Chapter 4
What is the magnitude of gravitational force between two 1−kg−kg bodies that are 1 m apart?
6.67 × 10−11 N
What is the magnitude of the gravitational force between Earth and a 1−kg−kg body at its surface?
9.8 N
A stone is thrown upward at an angle. Neglecting air resistance, what happens to the vertical component of its velocity along its trajectory?
At first it slows down, then reverses direction and speeds up.
Where do you weigh more—at sea level or atop one of the peaks of the Rocky Mountains? Defend your answer.
At sea level because your distance to the center of the Earth is least at sea level.
Under what conditions is your weight equal to mg?
If you stand in equilibrium on a surface and drop an object that free-falls at G due to gravity or the acceleration of the surface, or a combination of both, your weight is mg.
The perturbations of Uranus led to what greater discovery?
Pluto
What is the status of Pluto in the family of planets?
Pluto is a dwarf planet.
Why does the force of gravity change the speed of a satellite in an elliptical orbit?
The force of gravity has a component parallel to the velocity of the satellite.
What did Newton discover about gravity?
The same laws of gravity apply on the Earth and in the heavens.
What connection does Earth's curvature have with the speed needed for a projectile to orbit Earth?
The speed has to be great enough that the distance the projectile falls each second matches the Earth's curvature.
Why doesn't the force of gravity change the speed of a bowling ball as it rolls along a bowling lane?
There is no component of the force in the direction of motion of the ball.
Why doesn't the force of gravity change the speed of a satellite in circular orbit?
There is no component of the force in the direction of motion of the satellite.
A projectile is launched upward at an angle of 75∘ 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∘
Explain why occupants of the International Space Station are firmly in the grip of Earth's gravity, even though they have no weight.
There is no support force in free fall so they are weightless, but Earth's gravity still pulls on them and accelerates them.
State Newton's law of universal gravitation in words. Then express it in one equation.
Two bodies attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. F ~ m1m2/d2
The Moon falls toward Earth in the sense that it falls
beneath the straight-line path it would take without gravity
When a satellite travels at constant speed, its shape is a(n)
circle
A satellite in elliptical orbit about Earth travels fastest when it moves
close to Earth
Which of the following is thought to be more prevalent in the universe: ordinary matter, dark matter, or dark energy?
dark energy
At what part of an elliptical orbit does an Earth satellite have the greatest speed? The least speed?
greatest, when closest; least, when furthest
When an astronaut in orbit is weightless, he or she is
still in the grips of Earth's gravity
Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Accelerated downward?
upward, more compressed; downward, less compressed
Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that moved upward at constant velocity? What about in an elevator that moved downward at constant velocity?
upward, no change; downward, no change.
When a projectile achieves escape speed from Earth, it
outruns the influence of Earth's gravity, but is never beyond it
A projectile is launched vertically at 100 m/s. If air resistance can be neglected, at what speed does it return to its initial level?
100 m/s
Why is it important that a satellite remain above Earth's atmosphere?
Friction with the air will exert forces on the satellite slowing it down.
In what sense does the Moon "fall"?
It falls away from the straight line it would follow if there were no force on it.
What happens to an object close to Earth's surface if it is given a speed exceeding 11.2 km/s?
It has escape velocity and moves away from the Earth never returning. It then enters an orbit about the Sun.
How does the force of gravity between two bodies change when the distance between them is tripled?
It is 1/9 of the initial force
A stone is thrown upward at an angle. Neglecting air resistance, what happens to the horizontal component of its velocity along its trajectory?
It is constant.
A space vehicle can outrun Earth's gravity, but can it get entirely beyond Earth's gravity?
No, Earth's gravity extends to infinity, decreasing as the inverse square of the distance.
When a satellite is above Earth's atmosphere, is it also beyond the pull of Earth's gravity? Defend your answer.
No, gravity is an inverse-square law force and extends to infinite distance.
If a satellite were beyond Earth's gravity, what path would it follow?
a straight line
Newton did not discover gravity, for early humans discovered that whenever they fell. What Newton did discover is that gravity
extends throughout the universe
What was the cause of perturbations discovered in the orbit of planet Uranus?
gravitational pulls from Neptune
Is the period longer or shorter for orbits of greater altitude?
longer
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 of Earth
A dropped ball accelerates as it falls. But a ball rolling on a horizontal surface has zero acceleration because
no horizontal force acts on it
Consider a space probe three times as far from Earth's center as it would be at Earth's surface. Compared to at Earth's surface, its gravitational attraction to Earth at this distance is about
one-ninth as much
Earth is gravitationally pulled toward
the Sun Mars Jupiter