Newton’s Laws of Cooling & Universal Gravitation
Law’s of Cooling:
Newton's law of cooling is used measure the temperature change of an object of some temperature placed in a place of a different temperature. The law states that dT/dt= k(T-R)
where T is the temperature of the object at time t, R is the temperature of the surrounding of the place (constant) and k is a constant of proportionality. This law states that the rate of change of temperature is proportional to the difference between the temperature of the object and that of the surrounding environment.

In order to get the previous equation to something that we can use, we must solve the differential equation. The steps are given below.
1.Separate the variables. Get all the T's on one side and all the t's on the other side. The constants can be on either side. dT/T-R = k dt
2.Anti-differentiate both sides.
Ln( T-R ) = kt - C
3.Leave in the previous form or solve for T.
T= e^kt-C + R
When working with this law, remember that t is the variable, the other letters, R, k, C, are all constants. To find the temperature of the object at a given time, all of the constants first should have numerical values. In some cases of convection, you could apply this law and use it to get whatever it is you need.

Law’s of Universal Gravitation:
Isaac Newton compared the acceleration of the moon to the acceleration of objects on earth believing that gravitational forces were responsible for each other. Newton was able to draw an important conclusion about gravity depending on the certain distance. Fnet = m • a

Newton knew that the force that caused the apple's acceleration (gravity) must be dependent on the mass of the apple. Since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law) that force must also depend on the mass of the earth. The force of gravity acting between the earth and any other object is directly...

...Newton'sLaw of UniversalGravitation
Gravity if one of the four fundamental forces in the universe. Though
the fundamental principles of it eluded scientists until Sir Isaac Newton was
able to mathematically describe it in 1687 (Eddington 93). Gravity plays a
serious part in everyday actions as it keeps everything on the ground; without
gravity everything would be immobile unless a force was applied (then it would
move infinitely because there would be no force to stop it).
Perhaps, the best place to start then would be with such a simple item
as an apple (after all it is what "sparked" Newton's creativity). The apple is
one of the two curiosities (the other being the moon) that led Newton to
discover The Law of UniversalGravitation in 1666 (Eddington 93). As Newton
later wrote, it is the story of the sight of an apple falling to the ground (he
was resting at Woolsthorpe because of the plague at Cambridge) that caused
Newton to wonder if this same force was what held the moon in place (Gamow 41).
Newton knew that an object fell to the earth at a rate of about 9.8
meters (32 feet) per second second as pointed out by Galileo. Thus "the apple
that fell from the tree" fell to Earth at about this rate. For the first basic
explanation of this we will assume a linear plane, one in which all forces act
in only one direction. Therefore when the apple fell...

...UniversalGravitation
Objectives
* Compare and contrast gravitational force vectors as mass and distance are changed. (Explorations 1, 2, and 3)
* Discover how changes in the distance between two objects affects the gravitational force between them. (Explorations 1, 2, and 3)
* Describe how changes in the masses of two objects affects the gravitational force between them. (Explorations 1, 2, and 3)
Description of Activity
In this activity, you will explore how distance and mass affect the gravitational force between two objects. You will select one of three locations to work within: a 9 m2 room, a 9 × 104 m2 city block, or a 9 × 1022 m2 region of space. You will also change the mass of each object as well as manipulate the positions of both objects. For purposes of this simulation, masses will be represented as spheres and the distance between them will be the distance between their centers.
Jump Start
1. What is mass? Mass is a coherent, typically large body of matter with no definite shape.
2. Describe gravitational force. The force of attraction between all masses in the universe; especially the attraction of the earth's mass for bodies near its surface; "the more remote the body the less the gravity"; "the gravitation between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them".
3. How can you tell if one variable is...

...There is a popular story that Newton was sitting under an apple tree, an apple fell on his head, and he suddenly thought of the UniversalLaw of Gravitation. As in all such legends, this is almost certainly not true in its details, but the story contains elements of what actually happened.
What Really Happened with the Apple?
Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines: The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground. Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "accleration due to gravity". Then imagine the apple tree is twice as high. Again, we expect the apple to be accelerated toward the ground, so this suggests that this force that we call gravity reaches to the top of the tallest apple tree.
Sir Isaac's Most Excellent Idea
Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the...

