Chapter 4
If the mass of Earth were increased by a factor of 6.00 , by how many times would the force between Earth and the Sun increase?
6.00 times
Weight refers to the force of gravity acting on a mass. We often calculate the weight of an object by multiplying its mass by the local acceleration due to gravity. The value of gravitational acceleration on the surface of Mars is 0.38 times that on Earth.Assume your mass is 85.00 kg. Then your weight on Earth is 833.00 newtons (833.00 N = m × g = 85.00 kg × 9.8 m/s2). What would be your mass on Mars? What would be your weight on Mars?
85.00 kg; 316.54 N
Newton determined that the force of gravity on an object is proportional to its mass, causing its mass to be canceled out (Newton's second law) and resulting in a constant acceleration. If the laws of physics are universal, then Newton should be able to apply his discoveries about gravity on Earth to the motion of the planets in our Solar System. Newton's third law says that for every force there is an equal reaction force in the opposite direction. What does this imply about the force of gravity associated with a person standing on the Earth?
The Earth's gravity pulls downward on the person, and the person's gravity pulls upward on the Earth
When using Newtons law of universal gravitation it is important to remember that the variable 'r' represents what?
The distance between the center of mass of each object.
Newton's second law says that the acceleration (a) of an object depends on its mass (m) by the equation: a=F/m F is the force that is causing the object to accelerate. In the case of dropping objects from a height, the force that causes them to accelerate toward the Earth is gravity. If the acceleration of objects dropped from a height does not depend on the object's mass (as shown by Galileo's experiment), what does this imply about the force of gravity?
The force of gravity increases with increased mass
Newton developed a universal law of gravitation that can be used under most circumstances, not just for objects on the surface of the Earth. Here is the law: F=G(m1m2/r2) where G is a constant. Think about what happens when you increase and decrease each of the variables in Newton's equation for the gravitational force between two objects of mass m1 and m2, a distance r from one another. Given your results, what is the likely cause of Kepler's observation that planets travel faster when they are closer to the Sun?
The force of gravity is stronger closer to the Sun
If the Moon had twice the mass that it does, how would the strength of the lunar tides change?
The highs would be higher and the lows would be lower.
Astronauts in a space shuttle can float while orbiting Earth. Why are these astronauts weightless?
They are falling around Earth at the same rate as the shuttle
What features do the tidal forces of the moon acting on the Earth create?
Two tidal bulges, one one the side of the Earth closest to the moon and one on the side of the Earth farthest from the moon.
A neap tide occurs during
a first quarter or third quarter moon
A spring tide occurs during ___
a full moon or new moon
For a pair of objects, the center of mass is located
along the line between the two objects, closer to the more massive object
An object in a(n) ___ orbit in the Solar System will remain in its orbit forever. An object in a(n) ___ orbit will escape from the Solar System
bound; unbound
If Earth shrank to a smaller radius but kept the same mass, the weight of each person on Earth would
increase
If the distance between Earth and the Sun were cut in half, the gravitational force between these two objects would
increase by a factor of 4
Suppose you are transported to a planet with twice the mass of Earth, but the same radius of Earth. Your weight would ___ by a factor of ___
increase; 2
If you went to Mars, your weight would be
lower because Mars has lower mass and a smaller radius that together produce a lower gravitational force
Weight refers to the force of gravity acting on a mass. We often calculate the weight of an object by multiplying its mass by the local acceleration due to gravity. The value of gravitational acceleration on the surface of Mars is 0.377 times that on Earth. If your mass is 85 kg, your weight on Earth is 830 N (m × g = 85 kg × 9.8 m/s2 = 830 N). What would be your approximate mass and weight on Mars?
mass 85 kg; weight 310 N
The connection between gravity and orbits enables astronomers to measure the ___ of stars and planets
masses
If an object crosses from farther to closer than the Roche limit, it
may be torn apart
If Earth shrank to a smaller radius but kept the same mass, the gravitational force between Earth and the Moon would
stay the same
If I were to travel from the Earth to the Moon my mass would ___ and my weight would ___
stay the same; decrease
Spring tides occur only when
the Moon is in new or full phase.
Spring tides occur only when:
the Moon is in new or full phase.
The primary factor in Earth's tides is
the Moon's gravity
Subsequent semi-diurnal (twice daily) tides happen precisely once every 12 hours and 25 minutes. Given what you know of the motions of the Earth and Moon, where is this extra 25 minutes likely coming from?
the orbit of the Moon around the Earth
Compared to your mass on Earth, on the Moon your mass would be
the same; mass doesn't change
To maintain a bound orbit an object must have a velocity equal to or greater than ___ and less than ___
the velocity required for a circular orbit; escape velocity
The Roche limit is where the ___ overpower the __ causing the object to be pulled apart
tidal forces; internal gravitational forces
What causes the Moon to always keep the same face toward Earth?
tidal locking
A centripetal force is one that points ___ The force that provides the centripetal force for planets is the ___
towards the center of the circle; gravitational force
The "second" high tide is caused by
weaker gravity pulling on Earth on the side opposite the Moon.
