What is the difference between scalars and vectors?
A scalar quantity is a one dimensional measurement of a quantity, like temperature, or weight. A vector has more than one number associated with it. A simple example is velocity. It has a magnitude, called speed, as well as a direction, like North or Southwest or 10 degrees west of North.
How can an object that is moving with a constant speed still be accelerated?
Cite a specific example of how this can occur.
An object which experiences either a change in the magnitude or the direction of the velocity vector can be said to be accelerating. This explains why an object moving in a circle at constant speed can be said to accelerate – the direction of the velocity changes.
It is accelerating if it changes direction.
ex) car going in a circle at 30mph
What observational evidence led Galileo to believe that vertical motion (free fall) is an example of uniform accelerated motion?
He dropped two bodies at the same time and saw while the lighter one initially fell quicker but was overtaken by the heavier. Then he placed the objects in a vacuum and they fell at uniform rates.
Galileo used a form of what today is known as the hypothetico-deductive method as a way to determine what factors affect the free fall of objects. After eliminating mass he decided that the factors were either the time of fall or the distance because he used the concept of average velocity.
1. What is average velocity?
2.Why did Galileo decide to use this concept in deriving what he thought was the factor which controlled free fall?
3.How did Galileo eliminate one of these factors?
1.Average velocity is The average speed and direction of an object over time
2.he proposed that in free fall bodies dropped with a characteristic uniform speed determined not by their weight but by their specific gravity. Put this theory to the test by dropping bodies from heights and found that the experiments did not confirm his theory.
3. He simulated the process using an inclined plane and bronze ball to obtain data of the time and distance. After repeating the experiment the time never changed.
What were the practical problems that Galileo faced in his trying to show that it was time that was the key factor in the rate of fall and how did he overcome them?
Galileo’s experiments were problematic to scholars of the time. Scholars have pointed such passages to support their arguments that Galileo did not perform such experiments and that his references to experiments were only rhetorical devices. Galileo could not conceive of a friction-less plane that extended forever so he considered a moving boat with a stone dropped from the mast would fall at the foot of the mast because of inertia
1.What is meant by the term inertia?
2.Why did Galileo know that he could never prove the concept of inertia here on the Earth?
3. How do space probes illustrate the principle of inertia?
1. An object’s tendency to maintain its state of motion, whether moving or remaining at rest. (rock hanging in midair in zero gravity without resistance, action, etc.)
2. Gravity, friction and air resistance are all around us on Earth, and inertia requires no resistance.
3.Space probes are accelerating toward the moons because of their engines. After they have reached the outside of Earth’s orbit, the gravity of Earth is not as strong as before and they can now coast toward the moon because of this and the fact that there is no apparent resistance and they started in motion so they will continue in this way,(eventually the moons gravity will pull in the space probe when close enough)
When we think of inertia we usually associate it with horizontal motion. However Galileo believed that there could circular inertia. Why did he need to propose that there could be circular inertia given his advocacy of the Copernican system?
because there was no explanation currently for how the Earth could keep moving with nothing to push it. Galileo figured out that the earth coasts around the sun because there is nothing to stop it. There was also the question of why, if this is the case, Earth moves in a circle rather than a straight line. He answers that it is because the sun’s gravity bends earth’s path into a circle and it started moving because the gas and dust from which it was formed were already moving from the big bang.
Circular inertia we know from the work of Newton on circular motion is impossible. Why is this so?
Newton’s First Law
An object keeps moving unless another force acts upon it. It keeps its force of motion. The planets ability to keep moving in a circular motion.
1.Galileo would only accept a limited form of inertia. Why was this so?
2. What made Newton’s concept of inertia fundamentally different from that of Galileo?
1.He accepted that an object in motion also faces outside forces of friction and gravity but he could not conceive of the notion of an infinite universe. He believed an object had to be moving to a definite place.
2. Newton’s concept of inertia takes into consideration the idea of mass and states that “larger bodies -planets and comets-preserve for a longer time both their progressive and their circular motions, which take place in spaces having less resistance.”
According to Galileo what are the reasons why an object propelled outward from the top of a building will take the same amount of time to reach the ground as one that is dropped vertically?
Projectile motion that Galileo came up with was a combination of two different motions occurring simultaneously and independent of each other. Projectile motion will have a vertical component which Galileo determined to be an example of free fall UAM and governed by the principles he had discovered concerning UAM.
How did Newton use the motion of the Moon as a falling object as a way to explain to test of theory of universal gravitation?
