Technical Measurement and Vector
Chapter 1: Technical Measurement and Vector
5. Newton’s law of universal gravitation is represented by
[pic]
where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg ∙ m/s2. What are the SI units of the proportionality constant G?
8. The speed of light is now defined to be 2.99 7924 58 × 108 m/s. Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.
15. A rectangular building lot measures 100 ft by 150 ft. Determine the area of this lot in square meters (m2).
19. The speed of light is about 3.00 × 108 m/s. Convert this figure to miles per hour.
22. (a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while, federal law mandated that the maximum highway speed would be 55 mi/h. Use the conversion factor from part (a) to find the speed in kilometers per hour. (c) The maximum highway speed has been raised to 65 mi/h in some places. In kilometers per hour, how much of an increase is this over the 55-mi/h limit?
5. A plane flies from base camp to lake A, a distance of 280 km at a direction of 20.0° north of east. After dropping off supplies, the plane flies to lake B, which is 190 km and 30.0° west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.
6. Vector [pic] has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x-axis. Vector [pic] also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods, find (a) the vector sum [pic] + [pic] and (b) the vector difference [pic] – [pic].
15. A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120° with the positive x-axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0° to the positive x-axis. Find the
5. Newton’s law of universal gravitation is represented by
[pic]
where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg ∙ m/s2. What are the SI units of the proportionality constant G?
8. The speed of light is now defined to be 2.99 7924 58 × 108 m/s. Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.
15. A rectangular building lot measures 100 ft by 150 ft. Determine the area of this lot in square meters (m2).
19. The speed of light is about 3.00 × 108 m/s. Convert this figure to miles per hour.
22. (a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while, federal law mandated that the maximum highway speed would be 55 mi/h. Use the conversion factor from part (a) to find the speed in kilometers per hour. (c) The maximum highway speed has been raised to 65 mi/h in some places. In kilometers per hour, how much of an increase is this over the 55-mi/h limit?
5. A plane flies from base camp to lake A, a distance of 280 km at a direction of 20.0° north of east. After dropping off supplies, the plane flies to lake B, which is 190 km and 30.0° west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.
6. Vector [pic] has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x-axis. Vector [pic] also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods, find (a) the vector sum [pic] + [pic] and (b) the vector difference [pic] – [pic].
15. A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120° with the positive x-axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0° to the positive x-axis. Find the