than 8km/s, it will ??? its circular path and trace an ??? path - an 1a. An ellipse is a ??? curve taken by a point that moves such that the sum of its distances from ??? fixed points (foci) is ??? 1b. For a satellite orbiting a planet, one focus is at the ??? of the planet and the other could be ??? or external to the ??? 1c. A ??? is a special case of an ellipse where both foci are at the location ???

1. greater, overshoot, oval, ellipse. 1a. closed, two, constant 1b. center, internal, planet. 1c. circle, same

Projectile Motion - launched at an angle Would an increase in horizontal speed change this? Consider a cannon... The dashed lines are ideal trajectories for each scenario: horizontal, upward, and downward. Observations? In any of the three scenarios: 1. The ball travels horizontally until it hits the ??? 2. The dashed lines correspond with distances from a ??? toss 3. When the ball is thrown upward, the ball will go a little ??? 4. When the ball is thrown downward, the ball will go ??? ???

1. ground 2. horizontal 3. further 4. less far

Projectile Motion - launched at an angle 1. When projectiles are launched at the same speeds but at different angles, they reach different ??? above the ground in their ??? motion. ~~They would also have different ??? ranges then. Interestingly, horizontal ranges are complementary to one another based on their relative launch angle (assuming the same launch speed), totaling to ??? ~~An object kicked into the air at a 60degree angle will have the same range as at 30 degree (90-60) ~~Maximum range is usually attained at an angle of ???

1. heights (altitudes), parabolic ~~horizontal, 90 degrees ~~45 degrees

Escape Speed 1. So, the escape speed refers to the ??? speed given by a brief thrust, after which there is no force to assist motion (projectile!). 1a.It would still face ??? due to ??? but will be going fast enough as to not ??? down and be drawn back to Earth. 2. But we could ??? Earth at any sustained speed greater than ???, given enough time.

1. initial 1a. deceleration, gravity, slow 2. escape, zero

Projectile Motion - launched at an angle 1. The object's ??? velocity can be found as the resultant vector of the ??? horizontal and vertical vectors. 2.The resultant vectors will follow along the ??? line.

1. instantaneous, combined 2. trajectory

Projectiles launched at an angle: 1.Projectiles will be at their ??? speed at the top of their trajectories - when they have zero vertical velocity, and only their constant horizontal velocity. 2. Given their ??? motion, the speed an object has lost going upward against gravity is equal to the speed gained coming down with gravity for the same time frames.

1. minimum 2. parabolic

Escape Speed 1. This gives us the escape speed for earth - the ??? speed necessary for an object to escape ??? from a ??? field. 1a. When we are concerned with ???, we call it escape ??? 2. All large bodies of mass that are able to ??? and ??? satellites have an escape speed. 2a.Since this speed is dependent on ???, bodies of greater mass have a ??? escape speed, and vice versa. Escape speed can be determined with the formula: v = sqrt(2gm/d)

1. minimum, permanently, gravitational 1a.. direction, velocity 2. attract, contain 2a. mass, higher

Energy Conservation and Satellite Motion 1. An object in motion has kinetic energy (KE) due to its ??? 2. An object above the earth has potential energy (PE) due to its ???and the ??? forces of ??? 3. A satellite in orbit has both ??? and ??? at every point. 4. Due to the ??? ?? ???, the sum of KE and PE is a ??? through the orbit.

1. motion. 2. position, attractive, gravity. 3. KE, PE 4. conservation of energy, constant

Projectile Motion 1. the curved path that an object follows when thrown, launched, or otherwise projected ??? ??? ??? of Earth 2. To begin looking at projectile motion, we need to consider things to be in ??? scenarios. When we understand how things work in ideal scenarios, we have a baseline to which we can compare realistic scenarios. When examining any projectile we will assume the following (for now): 3. NO friction present, standard earth gravity Then, projectile motion can be broken down into an objects ??? and VERTICAL components of ??? separately.

