Chapter 4 Gravity
What is the magnitude of gravitational force between the earth and 1-Kilogram of body?
10 N
The force of gravity is the same on each because the masses are the same, as Newton's equation for gravitational force verifies. When dropped the crumpled paper falls faster only because it encounters less air drag than the sheet.
1000 N 220 lbs
As the ball leaves the girl's hand, one second later it will have fallen
5 meters below the dashed line
What is the magnitude of gravitational force between two 1-kilogram bodies that are 1 meter apart?
6.67 × 10-11 N.
A ball tossed at an angle of 30 with the horizontal will go as far downrange as one tossed at the same speed at an angle of
60
What is the minimum speed for orbiting the Earth in close orbit? The maximum speed? What happens above this speed?
8 km/s; 11.2 km/s; above this speed the satellite leaves the Earth permanently.
When a satellite travels at constant speed, the shape of its path is
A circle
If you weigh yourself in an elevator, you'll weigh more when the elevator
Accelerates upward
If a space vehicle circled Earth at a distance equal to the Earth-Moon distance, how long would it take to make a complete orbit?
Any satellite circling as far from Earth as the Moon would have a period of 1 month, the same as the period of the Moon.
You tell your friend that the force of gravity is measured from the center of the Earth, not from the ground up. Compared with the distance to the Earth's center, gravitational force is about the same on an object on the 10th and 20th floor. The difference is infinitesimal and can be neglected.
Astronauts in orbit lack a support force, which is the reason for their weightlessness. If they were beyond gravity they would travel in straight-line paths and not orbit Earth.
If the mass of one planet is somehow doubled, the force of gravity between it and a neighboring planet would
Double
State Newton's law of universal gravitation in words. Then do the same with one equation.
Every mass attracts every other mass with a force that for any two masses is directly proportional to the product of the masses involved and inversely proportional to the square of the distance separating them.
When an elevator accelerates upward, your weight reading on a scale is
Greater
Does the speed of a satellite change in an elliptical orbit?
Half the time it is moving with gravity and the other half it is moving without gravity. When it is moving without gravity it slows down and when it is moving with gravity it speeds up.
Is the horizontal component of velocity for a projectile affected by the vertical component? Defend your answer.
Horizontal and vertical components of velocity for projectiles are independent of each other. One has no effect on the other.
What would be the path of the Moon if somehow all gravitational forces on it vanished to zero?
In accord with the law of inertia, the Moon would move in a straight-line path instead of circling both the Sun and Earth.
If a cannonball is fired from a tall mountain, gravity changes its speed all along its trajectory. But if it is fired fast enough to go into circular orbit, gravity does not change its speed at all. Why?
In circular orbit the force of gravity is everywhere at right angles to the satellite's path. There is no force component in the direction of motion. No force in a direction means no change in motion in that direction.
A heavy crate accidentally falls from a high-flying airplane just as it flies directly above a shiny red sports car parked in a car lot. Relative to the car, where will the crate crash?
In the absence of air drag, the crate will continue falling beneath the airplane and hit the ground a distance away from the car equal to the distance the airplane traveled while the crate dropped. It will not hit the car!
How can a projectile "fall around the Earth"?
It can fall around the earth if its tangential velocity is sufficient to ensure its curved path matches the curve of Earth.
How does the moon fall?
It falls in a straight-line path with the absent of gravity.
When does a satellite moving in an elliptical orbit have the greatest and least speed?
It has the greatest speed on earth and the slowest when it is further away.
What does it mean when something is moving in a curve that has a tangential velocity?
It is when the velocity is parallel that is parallel to the cure at every point.
What happens to the horizontal component of velocity for a batted baseball with no air drag?
It remains the same
When an elevator accelerates downward, your weight reading is
Less
The force of gravity between two plants depends on their ?
Masses and distance apart
At what point in its trajectory does a batted baseball have its minimum speed? If air drag can be neglected, how does this compare with the horizontal component of its velocity at other points?
Minimum speed occurs at the top, which is the same as the horizontal component of velocity anywhere along the path.
Why was the measurement of G called the "weighing the earth experiment" ?
Once G was known all you had to go was calculate the mass of Earth.
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
Remains the same
The Earth and the Moon are attracted to each other by gravitational force. Does the more massive Earth attract the less massive Moon with a force that is greater, smaller, or the same as the force with which the Moon attracts the Earth?
The Earth and Moon equally pull on each other in a single interaction. In accord with Newton's third law, the pull of the Earth on the Moon is equal and opposite to the pull of the Moon on the Earth.
Since Earth is gravitationally attracted to the Sun, why doesn't it simply crash into the Sun?