...Physics 31N: Newton’s First Law
Item 1
Two forces have the same magnitude F.
Part A
What is the angle between the two vectors if their sum has a magnitude of 2F?
θ = 0∘
Part B
What is the angle between the two vectors if their sum has a magnitude of 2√F?
θ = 90∘
Part C
What is the angle between the two vectors if their sum has a magnitude of zero?
θ = 180∘
Item 2
An object is moving in the absence of a net force. Which of the following best describes the object's motion?
*The object will continue to move with a constant velocity.
Item 3
An object is moving with constant velocity. Which of the following best describes the force(s) acting on the object?
*The net force acting on the object is zero.
Item 4
A constant net force acts on an object. Which of the following best describes the object's motion?
*The object is moving with a constant acceleration.
Item 5
The same net force is applied to two different objects. The second object has twice the mass of the first object. Compare the acceleration of the two objects.
*The acceleration of object 1 is twice the acceleration of object 2.
Item 6
An object is at rest on a tabletop. Earth pulls downward on this object with a force equal in magnitude to mg. If this force serves as the action force, what is the reaction force in the action–reaction pair?
*The object pulling upward on Earth
Item 7
A large truck collides head-on with a small car. The car is severely...

...7.1 Newton’sLaw of UniversalGravitationNewton’sLaw of UniversalGravitation states that:
Every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Consider two particles of masses m1 and m2 separated by a distance r. Each will exert a force F on the other, given by
where F : gravitational force between the two particles.
m1, m2 : masses of the two particles.
r : distance between the two particles.
G : constant of universalgravitation.
m1
m2
F
F
r
m1
m2
F
F
r
Figure 1
The two forces form an action-reaction pair and have the following characteristics,
* are equal in magnitude,
* are opposite in direction,
* act on different bodies
* are of the same type (gravitational force).
G is a universal constant called the gravitational constant (or constant of universalgravitation), which has been measured experimentally to be : G = 6.67 x 10-11 N m2 kg-2.
Important points to note about Newton’sLaw of Gravitation
1. Newton’sLaw of Gravitation is a universallaw. It applies everywhere in the...

...NEWTON’SLAWS OF MOTION
Newton's First Law of Motion
An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
There are two parts to this statement - one that predicts the behavior of stationary objects and the other that predicts the behavior of moving objects. The two parts are summarized in the following diagram.
The behavior of all objects can be described by saying that objects tend to "keep on doing what they're doing" (unless acted upon by an unbalanced force). If at rest, they will continue in this same state of rest. If in motion with an eastward velocity of 5 m/s, they will continue in this same state of motion (5 m/s, East). If in motion with a leftward velocity of 2 m/s, they will continue in this same state of motion (2 m/s, left). The state of motion of an object is maintained as long as the object is not acted upon by an unbalanced force. All objects resist changes in their state of motion - they tend to "keep on doing what they're doing."
EXAMPLES:
1. Suppose that you filled a baking dish to the rim with water and walked around an oval track making an attempt to complete a lap in the least amount of time. The water would have a tendency to spill from the container during specific locations on the track. In general the water spilled when:
* the container was at rest and you attempted...

...expect to impart to a block of mass 2.5 slugs resting on a frictionless plane if you push it with a force of 20 lb.?
A) 8 ft/sec2 B) 5 ft/sec C) 9 ft/sec2 D) 11 ft/sec2
____ 8. A 50 kilogram mass ball-bearing moves through a mark on the floor with an acceleration of 4 m/sec2. What was the force (in Newton's) acting on the ball-bearing at that point?
A) 150 Newton's B) 200 Newton's C) 175Newton's D) 196 Newton's
_____9. If a bird had a mass of .78 kg and a velocity of 2.2 meters per sec. and a mosquito had a mass of .0842 kg and a velocity of 17.5 meters per sec. which would have the most acceleration?
A) neither B) mosquito C) bird D) they are equal
_____10. Which of Newton'sLaws Of Motion states "anybody moving uniformly in a straight line or at rest will remain in uniform motion or at rest, unless acted upon by some outside force"
A) Newton's second Law B) Newton's first Law C) Newton's third Law D) Newton's forth Law
II. Match the correct law with the example given.
A = 1st Law of Motion B = 2nd Law of Motion C = 3rd Law of Motion
11.________ The acceleration of an object...

...dtunName_________________________________
Home Challenge Lab 2- The force of Gravity
Topics covered in this lab:
The force of gravity
Newton’sLaws
One of the topics we have discussed is acceleration, meaning that the velocity of the object under study was changing. What causes something to accelerate? In this lab you will investigate the forces that affect the motion of objects.
Gravity
Materials:
<!--[endif]-->Something to toss (Please choose an object that will not break)
Toss an object straight up into the air and catch it as it falls back down. Carefully watch the objects vertical position as a function of time. Repeat your toss enough times that you are sure that you understand the motion of the object.
In order to answer the following questions, imagine that you were able to measure the distance of the object above your hands, the velocity of the object, and the acceleration of the object, all as a function of time. You may want to reference the power point lecture of the diagrams in your text to help answer these questions. Please give detailed answers in complete sentences.
What is the velocity of the object at the very top of its path?
Is the velocity of the object changing during the entire flight or just at certain times?
Explain.
What is the acceleration of the object at the very top of its path?
Does the acceleration of the object change while it is in flight?no...