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# Gravity

Gravity is a natural phenomenon in which all physical bodies are attracted to each other. It is commonly witnessed as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. It is also the same agent that allows your feet to stay on the ground.
Gravity is one four fundamental interactions of nature. The other three include electromagnetism, nuclear strong force and weak force. Gravitational force is the only fundamental force that affects all matter. This force is proportional to the masses of the interacting bodies.

The cosmological perspective of gravitation says it causes dispersed matter to coalesce matter to remain intact. This accounts for the existence of planets, galaxies, stars and most macroscopic objects in the universe. Gravity is also responsible for keeping the Planets in orbit around the sun.
Gravity is what keeps the moon in its orbit around the Earth. The moons gravitational pull is what influences the tides. This occurs by natural convection by the density gradient.

Every planet is surrounded by its own unique gravitational field. The gravitational field is numerically equal to the acceleration of objects under its influence. Earth’s acceleration due to gravity is 9.80665 m/s2 or 32.1740 ft/s2. This is ignoring air resistance.

### Lorentz transform of the components of the velocity

A photon moves at an angle θ with respect to the x' axis in frame S'. Frame S' moves at speed v with respect to frame S (along the x' axis). Calculate the components of the photon's velocity in S, and verify that the speed is c.

### Gravitational time dilation

Someone moves to the top of the World Trade Center in New York and moves back to the ground floor after one year according to a clock located at the ground floor. By how much did this person age?

### Gravitational waves: Computing full metric

Write down the full metric (flat metric plus the perturbation) which represents a sinusoidal wave of frequency 200Hz traveling in the z direction with the cross polarization. The maximum strain of 10^-21 occurs when t=0.

### Converging Lens with Focal Length

See the attached file. 1. A converging lens with a focal length of 3.1 cm is used to image an object which is 3.4 cm away from the lens. How far from the lens is the image? 2. A light beam (initially in air) strikes a substance with an index of refraction of 1.4 at an incident angle of 18.0 degrees. What is the refracted a

### Acceleration Due to Gravity, Time and Horizontal Velocity

1. (PART ONE OF TWO): You drop a stone from a position of rest. How far will it fall vertically in the ?rst 5 s? The acceleration of gravity is 9.8 m/s. 2. ( PART TWO OF TWO): If you instead toss it horizontally at 1.6 m/s, how far will it fall vertically in the ?rst 5 s? 3. A cat chases a mouse across a 1.7 m high table.

### Archimedes' Principle

1. A copper penny has a mass of 2.7 g. What is the buoyant force acting on this penny when dropped into water? (The answer should be 3.0 mN) 2. An iceberg (917 kg/m^3) is floating in the ocean (1,025 kg/m^3). What percentage of the total volume of the iceberg is below the surface of the water? (The answer should be 89.5%)

### Satellites and Gravity

The only force acting on a satellite in its orbit around Earth is the force of gravity from Earth. Why does a satellite not fall down to earth? If you share your idea with reference it helps me to understand the subject more.

### Calculation of Acceleration due to Gravity on Moon's Surface

The mass of the Moon is 7.4 x 10 22 kg and its mean radius is 1.75 x 103 km. What is the acceleration due to gravity on the surface of the Moon? Please provide detailed explanation and reflect your work with units.

### Spring Constant, Length; Work Done by Gravity and Compression

One safety mechanism used in elevators consists of a giant spring located at the bottom of the elevator shaft. In one particular shaft, the spring has a spring constant of 8.00x10^4 N/m, and the elevator car weighs 8250 N. a. Exactly 28.0 m above the spring, the resting elevator's cable snaps and the car falls to the bottom o

### Centripetal acceleration, Angular speed and Tangential speed

1. When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 80.4-kg man just before contact with the ground has a speed of 8.27 m/s. (a) In a stiff-legged landing he comes to a halt in 3.85 ms. Find the magn

### Energy and Gravity

See attached image for picture of problem. A particle P of mass m is fastened to the end of a string with length L. The particle starts from rest, in a position where the string is taut, and the direction of the string forms an angle of 60 degrees with the vertical. In the lowest point of the circular arc, the particle P hits

### Young's Modulus from the slope of the graph and find the error

Calculations: Young's Modulus The Cross section of the wire is 9.07 x 10 -8 m2 length = 0.877 m Net Load (g) Elongation 100 1.11.x 10-4m 200 2.15.x 10-4m 300 3.33.x 10-4m 400 4.37.x 10-4m 500 5.34.x 10-4m 600 6.23.x 10-4m 700 7.11

### Density of Energy in a Point and Specific Gravity of Material

Please show all the work. 1. Determine the density of energy in a point if v=15m/s and P=30N/cm2 for a liquid with &#1139;x=1.4(specific gravity). 2. A hollow sphere with R (exterior) = 10cm and r (interior) = 8.5cm, floats in water with 30% of its volume submerged. Determine the specific gravity of the material of the spher

### Water flow rate through an opening in a tube

Please see attached file for the illustration. Tube B (full of air) is sealed on the top and a 16" OD opening on the bottom. B is 104.6' long. Container E (full of air) is inserted into section H and permanently fixed in place. B is inserted fully into container C. Water rises 59.6' into B. H is 45' feet of air. See Illus