To keep the Moon moving in the circle around the Earth, the Earth must exert a pull on the Moon. Therefore, the sun’s gravity is what hold the planets in their orbits.
1. How was Newton’s view of natural motion in nature different from that of Aristotle?
2. Why did Newton know that his first principle of motion would never be experimentally proven in his lifetime?
1. Aristotle à said that forces cause our velocities and it is necessary in order to keep something in motion
2.Newton knew it would not be proven in his lifetime, but we do not know why
According to Newton what is the magnitude of the force needed to move a 500Kg planetary probe thru space at a constant velocity of 1000m/s? Give a reason for your answer.
(500kg)(1000m/s) = 500,000 N
because force equals mass time acceleration
Why is it about mass that makes it an absolute measurement whereas weight can vary?
If you were transported to a planet which had a radius which was 3 times that of the Earth but a mass ½ of the Earth on a relative basis by what factor would your mass change?
1.Mass will remain the same anywhere in the world and is a fundamental property of objects. Weight is a measure of the force of gravity on an object and is dependent on the context.
2. It wouldn’t
Answer the same question with respect to where your weight would be greater and why in the following situations:
1.South Pole vs. Equator
2.Center of the Earth vs. the surface of the Earth
1.Weigh more at the South Pole because being closer to the poles means that the gravitational force is stronger.
2.The surface of the Earth because if you are in the center then you’re being pulled equally in all directions and they cancel out, therefore you’d be weightless.
1. In analyzing uniform circular motion why did Newton come to the conclusion that a force was needed for objects to stay in circular motion?
2.What is this force in nature and what are the parameters that contribute to the magnitude of this force?
1.Newton came to the conclusion that a force was needed for objects to stay in circular motion because otherwise they would be moving in straight lines. Newton’s first law states that there must be a force acting to accelerate them that is to change the direction of their motion.
2. This force is called centripetal force, which is center seeking and pulls planets back into a circle when their natural tendency is to move off in a straight line. The parameters that contribute to the magnitude of this force are that the force on a planet or object is equal to the force of gravity exerted on the object.
What is it about the universal law of gravitation that ensures that unless you have extremely large masses at relatively short distances you will not see the objects drawn to each other as you would for example with magnets having opposite poles placed near each other?
The universal law shows that the force of gravity is proportional to the masses of the two objects and inverse to the distance between the two objects. Therefore, two masses must be large and the distance must be short to show an effect.
You have two objects with one having a mass five times that of the other and they are separated from each other by a distance of one unit. How would the force of gravity change if you now increased the mass of each object by a factor of five and reduced the distance between to one-half of its former amount?
The force of gravity would change by a factor of 50N.
Force of Gravity = G(Mass1xMass2)/Distance^2
What are the reasons why if you were in the space shuttle you are able to float around as if you were weightless? Has your mass changed in any way?
The shuttle is in free fall but it will not fall to Earth because of its orbital velocity. As you accelerate towards the Earth, the Earth is curving away from the shuttle. Mass is constant and does not change as a result of the weightlessness.
How is the action of the force of gravity different from a conventional push or pull type of force exerted on an object on the Earth?
Gravity is different because it is strictly an attractive force. If it were repulsive, the entire universe would fall apart. It is different from the push or pull type of force because they can be both attractive or repulsive
If forces are equal and opposite, if you fell off the roof of a six-story building why would you fall rather then be suspended in mid-air?
Because the force that is acting equally and opposite to your fall is the Earth’s gravity. Since the Earth’s mass is so huge, the acceleration imparted to the Earth by your body’s acceleration is negligible, which is why your body falls to the ground.
Why is gravity the only force in nature that is responsible for the large-scale structure of the universe?
Because it is the only force that acts on al particles with mass, has an infinite range, is always attractive, and cannot be absorbed, transformed, or shielded against.
How does the principle of universal gravitation explain why it is the Earth that orbits around the Sun and not the reverse?
because the sun has a much larger mass than the Earth. The strength of the gravitational force depends on the mass of an object, and since the sun has a greater mass, the Earth must be attracted to the Sun’s gravitational force rather than falling through space.
Why did Newton believe that it would be possible for artificial earth satellites to be placed into orbit?
Why must a satellite have a minimum velocity in order to stay in orbit?
What happens that will eventually causes all the satellites that have been placed in orbit around the Earth to eventually fall out of orbit and burn up in the atmosphere?
