Newton's Law of Universal Gravitation
Apples had a significant contribution
to the discovery of gravitation. The
English physicist Isaac Newton
(1642-1727) introduced the term
"gravity" after he saw an apple
falling onto the ground in his garden.
"Gravity" is the force of attraction
exerted by the earth on an object.
The moon orbits around the earth
because of gravity too. Newton later
proposed that gravity was just a
particular case of gravitation. Every
mass in the universe attracts every
other mass. This is the main idea of
Newton's Law of Universal
Gravitation.
A portrait of Issac Newton.
Courtesy of AIP Emilio Segre Visual
Archives, W.F. Meggers Collection.
The law was published in Newton's
famous work, the Principia
("Mathematical Principles of Natural
Knowledge") in 1687. It states that every
particle in the universe exerts a force
on every other particle along the line
joining their centers. The magnitude
of the force is directly proportional
to the product of the masses of the
two particles, and inversely
proportional to the square of the
distances between them.
In mathematical terms:
By team C007571, ThinkQuest2000.
where and are the masses of the two
particles,
r is the distance between the two
masses,
F is the gravitational force between
them, and
G is the universal gravitational
constant,
.
The above equation only calculates the
gravitational force of the simplest case
between two particles. What if there are
more than two? In that case, we
calculate the resultant gravitational force
on a particle by finding the vector sum of
all the gravitational forces acting on it:
By adding the unit vector to the
equation, F now processes a direction!
Interactively test the effects of
gravitation on planets!
Newton derived the relation in such a
way that F is proportional to m
because the force on a falling body
(remember the apple?) is directly
proportional to its mass by Newton's
2nd law of motion: F...

...LAB: Force Lab
Research Question: How does the change in mass of an object affect the force and time while the object is moving down a height of 31cm?
Hypothesis: My prediction is that the greater the mass of the toy car the larger the force of gravity, as the product of the masses of two objects increases, the force of gravity that attracts them toward each other increases. According to Newton’s law of universal gravitation, “gravity and mass are directly proportional” hence, creating a greater force of gravity and a faster speed. As well as, Newton’s second law of motion is: “Force = Mass x Acceleration” and if the mass is larger the force will be greater.
Newton’s law of universal gravitation.
Newton’s law of universal gravitation.
Variables:
IV (Independent Variable): The mass of the car (kg)
DV (Dependent Variable): The time (seconds)
CV (Control Variable): same timer , same distance travelled (1.2 m), same weighing scale, height of the ramp (31 cm), surface of ramp, the same toy car.
Materials:
* A timer set to 0.00 (seconds)
* A weighing scale
* A measuring tape (meters)
* A toy car
* 5 weights, each measuring 10 grams
* A wooden ramp
* Laboratory Jack
* Scotch tape
* Calculator (for the calculations)
* Pencil/Pen
* Paper (for results table)
Method:
1. Get into groups of three or four...

...The History of Classical Gravitational Theory and General Relativity
In the beginning scientists and religious men of their era tried to explain the universe both biblically and scientifically. One of the foremost Greek scientists was Aristotle; taught by Plato, that the circle and sphere are the two most perfect shapes in a 2 and 3 dimensional universe, Aristotelian system placed Earth at the center of the universe; and all other heavenly bodies revolved around the earth in crystalline orbitals.
Another Greek Mathematician, Aristarchus theorized that the sun was the center of the universe and that the Earth revolved around it. His simple reasoning was constituted purely by the fact that the Earth is a much smaller body than the sun, and the smaller should orbit the greater.
By the 2nd century CE it became more and more apparent that the simplistic models derived nearly 2000 years before, were flawed. Kepler, a Scientist of the early 1600s concluded not only that the previously stated purely circular orbitals around the sun were in fact ellipses, and that planets travel faster when near the sun, and slower when farther from the sun, and lastly he found that the mathematical relationship between the orbital period, and the orbital radius of any given planet.
While Kepler was creating a new model of the universe Galileo Galilei was tearing apart the out dated Aristotelian system. Conceiving the theory of inertia, disproving the...

...CENTRIPETAL FORCE ON A PENDULUM
OBJECTIVE
To measure centripetal force exerted on a pendulum using the force sensor bob and in so doing compare this value determined by force calculations based on the height of the pendulum.
THEORY
Newton’s laws of motion are the basis for this experiment. Newton’s first law of motion states that a body in motion will remain in motion unless acted upon by an external force. Newton’s second law of motion states that the rate of momentum of a body is dependent on the product of its mass and acceleration. Where rate of change of momentum is given by
=
A pendulum bob follows a circular path and is therefore acted upon by centripetal force. In this experiment the tension in the string causes the bob to follow a circular path. From Newton’s second law of motion above it is related to the experiment as shown
= T- mg =ma =
Where T is the tension in the string
m is the mass of the pendulum
g is acceleration due to gravity
is the centripetal force
The force measured by the force sensor when the pendulum passes through the lowest point of the swing is equal to centripetal force. This is because the force sensor is zeroed when the pendulum is at rest in its equilibrium position, where T= mg.
Centripetal force can also be found from the relationship below...

