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Name: _____________________ ____________________ Period: ____ Date: _____________________ Dynamics: Forces of Nature and Gravity - There are only 4 different natural forces. “Natural forces” are those that can exist anywhere in the universe. o o o o - Gravity is the weakest force but has shaped the universe due to it having the longest range. The Force of Gravity All masses are surrounded by a gravitational force field. The Force of gravity per 1.0 kg mass on surface greater the mass, the ________________the gravitational force. The table at the right compares the gravitational forces Mass of Earth 5.98 x 1024 kg 9.8 Newtons on the surfaces of the Earth and moon. Mass and Weight: recall the important distinction between the mass and weight of an object. Mass is a measure of the Radius of Earth 6.38 x 106 m Mass of Moon 7.35 x 1022 kg amount of _____________________ there is in an object and is measured in kilograms. Weight, however, is the measure of Radius of Moon 1.74 x106 m ____________________ ____________________ on an object and is measured in ___________________. Thus, when you go from Earth to the moon, your mass stays constant, while your weight reduces to about 1/6th of your Earth weight. The relationship between mass and weight is given by the formula Fg = mg Fg is the force of gravity (i.e., weight) on an object measured in Newtons m is its mass in kg g is the gravitational field strength of 9.8 N/kg which results in an acceleration of 9.8 m/s2 near the Earth’s surface (sea level) 1.6 Newtons The changing values of “g” can be seen in the following table. Location Equator Value of “g” 9.781 m/s2 or N/kg 9.832 m/s2 or N/kg north or south pole Location 6400 km above Earth’s surface surface of the moon Value of “g” 2.45 m/s2 or N/kg 1.60 m/s2 or N/kg Sample Questions Q1. On the surface of Earth, the mass of an object is 6.3 grams. What is its weight in Newtons? Q2. Calculate the mass, in kg, of an object which has a weight of 35 N on the moon. The value of “g” on the moon is 1.6 m/s2. The Law of Universal Gravitation The force of gravity between two objects is as follows: F is __________________________________________________________ m1 and m2 are __________________________________________________ d is __________________________________________________________ G is the ____________________ ____________________ of 6.67 x 10-11 Nm2/kg2 Sample Questions Ex. 1. Calculate the weight (force of gravity) on a 75 kg person near sea level on Earth using the above formula and the Earth’s data from the first page. Ex. 2. An object on our moon is attracted towards the moon by a 320 N force. What is the object’s mass? Ex. 3. Calculate the gravitational field strength, “g,” on Mercury, which has a mass of 3.303 x1023 kg and a radius of 2,440 km. Some Confusing Things About Units MKS units There are, in fact, many different units of force. Three common units are newtons, dynes, and pounds. In physics 11/12, we will focus on a system of units based on the fundamental units of the Meter, Kilogram, and Second, or MKS for short. Therefore, when a force is measured in newtons, distances should be measured in _______________, mass in ________________, and time in ________________. A force in “pounds” is used in the English system where distance is measured in feet, mass in slugs and time in seconds. A force measured in “dynes” uses the centimeter, gram, and second as its fundamental units (CGS units). Blaise Pascal Equivalent Units Units like “Newtons,” “Pascals (pressure), or “Joules” (energy) are not fundamental units (e.g., kg, meters, and seconds), but rather, special unit names usually given to honour famous scientists of the past (i.e., Isaac Newton, Blaise Pascal, and James Joule). All special unit names have fundamental unit equivalents. The fundamental units of force can be obtained from weight <==> mass conversion formula Fg = mg. A rule of any formula is that the units of the left hand side of the equal sign MUST be the same as the units on the right hand side. Therefore: Incorrect Units Unfortunately, the general public incorrectly uses kilograms to indicate weight. Weigh scales are incorrectly calibrated in kilograms (instead of ____________________). Summary Please re-read the notes package on your own (or with a partner ) and come up with your own summary. Exercises 4.1 (Forces and Gravity) 1. Define a "force". _____________________________________________________________________________________ 2a Scientists believe that there are only four "natural" forces in the universe. These are: 1)______________________________________ 2) _______________________________________ 3) _________________________________________ 4) _______________________________________ 2b Two of the above forces are probably not very familiar to you. Where do these two little known forces act? _____________________________________________________________________________________ 3. Distinguish between the terms "mass" and "weight". Use an example which clearly shows the difference between the two. Mass: ________________________________________________________________________________ Weight: ______________________________________________________________________________ Example ______________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ 4a The gravitational acceleration constant "g" is also called the "gravitational field strength" because it is related to the strength of the force of gravity. How does the value of "g" change relative to the height above the surface of the Earth? _____________________________________________________________________________________ _____________________________________________________________________________________ 4b Explain why the value of "g" is slightly larger at the poles compared to the equator? _____________________________________________________________________________________ _____________________________________________________________________________________ 5. What is the formula used to convert between mass and weight? _________________________________ 6a What is meant by the “MKS” system of units? _____________________________________________________________________________________ _____________________________________________________________________________________ 6b The “Newton” is a special unit name of force. What are the equivalent fundamental units of force? _____________________________________________________________________________________ 6c As you know, the fundamental units of “g” are m/s2. But “g” also has a set of equivalent units. From the equation Fg = mg, g can be isolated as g = Fg . Using this form of the equation what are alternate units m for “g”? ____________________________ 6d In the MKS system, the unit of Energy is the “joule”. Energy is also defined by the formula E = Fd (Energy = force x distance). Using this equation and your answer to question 6b, determine the fundamental units of energy. ____________________________ 7. Calculate the weight , in newtons, of... a) a 50 kg bag of sugar b) a 75 gram pen. c) At the equator "g" has a value of 9.781; at the north pole its value is 9.832. What is the difference in weight between an 85.0 kg person at the North pole and an 85.0 kg person at the equator? 8) Calculate the mass, in kilograms, of... a) a 500 Newton bale of hay. b) 6.5 N. 9) A 250 kg spacecraft weighs 2.04x103 N on the surface of the Mars. What is the value of "g" on the Mars? 10. A 20 kg object out in space is attracted to the Earth by a force of gravity of 100 N. What is the rate of acceleration of this object toward the Earth in free fall? 11) A 1250 kg spacecraft is 6.38 x 107 m from the center of the Earth. What is the force of gravity between the craft and Earth ? 12. Calculate the force of gravity between two 2575 kg asteroids 50.0 cm apart? What is the force when they are 5.00 cm apart? How much stronger as a ratio is the force when the distance is a tenth? Answers: 6c) N/kg, 6d) kg.m2/s2 , 7a) 490 N, 7b) 0.74 N, 7c) 4.3 N, 8a) 51 kg 8b) 0.66 kg, 9) 8.16 m/s2, 10) 5.0 m/s2. 11) 122 N 12) 1.77 x 10-3, 1.77 x 10-1, 100