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4. (a) Assume the equation x = At + Bt describes the motion of a particular object, with x having the dimen- sion of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt= 3At + B.3 7. FAT T.B

4. (a) Assume the equation x = At + Bt describes the motion of a particular object, with x having the dimen- sion of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt= 3At + B.3 7. FAT T.B

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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16 Chapter 1 Physics and Measurement 30.231 (a) Determine the proper units for momentum using dimensional analysis. (b) The unit of force is the new-61o24 ton N, where 1 N 1 kg m/s. What are the units.of momentumpin terms of a newton and anothher funda- piental SI uit? 12 Newton's law of universal gravitation is represented by GMm 30.131 MM.X where F is the magnitude of the gravitartional force exerted by one small object on another, M and m are the masses of the objects, and ris a distance. Force has the SI units kg m/s. What are the SI units of the pro- W (a portionality constant G? G2 13. The position of a particle moving under uniform accel- eration is some function of time and the acceleration. 22. A ta Suppose we write this position as x = ka e, where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m 1 and n 2. Can this analysis give the value of k? = 14. (a) Assume the equation x =At + Bt describes the motion of a particular object, with x having the dimen- sion of length and t having the dimension of time. Determine the dimensions of the constants A and B. 23. 24. M (b) Determine the dimensions of the derivative dx/dt = 25. トミドー Section 1.4 Conversion of Units 3A + B.L tT L AT T.B FAT! to 15. A solid piece of lead has a mass of 23.94 g and a volume W of 2.10 cm3. From these data, calculate the density of 26 lead in SI units (kilograms per cubic meter). 23.9L10 23.95 6. An ore loader moves 1 200 tons/h from a mine to the surface, Convert this rate to pounds per second, using 20 1 ton 2 000 lb. 1200 fors 62- 36బది్వ 7. A rectangular building lot has a width of 75.0 ft and a length of 125 ft. Determine the area of this lot in square meters. 3.281f=1m 8. Suppose your hair grows at the rate 1/32 in. per day. V Find the rate at which it grows in nanometers per sec- ond. Because the distance between atoms in a mole- cule is on the order of 0.1 nm, your answer suggests how rapidly layers of atoms are assembled in this pro- tein synthesis. 75.0x125k 1m 3-2g* 24 32 T 146) 9. Why is the following situation impossible? A student's dor- mitory room measures 3.8 m by 3.6 m, and its ceiling is 2.5 m high. After the student completes his physics course, he displays his dedication by completely wall- papering the walls of the room with the pages from his 2.
Transcribed Image Text:16 Chapter 1 Physics and Measurement 30.231 (a) Determine the proper units for momentum using dimensional analysis. (b) The unit of force is the new-61o24 ton N, where 1 N 1 kg m/s. What are the units.of momentumpin terms of a newton and anothher funda- piental SI uit? 12 Newton's law of universal gravitation is represented by GMm 30.131 MM.X where F is the magnitude of the gravitartional force exerted by one small object on another, M and m are the masses of the objects, and ris a distance. Force has the SI units kg m/s. What are the SI units of the pro- W (a portionality constant G? G2 13. The position of a particle moving under uniform accel- eration is some function of time and the acceleration. 22. A ta Suppose we write this position as x = ka e, where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m 1 and n 2. Can this analysis give the value of k? = 14. (a) Assume the equation x =At + Bt describes the motion of a particular object, with x having the dimen- sion of length and t having the dimension of time. Determine the dimensions of the constants A and B. 23. 24. M (b) Determine the dimensions of the derivative dx/dt = 25. トミドー Section 1.4 Conversion of Units 3A + B.L tT L AT T.B FAT! to 15. A solid piece of lead has a mass of 23.94 g and a volume W of 2.10 cm3. From these data, calculate the density of 26 lead in SI units (kilograms per cubic meter). 23.9L10 23.95 6. An ore loader moves 1 200 tons/h from a mine to the surface, Convert this rate to pounds per second, using 20 1 ton 2 000 lb. 1200 fors 62- 36బది్వ 7. A rectangular building lot has a width of 75.0 ft and a length of 125 ft. Determine the area of this lot in square meters. 3.281f=1m 8. Suppose your hair grows at the rate 1/32 in. per day. V Find the rate at which it grows in nanometers per sec- ond. Because the distance between atoms in a mole- cule is on the order of 0.1 nm, your answer suggests how rapidly layers of atoms are assembled in this pro- tein synthesis. 75.0x125k 1m 3-2g* 24 32 T 146) 9. Why is the following situation impossible? A student's dor- mitory room measures 3.8 m by 3.6 m, and its ceiling is 2.5 m high. After the student completes his physics course, he displays his dedication by completely wall- papering the walls of the room with the pages from his 2.
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