Physics CH: 9 Gravity REVIEW
why arent tides due to the sun 180 times as large as tides due to the moon?
because the sun's greater distance, the difference in gravitational pulls on opposite sides of Earth is very small.
why do tides not occur at the same time every day?
because while the earth spins, the Moon moves in its orbit and appears at the same position in our sky every 24 hour and 50 minutes, so the two high tide cycle is actually at 24 hour and 50 minute intervals.
The Universal Gravitational Constant, G
6.67 x 10^-11 Nm^2/kg^2 (small). - Gravity is a very weak force compared w electrical forces. The large net gravitational forces we feel as weight is because of the enormity of atoms in planet Earth that are pulling on us. -Henry Cavendish--> calculated G alone by measuring tiny force between lead masses w an extremely sensitive torsion balance. --> Jolly later developed a simpler method.
Tides in Earth and atmosphere
Moon-Sun tidal forces produce Earth tides and ocean tides. - twice a day--> solid surface of Earth rises and falls as much as 1/4m. -Volcanoes are more likely when Earth experiences a spring tide ( full or new Moon). Magnetic tides--> tidal effects in the upper part of the atmosphere(ionosphere) produce electric currents that alter the magnetic field that surrounds Earth, magnetic tides. -The highs and lows of magnetic tides are GREATESTS when atmosphere is having spring tides.
Gravitational force acts on all bodies in proportion to their masses. why then doesnt a heavy body fall faster than a light body?
Newton's second law(a=F/m) reminds us that a greater force acting on greater mass does not result in greater acceleration.
Consider an apple at the top of a tree that is pulled by earths gravity with a force 1 N. If the tree were twice as tall, would the force of gravity be 1/4 as strong?
No, because an apple at the top of the twice-as-tall tree is not twice as far from Earth's center. The taller tree would need a height equal to the Earth's radius for the apple's weight to reduce to 1/4N.
We know that both the Moon and the Sun produce our ocean tides. And we know the Moon plays a greater role because it is closer. Does its closeness mean that it pulls on Earth's oceans with more gravitational force than the Sun?
No, the Sun's pull is much stronger(180 times). BUt the DIFFERENCE in lunar pulls is more than the difference in solar pulls, So our tides are due primarily to the Moon.
The universal law of gravity
The moon "falls around" the Earth because of its tangential velocity. EVERYTHING pulls on everything in a simple way that involves only mass and distance. FORMULA--> Force~ mass1 x mass2 / distance^2. - Force is directly proportional to the product of their masses - Force is inversely proportional to the square of the distance separating them.
Black Hole
Your weight on a star depends on... 1. your mass 2. star's mass 3. distance between star's center and ur belly button. - If a star collapsed to half its radius w no change in mass, your weight at the surface would be 4 times greater. - If a star collapsed to tenth of its radius w no change in mass, ur weight will be 100 times as much at surface. === if star kept shrinking--> gravitational field at surface becomes stronger. (escape velocity would increase).
gravitational field
a force field that exists in the space around every mass or group of masses. The Moon is in contact and interacting w the gravitational field of Earth. -gravitational field is an example of a force field--> any body w mass experiences a force in the field. (ex: magnet w iron fillings) -Field lines represent the gravitational field about Earth. Where the field lines are closer together(near earth) grav. field is stronger. Farther away from earth, where the field lines are farther apart, the grav. field is weaker--> follows the inverse-square law. ALL POINT TO CENTER OF EARTH. - gravitational field AT earth's surface varies from location to location.
inside a spherical shell of uniform thickness and composition....
a hollow planet would have no gravitational field anywhere inside it because complete cancellation of gravitational forces occurs everywhere inside. (involves distance but also mass). (doesnt have to be at the center to have zero grav. force). anywhere inside will be WEIGHTLESS.
figure 9.23
as you fall faster and faster in a hole through earth, your acceleration decreases because the part of earths mass beneath you becomes smaller and smaller. Less mass means less attraction, until at the center net force is zero and acceleration is also zero. Momentum carries you past the center and against a growing acceleration to the opposite end of the tunnel, where acceleration is again g, directed back towards the center.
Ocean Tides
caused by differences in the gravitational pull of the moon on opposite sides of the earth. -Gravitational force--> between Moon and Earth is STRONGER on side of Earth nearer to the moon. -Gravitational force--> between Moon and Earth is WEAKER on side of Earth that is farther from the Moon. These different pulls of the Moon stretch Earth, most notably in its oceans--> thats why we experience two high tides and two low tides daily.
Tilt of Earth's axis
causes the two daily high tides to be unequal most of the time. -Tides are NOT produced in--> ponds(no part of a pond is significantly closer to Moon or Sun than any other part), your body(ur not tall enough for tides).
Gravitational field inside a planet
gravitational field also exists inside Earth. -if you fall in the North Pole end youll fall and gain speed until you reach the center, then lose speed all the way down the south pole. -Your acceleration will be get less as you continue towards the center of Earth because as you fall toward Earth's center there is less mass pulling you towards the center. -At Earth's center--> youll have maximum velocity and minimum acceleration, so the gravitational field would be ZERO. -Earth is more dense at its core(center) -Earth is less dense at its surface. -inside a planet w uniform density--> gravitational field increases at a steady rate from zero at its center and g at its surface.