1. near the surface 2. ideal 3. HORIZONTAL, velocity

Projectile Motion - launched at an angle 1. For a projectile following a ??? trajectory, we need to consider the height and range of the trajectory. *Height = the vertical distance traveled upward until its initial velocity is ??? by the force of gravity. -- Maximum = The highest point of parabolic travel where vertical velocity is ??? but horizontal velocity remains the ??? **Range = The distance traveled ??? given a projectile's horizontal velocity and time of flight.

1. parabolic *overcome --zero, same ** horizontally

Kepler's Laws of Planetary Motion 1. Kepler did not see the simplicity of a satellite, whether a planet around the sun or the moon around earth, behaving as a ??? - working with or against ??? in its motion. 2. After 10 years of searching by trial and error for a connection between the ??? it takes a planet to orbit the Sun and its ??? from the Sun, Kepler discovered a third law.

1. projectile, gravity 2. time, distance

Circular Satellite Orbits 1. The satellite is always moving at a ??? ??? to the ??? ???. 1a. It does not move in the direction ???, which would ??? its speed. 1b. It does not move in a direction ??? gravity, which would ??? its speed. 1c. ??? change in speed occurs - only a change in ??? (which is still a change in velocity). 2. For a satellite close to Earth, the time for a complete orbit around Earth (its period) is about ??? 2a. For higher altitudes, the ??? is less and the period ???. Why?

1. right angle, force of gravity 1a. of gravity, increase 1b. against, decrease 1c. No, direction 2. 90 minutes 2a. orbital speed, longer

Circular Satellite Orbits Let's compare a satellite in orbit to a bowling ball rolling along a bowling alley. 1. Gravity acting on the bowling ball doesn't change ???. 2. Gravity pulls ???, ??? to the ball's motion. 3. The ball hasn't a component of ??? ??? along the direction of the alley. 4. The speeds of the bowling ball and the satellite are not affected by the force of gravity because there is ??? 5. The satellite is always moving at a ??? to the force of gravity. 5a.It does not move in the ??? of gravity, which would ??? its speed. 5b. It does not move in a direction ??? gravity, which would ??? its speed. 5c.No change in ?? occurs - only a change in ??? (which is still a change in velocity)

1. speed 2. downward, perpendicular 3. gravitational force 4. no horizontal component of gravitational force. 5. right angle (90 degrees) 5a. direction, increase 5b. against, decrease 5c. speed, direction (which is still a change in velocity)

Energy Conservation and Satellite Motion 1. Things are more complicated with elliptical orbits - both ??? and distance ??? 1a. The apogee is the point at which the satellite is the ??? away from the Earth's center. 1b. The perigee is the point at which the satellite is ??? [to the Earth's center]. 2. The PE of the satellite is greatest at the ??? and ??? when at the perigee. 3. The ??? of the satellite will be ??? when PE is the ???; and vice versa.

1. speed, vary 1a. farthest 1b. closest 2. apogee, least 3. KE, least, most

Projectile Motion: Vertical Motion 1. Ideal vertical motion also occurs as described by Galileo - if no friction, then the object is in a ??? ??? ??? 2. The longer that an object falls, the more ??? it covers as its ??? increases due to the ??? ??? ??? (9.8 m/s^2) 3. If an object is projected upward, the vertical distances of travel ??? with time on the way up due to the ??? ??? ??? Free Fall Vertical Formula: ∆y = ½ gt^2

1. state of free fall 2. distance, velocity, constant force of gravity 3. decrease, constant force of gravity.

Projectiles Launched Horizontally parabola definition the trajectory of a projectile that accelerates only in the ??? direction while moving at a ??? horizontal velocity

1. the curved path followed by a projectile under the influence only of constant gravity. 2. vertical, constant

Elliptical Orbits 1. The parabolic path of a projectile is actually part of an ellipse (elliptical trajectory) that extends ??? and just beyond the ??? of the Earth. 1a. At low speeds, the center of the Earth is the ??? foci 1b At high speeds, the center of the Earth is the ??? foci 1c. At just the right speed (8km/s), we have a ??? orbit with the center of Earth as the ??? foci.

