Metric System Problem: 1.2.6 The diameter of an aluminum atom is about 0.24 nm and the nuclear diameter is about 7.2 fm (femtometer = 10-15 meter). (a) If the atom’s diameter were expanded to the length of an American football field (91.44 m) and the nuclear diameter expanded proportionally what would be the nuclear diameter in meters? (b) Is the saying that “the atom is mostly empty space” confirmed by these figures? (a) m (b) Yes No Problem: 1.8.2 Freefall acceleration g is the acceleration due to gravity. It equals 9.80 meters per second squared near the Earth’s surface. (a) What does it equal in feet per second squared? (b) In miles per second squared? (c) In miles per hour squared? (a) ft/s2 (b) mi/s2 (c) mi/h2 Problem: 1.8.4 You are on the phone with a friend in Greece who tells you that he has just caught a fish L cm long in the Mediterranean Sea. Assuming he is telling the truth what is the length of the fish in inches? in Problem: 1.8.7 Mercury orbits the Sun at a mean distance of 57 900 000 kilometers. (a) What is this distance in meters? Use scientific notation to express your answer and state it with three significant figures. (b) Pluto orbits at a mean distance of 5.91×1012 meters from the Sun. What is this distance in kilometers? (a) m (b) Problem: 1.8.8 In 2003 Bill Gates was worth 40.7 billion dollars. (a) Express this figure in dollars in scientific notation. (b) Assume a dollar is worth 2 060 Italian lire. State Bill Gates’s net worth in lire in scientific notation. (a) dollars (b) lire Dimensional Analysis Problem: 1.10.2 The dimensions for force are the product of mass and length divided by time squared. Newton’s law of gravitation states that the gravitational force between two objects equals a constant G times the product of the mass of each object divided by the square of the distance between them. What must the dimensions of the constant be? L3/MT2 L2/T3 M2T Problem: 1.10.4 The kinetic energy of an object is given by the equation KE = (1/2)mv2 where m is mass and v is speed with dimensions L/T. What are the dimensions of KE? ML2/T2 L2/T2 LM/T Problem: 1.11.2 Evaluate (5.7×106 kg) × (6.3×10-2 m/s2) and express the answer in scientific notation. kg·m/s2 Problem: 1.13.4 You have $1.14×104 in your checking account but must pay $3.30×103 in tuition. What is the balance in your checking account after you pay your tuition? Express the answer in scientific notation. dollars Problem: 1.17.2 Suzy is holding her kite on a string 25.0 m long when the kite hits the top of a flagpole which is f m higher than her hands. Assuming that the string is taut and forms a straight line what is the horizontal distance from her hands to the flagpole? m Graphical Analysis of Motion Problem: 2.C.8 Elaine wants to return a video she rented at the video store which is 5.0 kilometers away in the positive direction. It takes her 10 minutes to drive to the store 1.0 minute to deposit the videotape and 9.0 more minutes to drive home. What is her average velocity for the entire trip? m/s Problem: 2.2.2 The school bus picks up Brian in front of his house and takes him on a straight-line x km bus ride to school in the positive direction. He walks home after school. If the front of Brian’s house is the origin (a) what is the position of the school (b) what is his displacement on the walk home and (c) what is his displacement due to the combination of the bus journey and his walk home? (a) km (b) km (c) km Problem: 2.3.2 A jogger is moving at a constant velocity of 3.0 m/s directly towards a traffic light that is 100 meters away. If the traffic light is at the origin x = 0 m what is her position after running 20 seconds? m Problem: 2.4.4 You made a journey and your displacement was 95.0 km. Your initial velocity was 167 km/h and your final velocity was -26.0 km/h. The journey took 43.0 minutes. What was your average velocity in kilometers per hour? km/h Problem: 2.9.2 A graph of the velocity versus time of a hockey puck is shown. Calculate the puck’s displacement from t = 1.0 s to t = 4.0 s. m Problem: 2.10.2 A sailboat is moving across the water at 3.0 m/s. A gust of wind fills its sails and it accelerates at a constant 2.0 m/s2. At the same instant a motorboat at rest starts its engines and accelerates at 4.0 m/s2. After 3.0 seconds have elapsed find the velocity of (a) the sailboat and (b) the motorboat. (a) m/s (b) m/s