The Moon's tangential velocity is what keeps the Moon coasting around the Earth rather than crashing into it. If its tangential velocity were reduced to zero, then it would fall straight into the Earth!
What is the brightness on a flashlight when it is held twice as far?
The brightness is 1/4 as much, which follows the inverse-square law.
What change happens to force between two people when they walk away from each other?
The force is 1/4 as much, which follows the inverse-square law.
In accord with the law of inertia, the Moon would move in a straight-line path instead of circling both the Sun and Earth.
The force of gravity is the same on each because the masses are the same, as Newton's equation for gravitational force verifies.
Is the force of gravity stronger on a crumpled piece of paper compared with the same paper uncrumpled? Defend your answer.
The force of gravity is the same on each because the masses are the same, as Newton's equation for gravitational force verifies. When dropped the crumpled paper falls faster only because it encounters less air drag than the sheet.
What happens to the force of gravity when two plants masses has somehow doubled?
The gravity has quadrupled
When an Earth satellite is placed into a higher orbit, what happens to its time for making a complete orbit? In other words, what happens to its period?
The higher the orbit, the longer the period.
A park ranger shoots a monkey hanging from a branch of a tree with a tranquilizing dart. The ranger aims directly at the monkey, not realizing that the dart will follow a parabolic path and thus fall below the monkey. The monkey, however, sees the dart leave the gun and lets go of the branch to avoid being hit. Will the monkey be hit anyway? Defend your answer.
The monkey is hit as the dart and monkey meet in mid air. For a fast-moving dart, their meeting place is closer to the monkey's starting point than for a slower-moving dart. The dart and monkey fall equal vertical distances—the monkey below the tree, and the dart below the line of sight
Gravitational force acts on all bodies in proportion to their masses. Why, then, doesn't a heavy body fall faster than a light body?
The reason that a heavy body doesn't fall faster than a light body is because the greater gravitational force on the heavier body (its weight), acts on a correspondingly greater mass (inertia). The ratio of gravitational force to mass is the same for every body—hence all bodies in free fall accelerate equally. And it's true not just near the Earth, but anywhere.
What would be the difference in a fall that is far below a straight line path compared to the distance of a free fall?
The same
What is the thickness of spray paint when it is held twice as far?
The spray paint is 1/4 as think, which follows the inverse-square law.
The orbital velocity of the Earth about the Sun is 30 km/s. If the Earth were suddenly stopped in its tracks, it would simply fall directly into the Sun. Devise a plan whereby a rocket loaded with radioactive wastes could be fired into the Sun for permanent disposal. How fast and in what direction with respect to the Earth's orbit should the rocket be fired?
The tangential velocity of the Earth about the Sun is 30 km/s. So if a rocket carrying the radioactive wastes were fired at 30 km/s from the Earth in the direction opposite to the Earth's orbital motion about the Sun, the wastes would have no tangential velocity with respect to the Sun. They would simply fall into the Sun.
What happens to a balls vertical component velocity as it rises and as it falls?
The vertical component changes when it is tossed up and when when it is free falling.
What is the connection Newton made between a falling apple and the moon?
They are both under the influence of the Earth's gravity.
The speed of a satellite in an elliptical orbit
Varies
What makes the Earth round?
What makes the Earth round?
Consider a high-orbiting spaceship that travels at 7 km/s with respect to the Earth. Suppose it projects a capsule rearward at 7 km/s with respect to the ship. Describe the path of the capsule with respect to the Earth.
When a capsule is projected rearward at 7 km/s with respect to the spaceship, which is itself moving forward at 7 km/s with respect to the Earth, the speed of the capsule with respect to the Earth will be zero. It will have no tangential speed for orbit. What will happen? It will simply drop vertically to Earth and crash.
Are plants projectiles falling around and around the sun?
Yes
What do you say to a friend who says that if gravity follows the inverse-square law, that when you are on the 20th story of a building gravity on you should be one-fourth as much as if you're on the 10th story?
You tell your friend that the force of gravity is measured from the center of the Earth, not from the ground up. Compared with the distance to the Earth's center, gravitational force is about the same on an object on the 10th and 20th floor. The difference is infinitesimal and can be neglected.
What do you call the gravitation force between the Earth and you?
Your weight
When the elevator cable breaks, the elevator falls freely so your weight reading is
Zero
When no air resistance acts on a fast-moving baseball, its acceleration is
downward, g.
When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it makes
matches the curved surface Earth.
When a projectile achieves escape speed from Earth, it
outruns the influence of Earth's gravity but is never beyond it.
The universal gravitational constant, G, which links force to mass and distance, is similar to the familiar constant
pie symbol