1. within, center 1a. far, 1b. near 1c. circular, only

PROJECTILE: any object that is "projected" by some means and continues in motion by its own inertia. can be acted upon by gravity, friction, etc. as well during flight, but NO continually applied force moving the object. Gravity causes a curved path bath toward Earth HORIZONTAL launch: free fall, Galileo, no gravity, constant force of gravity, own inertia, same time and distance. Vertical: Galileo, no friction=free fall, greater the fall=greater distance b/c greater speed, constant force of g, projected=upward=shtr distance, contant force of g PARABOLA: the curved path followed by a projectile under the influence only of constant gravity. the trajectory of a projectile that accelerates only in the vertical while moving at a constant horizontal velocity ANGLE: BOTH horizontal (constant) & vertical (changes) velocities, minimum speed top of projectory=0 SATELLITES definition: a projectile body that orbits a larger celestial body, speed must be GREAT enough to ensure its falling distance matches the Earth's CURVATURE CIRCULAR SATELLITE ORBITS: The speed is not changed by GRAVITY. Only the DIRECTION changes. Always at a 90 deg angle to the force of gravity. The speeds of the bowling ball and the satellite are not affected by the force of gravity because there is no horizontal component of gravitational force. ELLIPTICAL ORBITS: If a projectile just above the resistance of the atmosphere is given horizontal speed somewhat greater than 8km/s, it will overshoot its circular path and trace an oval path - an ellipse. An ellipse is a closed curve taken by a point that moves such that the sum of its distances from two fixed points (foci) is constant. For a satellite orbiting a planet, one focus is at the center of the planet and the other could be internal or external to the planet. A circle is a special case of an ellipse where both foci are at the same location. In a circular orbit, the speed of a satellite is constant (if no resistance), but speed varies in an elliptical orbit. An object in motion has kinetic energy (KE) due to its motion. ENERGY CONSERVATION AND SATELLITE MOTION: The apogee is the point at which the satellite is the farthest away from the Earth's center. The perigee is the point at which the satellite is closest [to the Earth's center]. The PE of the satellite is greatest at the apogee and least when at the perigee. The KE of the satellite will be least when PE is the most; and vice versa. KEPLERS LAWS: Kepler worked in an early observatory in Denmark (before telescopes were invented around 1604). Kepler's First Law - The path of each planet around the Sun is an ellipse with the Sun as one focus. Kepler's Second Law - The line from the Sun to any planet sweeps out equal areas of space in equal time intervals. Kepler's Third Law - the square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet to the Sun (T2 ~ r3 for all planets).

