Ph Ch 6 Define Law of universal gravitation
everybody in the universe attracts every other body w/ a force that, for two bodies, is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them: (hand write the equation on here)
Ph Ch 6 Define inverse square law
a law relating the intensity of an effect to the inverse square of the distance from the cause:
Intensity = 1/distance squared
gravity follows an inverse square law, as do the effects of electric, magnetic, light, sound, and radiation phenomena
Ph Ch 6 Define weight
the force that an object exerts on a supporting surface (or, if suspended, on a supporting string), which is often, but not always, due to the force of gravity
Ph Ch 6 Define projectile
any object that moves through the air or through space under the influence of gravity
Ph Ch 6 Define parabola
the curved path followed by a projectile under the influence of constant gravity only
Ph Ch 6 Define ellipse
the oval path followed by a satellite. The sum of the distances from any point on the path to two points called foci is a constant. When the foci are together at one point, the ellipse is a circle. As the foci get farther apart, the ellipse becomes more "eccentric."
Ph Ch 6 Define escape speed
the speed that a projectile, space probe, or similar object must reach to escape the gravitational influence of earth or of another celestial body to which it is attracted
Ph Ch 6 Check Yourself The Moon falls around Earth rather than straight into it. If the Moon's tangential velocity were suddenly reduced to zero, how would it move?
If the Moon's tangential velocity became zero, it would fall straight down and crash into Earth
Ph Ch 6 Check Yourself According to the equation for gravitational force, what happens to the force between two bodies if the mass of one of the bodies is doubled? If both masses are doubled?
~the force would double; the force would quadruple
Ph Ch 6 Check Yourself Gravitational force acts on all bodies in proportion to their masses. Why, then, doesnt' a heavy body fall faster than a light body?
Because Newton's second law (a=Flm) reminds us that a greater force acting on a greater mass does not result in a greater acceleration
Ph Ch 6 Check Yourself By how much does the gravitational field between two objects decrease when the distance between their centers is doubled? Tripled? Increased tenfold?
It decreases to 1/4; 1/9; and 1/100 (square it over 1)
Ph Ch 6 Check Yourself Consider an apple at the top of a tree that is pulled by Earth's gravity w/ a force of 1N. If the tree were twice as tall, would the gravitational fields be only 1/4 as strong?
No because an apple at the top of the twice as tall apple tree is not twice as far from the earth's center. The taller tree would need a height equal to the radius of the earth for the apple's weight at its top to reduce to 1/4 N. Before its weight decreases by 1%, an apple or any object must be raised 32km--nearly 4 times the height of Mt Everest. So as a practical matter, we disregard the effects of everyday changes in elevation
Ph Ch 6 Check Yourself In what sense is drifting n space far away from all celestial bodies like stepping off the edge of a table?
In both cases, you'd experience weightlessness. Drifting in deep space, you would remain weightless because no discernable force acts on you. Stepping off a table, you would be only momentarily weightless because of a momentary lapse of support force
Ph Ch 6 Check Yourself 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 fired downrange or the one dropped from rest, strikes the ground first?
Both cannonballs hit the ground at the same time, for both fall the same vertical distance.
Ph Ch 6 Check Yourself A baseball is batted at an angle into the air. Once the ball is airborne, and neglecting air resistance, what is the balls 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
Ph Ch 6 Check Yourself At what part of a baseballs trajectory does it have minimum speed?
A ball's 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.
Ph Ch 6 Check Yourself 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 w/ the ball's horizontal component of velocity?
they are the same
Ph Ch 6 Check Yourself A boy on a tower throws a ball 20m downrange, and the vertical drop is 5m. What is his pitching speed?
The ball is thrown horizontally, so the pitching speed is horizontal distance divided by time. A horizontal distance of 20m is given, but the time is not stated. However, the vertical drop is 5m and that a 5m drop takes 1s. from the equation for constant speed (which applies to horizontal motion), v=d/t=(20m)(1s)=20m/s
Ph Ch 6 Check Yourself 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
Ph Ch 6 Check Yourself T or F: The space shuttle orbits at altitudes in excess of 150 kilometers to be above both gravity and Earth's atmosphere.
false. What satellites are above is the atmosphere and air resistance--not gravity. It's important to understand that Earth's gravity extends throughout the universe in accord w/ the inverse square law
Ph Ch 6 Check Yourself Satellites in close circular orbit fall about 5 meters during each second of orbit. Why doesnt this distance accumulate and send satellites crashing into Earth's surface?
In each second, the satellite falls about 5m below the straight line tangent it would have followed if there were no gravity. Earth's surface also curves 5m beneath a straight line 8km tangent. The process of falling w/ the curvature of Earth continues from tangent line to tangent line , so the curved path of the satellite and the curve of Earth's surface "match" all the way around Earth. Satellites do, in face, crash to Earth's surface from time to time when they encounter air resistance in the upper atmosphere that decreases their orbital speed.
Ph Ch 6 Check Yourself The orbital path of a satellite is shown in the sketch (pg 123). In which of the positions A through D does the satellite have the greatest speed? The lowest speed?
The satellite has its greatest speed as it whips around A and has its lowest speed at position C. After passing C, it gains speed as it falls back to A to repeat its cycle
Ph Ch 6 Check Yourself The orbital path of a satellite is shown in the sketch (pg 124). In which positions A through D does the satellite have the greatest KE? The greatest PE? The greatest total energy?
KE is maximum at the perigee A; PE is maximum at the apogee C; the total energy is the same everywhere in the orbit
Ph Ch 6 Check Yourself 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 othe satellite moves does work to change its KE