### Find the gravitational force exerted by multiple objects

Objects with masses of 170 kg and a 470 kg are separated by 0.320 m. (a) Find the net gravitational force exerted by these objects on a 70.0 kg object placed midway between them. (b) At what position (other than infinitely remote ones) can the 70.0 kg object be placed so as to experience a net force of zero? _______ m fro

### Tension on a String, Centripetal Acceleration

4. A boy whirls a ball on a string 1.0 m long in a horizontal circle at 50 rpm. If the mass of the ball is 0.22 kg, what is the tension in the string? 5. A jetliner traveling at 600 km/h is turning in a circle of radius 2.5 km. What is its centripetal acceleration? 6. A 4.0-kg object is lifted 1.5 m. (a) How much work is d

### Motion Problems

Please provide a detailed step by step solution to this problem. Thanks. The space shuttle orbits the Earth in a near-circular orbit at a constant speed at approximately 100 miles above the Earth's surface. If we assume that the centripetal acceleration is equal to the acceleration due to gravity at sea level (9.8 m/s2) and t

### Simple pendulum period depends on length, amplitude, gravity

Consider an ideal pendulum consisting of a "bob" of mass m hanging from a light (massless) string of length L. The pendulum swings back and forth in simple harmonic motion (SHM). You may assume that the oscillations are small, so that the motion is "ideal" SHM. Which of the following statements are true? 1. If the string len

### Find momentum and force on an accelerating object

An 850 kg dragster accelerates from rest to 90 km/h in 0.90 seconds. (a) What is the change in momentum of the car? kg·m/s (b) What is the average force exerted on the car? N (c) What exerts that force? the dragster inertia the track through friction gravity the motor

### Gravitation: 4 Problems

1) The following formula represents the period of a pendulum,T. T = 2π(l/g) (a) What would be the period of a 1.8 m long pendulum on the moon's surface? The moon's mass is 7.34 1022 kg, and its radius is 1.74x10^6 m. 2) A force of 40.9 N is required to pull a 10.2 kg wooden block at a constant velocity across a smooth gla

### Insterstellar Travel and Difficulties

Will it be possible in the future to travel to other stars ? What difficulties are there? Please use the web for suitable, supporting articles. - Provide references (do not use Wikipedia)

### 4 Physics multiple choice: satellite orbit, airplane downward dive, force on the moon,

1) Imagine a 560 kg satellite in a circular orbit around the earth with a period of 4.8 hours. (a) Determine the height of the satellite above the surface of the earth (b) Determine the speed of the satellite in m/s. (c) Determine the force of gravity on the satellite. Mass of Earth = 6.0 x 1024 kg Radius of Earth = 6.4 x

### Specific Gravity and Density

What are the units of specific gravity? Assuming that the density of water is 0.997 g.mL^-1 and the specific gravity of gold is 19.28 what is the density of gold in g.mL^-1? In pounds per cubic foot? my attempt: no units for specific gravity. Density of gold in g.ml^-1 = 19.2 g/mL^-1 I have no idea how to convert to pounds p

### Magnitude of Gravitational Froce

A 509 kg uniform solid sphere has a radius of 0.409 m. Find the magnitude of the gravitational force exerted by the sphere on a 50.9 g particle located (a) 1.48 m from the center of the sphere _______ N (b) at the surface of the sphere _______ N (c) 0.206 m from the center of the sphere _______ N

### Gravitational attraction

Three masses are arranged on the vertices of an equilateral triangle. Find the gravitational force (magnitude and direction) on one of them according to the data given in the file. An equilateral triangle 59.0 m on a side has a m1 = 20.00 kg mass at one corner, a m2 = 35.00 kg mass at another corner, and a m3 = 115.00 kg mass

### Center of gravity

Please see the problem at the following link: http://books.google.com/books?id=LiRLJf2m_dwC&printsec=frontcover&dq=vector+calculus+marsden#PPA481,M1 It is problem 14 on page 481 (section 7.5). Please show me how to do this problem correctly. Thank you

### The force of gravity is calculated.

Please help with the following problems. 1. Calculate the force of gravity on a 65-kg person in the following: a. at the surface of the Earth (R=6400km) b. at twice the Earth's radius c. at four times the Earth's radius 2. Plot this gravitational force with distance. What pattern or relationship do you expect to

### Vertical motion under gravity

Please help with the following problem. You are standing on a balcony 30 feet off the ground. You want to throw your key to someone on the ground. You throw it angled upward with initial velocity of 55 ft/sec. assume that the acceleration due to gravity is -32 ft/sec/sec. A) find the position function in terms of time, t.

### Motion under Gravity

Two identical balls are thrown from the top of a building with the same speed. Ball (theta) above the 1 is thrown horizontally, while ball 2 is thrown at an angle horizontal. Neglecting air resistance, which ball will have the greatest speed when hitting the ground below?

### Density or Relative Density or Specific Gravity

A 0.53 kg piece of wood floats in water but is found to sink in alcohol (specific gravity = 0.79) in which it has an apparent mass of 0.040 kg. What is the SG or density or relative density of the wood?