1.A cannon is launching a cannonball 50m above the ground (its on a cliff). The projectile is fired at a 45 degree angle upward at a velocity of 440 m/s. Calculate the following: Given: Vert: Vi=0m/s, a=-9.8m/s,d=-50m,t=?? Horiz: Vi=440m/s, d or range=???, t=3.19 s (from a) a. the time it took the cannonball to hit the ground d=Vit + 1/2at^2 50=0+1/2(-9.8)t^2 50/4.9=4.9t^2/4.9 50/4.9 10.2s^2=t^2 3.19s=t b. the range of the cannonball (how far it went) d=vt d=440*3.19=1,403.6m d=1,405.5m c.. the velocity at which the cannonball hit the ground V^2=Vi^2 + 2ad v^2=0+2(9.8)50 v^2=980 v=sqrt980 v=31.3 m/s d.. the angle of change (the angle at which the cannonball hit the ground) R^8 sqrt(distance)^2 + (vertical distance)^2 R^8sqrt(440)^2+(31.3)^2 R=sqrt193,600+979.69 R=441 m/s tan^-1 vert velocity/d = 0 tan^-1 31.3/440 angle=4.1 2. Venus has a period of revolution of 225 earth days. Find the distance between the Sun and Venus as a multiple of Earth's orbital radius. K. third law: T^2~r^3 = T^2/r^3 (225/365)^2 = (rv) 3sqrt(225/365)^2 = 0.724 v 3.. If a small planet, D, were located 8.0 times as far from the Sun as Earth is, how many years would it take for the planet to orbit the Sun? (TdTe)^2=(RvRe)^3 Tdsqrt(Rd/Re)^2Td^2 = sqrt(8.0/1.0)(1.0)^2 = 22.63 = 23 years 4. Every 74 years, Halley's Comet is visible from Earth. Find the average distance of the comet from the sun in astronomical units (AU). (Ra/Rb)^3=(Ta/Tb)^2 Ra=3sqrtRb^3(Ta/Tb)^2= 3sqrt(1.0)^3(74/1.0)^2 = 17.63 = 18 Au 5. The Moon's mass is 7.3 x 10 22 kg and its radius is 1785km. If Newton's Cannon thought experiment of firing a cannonball from a high mountain were attempted on the Moon, how fast would the cannonball have to be fired to escape? V=sqrt2GM/r V=sqrt(6.67*10^-11)(7.3*10^22)2/1.785*10^6 G=6.67*10^-11N*^m2kg^2 V=2335.7n/kg*m 2.34 n/kg 5. A baseball is hit directly in line with an outfielder at an angle of 35.0 degrees above the horizontal with an initial velocity of 22.0 m/s. The outfielder starts running as soon as the ball is hit at a constant velocity of 2.5 m/s and barely catches the ball. Assuming that the ball is caught at the same height at which it was hit, what was the initial separation between the hitter and the outfielder? cos35=(x/22) x=22cos35 x=18.021 m/s sin35=(y/22) y=22sin35 y=12.619 m/s d=vb d=(2.5)(2.57) d=6.425m 6.43m Fielder v=2.5 m/s d=Vit+1/2at2 0=(12.619)+h(-9.8)t^2 0=-4.9t^2+12.619t 0=t(-4.9t+12.619) t=0 or -4.9+12.619=0 t=-12.619/-4.9 t=2.57

Projectiles Launched Horizontally: Checkpoint At the instant a cannon fires a cannonball horizontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground. Which ball, the one fires downrange or the one dropped from rest, strikes the ground first?

1.Both cannonballs hit the ground at the same time, for both fall the same vertical distance. 2.If the cannon were pointed at an upward angle, then the dropped cannonball would hit first, while the fired ball remains airborne. 3.If the cannon is pointed downward, then the fired one hits first.

Projectiles launched at an angle: Review 8. A projectile is launched upward at an angle of 75 degrees from the horizontal and strikes the ground a certain distance downrange. For what other angle of launch at the same speed would this projectile land just as far away?

15 (fig. 10.11 p. 176) 90 degrees - 75 degrees = 15 degrees

Escape Speed Relating this to energy: 1a. Gravity ??? rapidly with distance due to the ??? law. 1b. Most of the work done in launching a rocket occurs near ??? 2. So, how much energy would it take to get a payload off of earth, against the forces of gravity, to a very, very, very far distance?

1a. diminishes, inverse-square 1b. Earth. 2.

Projectiles launched at an angle: Without the effect of air, the maximum range for a baseball would occur when it is batted ??? above the horizontal. Without air drag, the ball rises just like it ???, covering the ??? amount of ground while rising as while falling.

45 degrees, falls, same

Fast-Moving Projectiles—Satellites The Earth's curvature surface drops a vertical distance of ??? for every ??? tangent to the surface.

5 m, 8000 m For example: If a baseball could be thrown fast enough to travel a horizontal distance of 8 k during the 1 s it takes to fall 5 m, then it would follow the curvature of Earth. (speed=8 km/s or 29,000 km/h or 18,000mi/h)

Projectiles Launched Horizontally Review Why must a horizontally moving projectile have a large speed to become an Earth satellite?

Because it needs to be at a speed that the earth will have turned by the time it stops moving

Elliptical Orbits C D | / | / | / B--Earth | A In which of the marked positions A through D does the satellite have the greatest speed? The lowest speed?

