Mechanics: Fundamental Units and Conversions Questions
Homework 1 1. What are the fundamental quantities in mechanics? 2. What are the chosen units for the three fundamental quantities in the SI system, what are them in the British system 3. What is the current standard for each of the three fundamental units in the SI system? 4. Convert the following magnitudes into the corresponding SI unit a. 12.4 miles b. 67 s c. 12.4 in d. 45 ft e. 35 tons (1 ton=1Mg) 5. Kinetic energy is defined a E= ½ mv2, where m is the mass of the object and v its speed. What are the SI units of energy? 6. What are the units of energy in the cgs system (a system where the three fundamental units are centime, gram, and second) 7. Estimate the distance travelled by light is 1.5 years 8. Imagine you have access to a time machine and decide to travel back in time to live the US declaration of independence (year 1776). While waiting for that event, you happen to be standing by a scientist. You remember you have a test in PHYS153 so you ask her for the name of the smallest particle matter is made of, a. What would this scientist answer? b. What would be today’s answer? 9. The atomic number of Au is 79 and its atomic mass is 197, how many protons and neutrons does a Au atom have? How many electrons? 10. Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration, x is distance, and t is time) a) v/t2 b) vx2 c) v2/t d) at 11. Which expression is dimensionally consistent with an expression that would yield a value for time−1?(v is velocity, x is distance, and t is time) a) v/x b) v2/x c) x/t d) v2t 12. If the displacement of an object, x, is related to the acceleration, a, according to the relation x = Aa, what is the dimension of A? 13. The speed of a boat is often given in knots, what would this unit be in the SI? 14. If a is acceleration, v is velocity, x is position, and t is time, then which equation is not dimensionally correct? a) t = x/v b) a = v2/x c) v = a/t d) t2 = 2x/a 15. Suppose an equation relating position, x, to time, t, is given by x = b t3 + c t4, where b and c are constants. What are the dimensions of b and c? 16. How many significant figures are in the following numbers a) 122.34 b) 23004.1 c) 1.23×103 d) 0.00340×102 17. Do the following operations and express the results with the appropriate number of figures a. 25.87+12.4+1.234×103-23.679011 b. 12.4 x 18.54 x 1.23×105 c. 1.23/2.1 d. (0.41143+0.0034)x25.1 18. On planet Q the standard unit of volume is called the guppy. Space travelers from Earth have determined that one liter = 38.2 guppies. How many guppies are in 150 liters? 19. On planet Z, the standard unit of length is the foose. Ann the Astronaut is 5.90 feet tall on earth. She lands on planet Z and is measured to be 94 foosi tall. Her partner Rachael is 88 foosi tall. How tall is Rachael on Earth? 20. Express Rachael height in the SI system 21. A cereal box has the dimensions of 0.19 m 0.28 m 0.070 m. If there are 3.28 feet per meter, then what is the volume of the box in cubic feet? 22. The distance from the the earth to the sun is 8min light. A light year is the distance traveled by light in one year; if the speed of light is 3 108 m/s, how far in km is the sun? 23. The mass of the sun is 2.0 1030 kg, and the mass of a hydrogen atom is 1.67 10−27 kg. If we assume that the sun is mostly composed of hydrogen, how many atoms are there in the sun? 24. Assume everyone in the United States consumes one soft drink in an aluminum can every two days. If there are 270 million Americans, how many tons of aluminum need to be recycled each year if each can weighs 1/16 pound and one ton = 2000 pounds? *
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