8/8/2011 Physics 111 Practice Problem Statements 01 Units, Measurement, Vectors SJ 8th Ed.: Ch , 3.1 – 3.4 Course Introduction What is Physics? Mechanics is the most basic field of Physics Measurement Measurements Systems of Units Conversion of Units Vectors Coordinate Systems Vectors and Scalars Vector Addition, and Subtraction Components of Vectors and Unit Vectors Adding Vectors by Components Scalar multiplication of Vectors Dot Product of Two Vectors Cross Product (Vector Product Contents: 1-7, 1-9, 1-10, 1-12, 1-15, 1-21* 3-5, 3-6, 3-15, 3-17, 3-19, 3-21*, 3-31*, 3-37

8/8/2011 Problem 1-7P: Antarctica is roughly semicircular, with a radius of 2000 km (Fig.1-5). The average thickness of its ice cover is 3000 m. How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of Earth.)

8/8/2011 Problem 1-9P: Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm dumped 2.0 in. of rain in 30 min on a town of area 26 km2. What volume of water, in acre-feet, fell on the town?

8/8/2011 Problem 1-10E: Physicist Enrico Fermi once pointed out that a standard lecture period (50 min) is close to 1 microcentury. (a) How long is a microcentury in minutes? (b) Using the formula find the percentage difference from Fermi's approximation.

8/8/2011 Problem 1-12E: A unit of time sometimes used in microscopic physics is the shake. One shake equals sec. (a) Are there more shakes in a second than there are seconds in a year? (b) Humans have existed for about 10 6 years, whereas the universe is about years old. If the age of the universe now is taken to be 1 “universe day,” for how many “universe seconds” have humans existed?

8/8/2011 Problem 1-15P: An astronomical unit (AU) is the average distance of Earth from the Sun, approximately km. The speed of light is about m/s. Express the speed of light in terms of astronomical units per minute.

8/8/2011 Problem 1-21P*: (a) Assuming that each cubic centimeter of water has a mass of exactly 1 g., find the mass of one cubic meter of water in kilograms. (b) Suppose that it takes 10.0 h. to drain a container of 5700 m 3 of water. What is the “mass flow rate,” in kilograms per second, of water from the container?

8/8/2011 Problem 3-5E: The x component of vector is m and the y component is m. (a) What is the magnitude of ? (b) What is the angle between the direction of and the positive direction of x?

8/8/2011 Problem 3-6E: A displacement vector r in the xy plane is 15 m long and directed as shown in Fig Determine (a) the x component and (b) the y component of the vector.

8/8/2011 Problem 3-15E: Vector a has a magnitude of 5.0 m and is directed east. Vector b has a magnitude of 4.0 m and is directed 35° west of north. What are a) the magnitude and (b) the direction of a + b ? What are (c) the magnitude and direction of b - a ? (e) Draw a vector diagram for each combination?

8/8/2011 Problem 3-17E: Two vectors are given by a = (4.0 m) i + (-3.0 m) j + (1.0 m) k and b = (-1.0 m) i + (1.0 m) j + (4.0 m) k In unit-vector notation, find (a) a + b, (b) a - b, and (c) a third vector c such that a - b + c = 0.

8/8/2011 Problem 3-19P: Three vectors a, b, and c each have a magnitude of 50 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 30°, 195°, and 315°, respectively. What are (a) the magnitude and (b) the angle of the vector a + b + c, and (c) the magnitude and (d) the angle of a - b + c ? What are (e) the magnitude and (f) the angle of a fourth vector d such that ( a + b ) - ( c + d ) = 0 ?

8/8/2011 Problem 3-21P*: The two vectors a and b in Fig have equal magnitudes of 10.0 m. Find (a) the x component and (b) the y component of their vector sum r, (c) the magnitude of r, and (d) the angle r makes with the positive direction of the x axis.

8/8/2011 Problem 3-31P*: Use the definition of scalar product, a ·b = ab cos , and the fact that a ·b = a x b x + a y b y + a z b z (see Exercise 30) to calculate the angle between the two vectors given by a = 3.0 i j k and b = 2.0 i j k.

8/8/2011 Problem 3-37P: The three vectors in Fig have magnitudes a = 3.00 m, b = 4.00 m, and c = 10.0 m. What are (a) the x component and (b) the y component of a ; (c) the x component and (d) the y component of b ; and (e) the x component and (f) the y component of c ? If c = p a + q b, what are the values of (g) p and (h) q?