Greatest Speed: as it whips around A Lowest Speed: C after passing C, it gains speed as it falls back to A to repeat its cycle

Energy Conservation and Satellite Motion- check: Why does the force of gravity change the speed of a satellite when it is in an elliptical orbit but not when it is in a circular orbit?

In circular orbit, the gravitational force is always perpendicular to the orbital path. With no component of gravitational force along the path, only the direction of motion changes - not the speed. In elliptical orbit, however, the satellite moves in directions that are not perpendicular to the force of gravity. Then components of force do exist along the path, which change the speed of the satellite. A component of force along (parallel to) the direction the satellite moves does work to change its KE.

Fast-Moving Projectiles—Satellites Checkpoint One of the beauties of physics is that there are usually different ways to view and explain a given phenomenon. Is the following explanation valid? Satellites remain in orbit instead of falling to Earth because they are beyond the main pull of Earth's gravity.

No...if any moving object were beyond the pull of gravity, it would move in a straight line and would not curve around Earth. Satellites remain in orbit because they ARE being pulled by gravity, NOT because they are beyond it. For the altitudes of most Earth satellites, Earth's gravitational field is only a few percent weaker than it is at Earth's surface.

Projectiles launched at an angle: Review 4. A stone is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? As it falls?

Rising or falling, it does not change. (p. 176, fig. 10-9)

Projectiles launched at an angle: Review 5. A stone is thrown upward at an angle. What happens to the vertical component of its velocity as it rises? As it falls?

Rising: decreases Falling: increases

Projectiles Launched Horizontally: Review Why does the vertical component of velocity for a projectile change with time, whereas the horizontal component of velocity doesn't?

The vertical component changes because vertical motion is influenced by the gravitational force (which acts in the vertical direction). The horizontal component of velocity doesn't change because the gravitational force is perpendicular to this component (not along it). And therefore can't influence it. (A force needs to have a component along the motion in order to influence that motion)

Projectiles launched at an angle: Checkpoint (no air drag) Consider a batted baseball following a parabolic path on a day when the Sun is directly overhead. How does the speed of the ball's shadow across the field compare with the ball's horizontal component of velocity?

They are the same.

Fast-Moving Projectiles—Satellites Review 12. Why is it important that the projectile in review question 11 be above Earth's atmosphere?

To follow a curve that matches the curvature of Earth, it is important that the projectile, moving horizontally at 8 k m / s, is above Earth's atmosphere. This is because if the projectile moves in the atmosphere, it will lose its horizontal speed and then will not move fast enough to follow the Earth's curvature.

Projectile Motion - launched at an angle An example of a projectile's combined vertical and horizontal velocities. The vertical component ??? while the horizontal is ??? throughout.

changes, constant

Energy Conservation and Satellite Motion The most simple case for this is a satellite in ??? orbit. 1a. The distance between the satellite and the center of the attracting body (mass) does not ???, so the ??? of the satellite is the same everywhere throughout the orbit. 1b. Then, by the ??? ?? ???, the KE must also be ??? 1c. So, an object in circular orbit has an ??? PE, KE, and speed.

circular 1a. change, PE 1b. conservation of energy, constant. 1c. unchanging

Projectile Motion A curved path is then a ??? of horizontal and vertical motion. Each component is ??? of the other in ideal environments. The combined effects produce the ??? of projectiles.

combination, independent, trajectories

Energy Conservation and Satellite Motion The sum of KE and PE for a satellite is a ??? at all points along its ???

constant, orbit.

Projectiles launched at an angle: Checkpoint Suppose the cannonball in figure 10.8, p. 175 were fired faster. How many meters below the dashed line would it be at the end of 5 s?

d = 5t^2 d = 5(5)^2 d = 5(25) d = 125 m

Fast-Moving Projectiles—Satellites Satellites a. falls ??? the earth ~ not into it b. speed must be ??? enough to ensure its falling distance matches the Earth's ???

definition: a projectile body that orbits a larger celestial body a. around b. great, curvature

Circular Satellite Orbits The speeds of the bowling ball and the satellite are not affected by the force of ??? because there is NO ??? component of ??? ???

gravity, horizontal, gravitational force.

