Problem 53
The density of air under standard laboratory conditions is 1.29 kg/m\(^3\), and about 20% of that air consists of oxygen. Typically, people breathe about \\(\frac{1}{2}\\) L of air per breath. (a) How many grams of oxygen does a person breathe in a day? (b) If this air is stored uncompressed in a cubical tank, how long is each side of the tank?
Problem 54
A rectangular piece of aluminum is 7.60 \(\pm\) 0.01 cm long and 1.90 \(\pm\) 0.01 cm wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional uncertainty in the area is equal to the sum of the fractional uncertainties in the length and in the width. (This is a general result.)
Problem 55
As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 \(\pm\) 0.02 cm and a thickness of 0.050 \(\pm\) 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the diameter to the thickness and the uncertainty in this ratio.
Problem 58
Two ropes in a vertical plane exert equal-magnitude forces on a hanging weight but pull with an angle of 72.0\(^{\circ}\) between them. What pull does each rope exert if their resultant pull is 372 N directly upward?
Problem 59
Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 21.0\(^{\circ}\) west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of each of these pulls and the direction of the smaller pull.
Problem 61
As noted in Exercise 1.26, a spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45\(^{\circ}\) east of south, and then 280 m at 30\(^{\circ}\) east of north. After a fourth displacement, she finds herself back where she started. Use the method of components to determine the magnitude and direction of the fourth displacement. Draw the vector-addition diagram and show that it is in qualitative agreement with your numerical solution.
Problem 62
A plane leaves the airport in Galisteo and flies 170 km at 68.0\(^{\circ}\) east of north; then it changes direction to fly 230 km at 36.0\(^{\circ}\) south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?
Problem 65
You leave the airport in College Station and fly 23.0 km in a direction 34.0\(^{\circ}\) south of east. You then fly 46.0 km due north. How far and in what direction must you then fly to reach a private landing strip that is 32.0 km due west of the College Station airport?
Problem 67
As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and finally 18.0 m in the direction 33.0\(^{\circ}\) west of south. After the specified displacements, a contestant will find a silver dollar hidden under a rock. The winner is the person who takes the shortest time to reach the location of the silver dollar. Remembering what you learned in class, you run on a straight line from the starting point to the hidden coin. How far and in what direction do you run?
Problem 68
An explorer in Antarctica leaves his shelter during a whiteout. He takes 40 steps northeast, next 80 steps at 60\(^{\circ}\) north of west, and then 50 steps due south. Assume all of his steps are equal in length. (a) Sketch, roughly to scale, the three vectors and their resultant. (b) Save the explorer from becoming hopelessly lost by giving him the displacement, calculated by using the method of components, that will return him to his shelter.