...Chapter 1 Vectors, Forces, and Equilibrium
1.1 Purpose
The purpose of this experiment is to give you a qualitative and quantitative feel for vectors and forces in equilibrium.
1.2
Introduction
An object that is not accelerating falls into one of three categories: • The object is static and is subjected to a number of diﬀerent forces which cancel each other out. • The object is static and is not being subjected to anyforces. (This is unlikely since all objects are subject to the force of gravity of other objects.) • The object is moving with constant velocity. In this case, the object may be subject to a number of forces which cancel out or no force at all. This case is not considered in this lab. The category of physics problems that involve forces in static equilibrium is called statics. Physicists and engineers are subjected to static problems quite frequently. A few examples of these principles in use are seen in the design of bridges and the terminal velocity of a person falling through the air. Mathematically, forces in equilibrium are just a special case of Newton’s Second Law of Motion, which states that the sum of all forces is equal to the mass of the object multiplied by the acceleration of the object. The special case of forces in equilibrium (static), occurs when the acceleration of the object is...

...Force in effect when car brakes
A car of mass m=1200 kg is traveling at a speed of 50km/h. Suddenly the brakes are applied and the car is brought to a stop over a distance of 20m. Assuming constant breaking force find:
(1) the magnitude of the breaking force,
(2) the time required to stop.
(3) What will be the stopping distance if the initial speed is 100km/h?
Solution.
Most of problems from Dynamics can be seen as “two parts problem”, one involving kinematics and the other - dynamics. This is a consequence of Newton’s Second Law - Force is a product of mass and acceleration.
Acceleration by itself is a purely “kinematical” problem. When mass is involved, we go into Dynamics.
In our problem the following are given:
m = 1200 kg – mass of the car,
v1 = 50 km/h – initial speed in the first case,
D1 = 20m – stopping distance in the first case,
v2 = 100 km/h – initial speed in the second case.
We are suppose to find:
F = ? – magnitude of breaking force,
t = ? – the time required to stop,
D2 = ?<="" p="">
We write down formulas which involved the unknown quantities,
F = ma (1)
a = v1/t (2)
D1 = v1t –(1/2) a t2 (3)
Some explanations:
Formula (1) is simply Newton’s Second Law of Motion,
formula (2) – the speed decreases from v1 to 0 during time t. Assuming constant breaking force means constant acceleration (deceleration or acceleration...

...HYDROSTATIC FORCE (EXPERIMENT 1)
INTRODUCTION
The determination of force which are exerted by liquid which are at rest on surface immersed in liquids. From the study by hydrostatic, the following principles have been established :
a) There are no shear stress present when the fluid is not in motion.
b) The pressure exerted by a fluid under hydrostatic conditions. This pressure acts perpendicular to an immersed surface.
c) Hydrostatic pressure various linearly, increasing with an increase in depth.
OBJECTIVES
1. To determine the hydrostatic thrust on a plane surface partly immersed in water.
2. To determine the position of the line of action of the thrust.
3. To compare the position determined by experiment with the theoretical position .
4. To verify the formula for calculating hydrostatic thrust.
THEORY
When the quadrant is immersed in water it is possible to analyze the forces acting on the surfaces of the quadrant as follows:
The hydrostatic force at any point on the curved surface is normal to the surface and therefore resolves through the pivot point because this is located at the origin of the radii. Hydrostatic forces on the upper and lower curved surfaces therefore have no net effect – no torque to affect the equilibrium of the assembly because all of these forces pass through the pivot.
The forces on the sides of the...

...Definition of Force
A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces onlyexist as a result of an interaction.
Velocity, Acceleration, Momentum, and Impulse
Velocity, in physics, is a vector quantity (it has both magnitude and direction), and is the time rate of change of position (of an object). However, quite often when you read ‘velocity’, what is meant is speed, the magnitude of the velocity vector (speed is a scalar quantity, it has only magnitude). For example: escape velocity (the minimum speed an object needs to escape from a planet, say); note that this can be easily turned into a velocity, by adding ‘in the direction radially out from the center of the planet’, and that this direction is sometimes implied (if not actually stated).
Velocity is a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion. In calculus terms, velocity is the first derivative of position with respect to time.
The most common way to calculate the constant velocity of an object moving in a straight line is with...

...IB PHYSICS HL
Lab: Centripetal Force
BACKGROUND/PURPOSE:
*In this section of your lab write-up, be sure to include all equations and
background information
-For motion along a straight line, a constant net force F acting on a body of mass m produces a constant acceleration a, related to the force through Newton's law:
F = ma
-When the same object is moving in a circle at a constant speed, the acceleration of the object is given by the following equation:
a = v2/r
-In this experiment, you will use these two equations and some simple measurements to determine the unknown mass of a rubber stopper as it rotates in a horizontal circle around a fixed center point.
PROCEDURE:
The equipment that you will use is as follows:
-Glass tube
-Rubber stopper
-String
-Hanging masses (washers)
When the glass tube is swung in a small circle above your head, the rubber stopper moves around in a horizontal circle at the end of a string. The string is threaded through the tube and fastened to some washers hanging below. The force of gravity on these washers, acting along the string, provides the centripetal force needed to keep the stopper moving in a circle.
Before taking any measurements, get a feel for the apparatus. With only one washer on the end of the string to keep the stopper from getting away, whirl the stopper over your head while holding onto the string below the tube.
The mass of the stopper...