Circular Satellite Orbits The speed of a satellite is not changed by ???. Only the ??? changes

gravity. direction

Projectiles launched at an angle: Review 6. A projectile falls beneath the straight-line path it would follow if there were no gravity. How many meters does it fall below this line if it has been traveling for 1s? 2s?

gravity=9.8 m/s^2 free fall equation:1/2gt^2 1s, 1/2g(t^2) = .5(9.8)(1^2) = 4.9m = 5m 2s, 1/2g(t^2) = .5(9.8)(2^2) = 19.6m = 20m

Fast-Moving Projectiles—Satellites If the speed of the stone is ??? ???, the stone may become a ???.

great enough (Herculean throw, or a much smaller planet), satellite

Fast-Moving Projectiles—Satellites Review 11. Why will a projectile that moves horizontally at 8 km/s follow a curve that matches the curvature of the Earth?

it is falling at the same speed as the pull of gravity at a given height. it will fall(orbit) around the earth until something slows it below orbital velocity.

Projectiles launched at an angle: NO air drag Without air drag, speed ??? while going up = speed ??? while coming down: Time going up ??? time coming down

lost, gained, equals

Projectiles launched at an angle: Checkpoint (no air drag) At what part of its trajectory does the baseball have minimum speed?

minimum speed occurs at the top of its trajectory. ~If it is launched VERTICALLY, its speed at the top is zero. ~If launched at an ANGLE, the vertical component of velocity is zero at the top, leaving only the horizontal component. So the speed at the top is equal to the horizontal component of the ball's velocity at any point.

Projectiles launched at an angle: With ??? ??? , the projectile would follow a straight-line path. But, because of gravity, the projectile falls beneath this line the same vertical distance it would fall if it were released from rest. (d = ½ gt^2) From figure 10.8 p.175 distance and time intervals: 5m & 1s 20m & 2s 45m & 3s g=9.8m/s^2

no gravity

Projectiles launched at an angle: With air drag Checkpoint The boy on the tower throws a ball 20 m downrange (fig. 10.15, p. 177). What is his pitching speed? Given: vertical distance: 5m horizontal distance: 20m

pitching speed = horizontal distance/time Calculate time from the constant speed equation=d/t=5m/5s=1s pitching speed = 20m/1s=20m/s

Fast-Moving Projectiles—Satellites A space shuttle is a ??? in a constant state of ??? Because of its tangential velocity, it falls ??? the Earth rather than ??? into it.

projectile, free fall, around, vertically

Fast-Moving Projectiles—Satellites Review 10. How can a projectile fall around the Earth?

the projectile will fall towards the Earth with a trajectory which matches the curvature of the Earth. As such, the projectile will fall around the Earth, always accelerating towards it under the influence of gravity, yet never colliding into it since the Earth is constantly curving at the same rate. Such a projectile is an orbiting satellite.

Projectiles launched at an angle: With air drag In the presence of air resistance, the ??? of a high-speed projectile falls short of the idealized ??? ???

trajectory, parabolic path

Fast-Moving Projectiles - Satellites From our marble drop experiment, we saw that horizontal velocity does not affect ??? motion. a. Two marbles dropped from the same height, one with a horizontal velocity of zero and the other moving, they both fall to the ground at the ??? b. The difference is that the marble moving horizontally travels farther from the "???". c. The faster the horizontal motion, the ??? it will travel, relative to the "???".

vertical a. same time b. release point c. farther, release point

Projectiles launched at an angle: Checkpoint (no air drag) A baseball is batted at an angle into the air. Once airborne, and neglecting air drag, what is the ball's acceleration vertically? Horizontally?

vertical: acceleration is g because the force of gravity is vertical. horizontal: acceleration is zero because no horizontal force acts on the ball

Projectiles launched at an angle: Checkpoint If the horizontal component of the cannonball's velocity is 20m/s in figure 10.8, p. 175, how far downrange will the cannonball be in 5s?

with no air drag: d = vt d = (20m/s)(5s) d = 100m