A)Because a satellite would fall toward the Earth but it would be moving as the Earth curved away from it on its orbital path. He believed that the force would push the satellite into orbit.
b) because it is helping the satellite maintain the minimal centripetal force that will allow it to remain in orbit.
c) because they lose the velocity necessary to maintain orbit around the Earth (orbital decay)
Why were Newton’s ideas about satellites not actually be able to put into practice until 1957?
The first artificial satellite was launched by the Soviets in 1957.
How did Newton explain the phenomenon of the tides?
The lunar gravity on the near side of Earth is stronger than on the far side. Since water distorts and moves more, it is more easily pulled toward the moon. The largest tides occur when the moon and sun tug in the same direction, which occurs twice a day.
What events can lead to extraordinary high tides each lunar month?
When the moon is full, the gravitational pull of the moon and sun are combined. At these times, the high tides are very high and the low tides are very low. This is known as a spring high tide. They occur when the Earth, the Sun, and the Moon are in a line. The gravitational forces of the Moon and the Sun both contribute to the tides.
If an object on the surface of the Earth has a mass of 100 kg, what would its weight be in Newton’s and in pounds?
Newtons à 980.665002864
Pounds à 220.462
What major aspect concerning gravity could Newton never explain in his lifetime?
Astronomers discovered the discrepancy between the observed characteristics of the orbit of mercury. He couldn’t explain the orbit that appeared to rotate.
According to Einstein what is the origin of the phenomenon of gravity?
The origin to the phenomenon of gravity is a warping of space and time which is described in his theory of relativity.
If the third law says to every action there is an equal reaction then why did an apple fall
and hit Newton on his head?
Newton explains that while these forces are equal they cause different effects on each object because of differences in mass. An apple is much smaller than the earth, so while each object could be exerting a force of 2 N, the apple only causes a slight acceleration of the Earth because its mass is so large. Additionally, because the apple is so small, the Earth’s force on the apple will have more visible results in the form of the apple falling from the tree.
According to Hobson why “is it a good thing for us that the force of gravity declines at larger distances in just the way it does.”
It is a good thing for us that the force of gravity declines at larger distances in just the way it does because if the gravitational force declined a little faster, the planets would not move in elipses but would instead spiral into the sun. If the gravitational force declined a little more slowly, the gravity from distant stars would dominate the gravity from Earth and again we would not be here.
31. How is Einstein’s view of space and time different than that of Newton’s?
Einstein – space is curved, space and time are interchangeable, mass-energy tells space time how to curve, curved space time tells mass-energy how to move
Newton – space is static and flat and space and time are different things
How did the observation of the position of a specific star as seen in a solar eclipse offer evidence for Einstein’s theory of gravitation?
The positions of starts were recored…The bending of light around massive objects reflected gravitational lensing
Why according to Einstein’s work on light is Newton’s explanation of gravity being an instantaneous force incorrect?
Gravity moves at the same speed as the speed of light in a vacuum
According to Einstein what is the mechanism why the Earth revolves about the Sun and not the reverse?
Theory of relativity
What are gravitational waves?
Why are they so difficult to detect?
Why has the detection of gravitational waves very recently show that Einstein’s theory of gravity and its origins is correct?
Gravitational waves are ripples in the curvature of spacetime that propagate as waves
Gravitational waves are not easily detectable. When they reach the Earth, they have a small amplitude
Weber bar found it by sending signals of light and seeing disruptions in the signals
36. Using Newton’s principles of force and motion and gravitation show why all objects no matter what their size fall to the ground at the same time.
Acceleration= Force/mass. The higher the mass of an object, the higher the force because of this relation as force increases, so does mass. Thus they will equal out since they are being divided by one another.
On page 110 Hobson summarizes one of the lasting achievements of Newton which is the mechanical view of the universe. In your own words what is this view of nature?
This mechanical view of nature compares the universe to a clockwork mechanism whose operating principles were the laws of nature and who’s parts were atoms. This describes that basically every physical system is entirely predictable and that the future is entirely determined by what all the atoms of the universe are doing right now or at any other time. It draws out a universe where there is a loss of free will and the absence of a continuously creative God.
An object is sent outward with a v=20m/s from a building which is 32 m in height. How long will it take the object to reach the ground and how far from the edge of the building will it land?
An object is accelerated at a rate of 4 m/s/s and covers a distance 50m.
What is the amount of time this has taken?
An object is accelerated at a rate of 4 m/s/s and covers a distance 50m.
What is the amount of time this has taken?
What is the velocity of the object at the end of this time period?
A force of 40 N acts on an object to produce an acceleration of 4 m/s/s. What must the mass of the object have been to produce this acceleration?