A Black Hole
gravitational fields are enormous closer distance near the vicinity of a black hole. Only mass, angular momentum, and electric charge are retained by the black hole. -wormhole--> distortion of space and time, can lead to time travel.
halfway to the center of earth, would the force of gravity on you be less than at the surface of earth?
gravitational force on you would be less, because there is less mass of earth below you, which pulls you with less force. -If earth were a uniform sphere of uniform density, gravitational force halfway to the center would be exactly half that at the surface.
Neap Tides (moon at 90degree angle from sun)
occur when the Moon is halfway between a new Moon and a full Moon. The high tides are lower than average and the low tides are not as low as average low tides.
spring tides
occur when the attraction of the Sun and the Moon are lined up with eachother. We have higher-than-average high tides and lower-than-average low tides. -Spring tides occur at the times of a new or full Moon. --> full Moon= Earth is between sun ans Moon. --> new Moon= Moon is between Sun and Earth. -HIGHEST spring tides occur when the Moon and Sun are closest to Earth.
Einstein's Theory of Gravitation
percieved the gravitational field as a geometrical wrapping of 4-dimensional space and time, he realized that bodies put dents in space and time. -the more massive the ball--> greater the dent or wrap. --> if you roll a marble away from the ball across the top of a bed, it will roll in a straight-line path. --> if you roll a marble near the ball across the bed, it will curve. if the curve closes on itself the marble will orbit the ball in circular path.
Universal Gravitation
planets are round because of gravitation. everything pulls on eachother and planets pull on each other. When planets pull on eachother they "wobble" in their orbits. -Perturbation--> force that causes this wobbling. recent evidence shows that the universe is expanding and accelerating outwards, pushed by an antigravity dark energy. (makes 73%)
Newtonian Synthesis
recognized that forces must act on planets otherwise their paths would be straight lines. He realized that any force on a planet would be directed towards the sun. This union of terrestrial laws and cosmic laws got rid of the belief that there were two sets of natural laws.
Gravity and Distance: The Inverse-Square Law
shows that gravity weakens with distance. Gravitational force = 1/d^2 - If the same amount of paint travels in straight lines for 2m, it will spread to a patch twice as tall and twice as wide. The paint will then spread over an area 4 times as big, and its thickness would be only 1/4 mm. - 1 unit of distance--> 1 area unit--> 1 layer thick - 2 units of distance--> 4 area unit-> 1/4 layer thick - 3 units of distance--> 9 area units-> 1/9 layer thick - 4 units of distance--> 16 area units-> 1/16 layer thick. =layer thick represents gravity. the distance term d in Newton's equation is the distance between the CENTERS of masses of the objects. The GREATER the distance from Earth's center, the LESS the weight of an object. For very great distances Earth's gravitational force approaches zero BUT NEVER reaches zero.
Weight and Weightlessness
the PRESSING against Earth is the sensation we interpret as weight. When you step on a weighting scale two forces act on you--> downward force of gravity, mg, and upward support force. THESE forces are EQUAL and OPPOSITE when NO ACCELERATION occurs. - if elevator accelerates upward= increase in ur weight (since scale and floor push harder against ur feet). -if elevator accelerates downward= decrease in ur weight. -if elevator is in free fall= scale would read zero (you will be weightless). EVEN in weightless condition there is still a gravitational force acting on you but you don't feel it cause u have no support force. (mg that acts on u remains the same even if ur weight changes).
if there is an attractive force between all objects, why do we not feel ourselves gravitating towards massive buildings in our vicinity?
the forces between buildings and us is relatively small because their masses are small compared with the mass of Earth.
uniform density planet
the gravitational field intensity inside a planet of uniform density is directly proportional to the radial distance from its center and its maximum at its surface. OUTSIDE it is inversely proportional to the square of the distance from its center.
Tidal bulges on the Moon
there are two tidal bulges on the moon (just like on earth) near side and far side get pulled differently. - unlike Earth's tides, Moon's tidal bulges remain in fixed locations, with no daily raising and falling. - Moon rotates about its own axis (or Earth-Moon axis). --> The SAME side of the Moon faces Earth all the time BECAUSE... the moon's center of gravity is displaced from its center of mass, so the Earth pulls on the Moon at its center of gravity and produces a torque about the Moon's center of mass, which tends to rotate the long axis of the Moon into alignment w Earth's gravitational field.
Gravitational force (WEIGHT)
we sense gravitation only when masses are involved. The force of attraction between you and the earth is your weight. Your weight depends on your mass and distance from the center of the earth. - At top of a mountain= ur weight is less (because ur distance from center is greater). - Mass of Earth--> 6 x 10^24 kg.
suppose you stepped into a hole throught the center of earth and made no attempt to grab the edges at either end. Neglecting air drag, what kind of motion would you experience?
you would oscillate back and forth. simple harmonic motion. if you failed to grab the edge of the hole when you reached the south pole, youd fall back toward the center, and return to the north pole in the same time.