1 NAME PERIOD Chapter 3 - RATE IN MECHANICAL SYSTEMS ACTIVITY LESSON DESCRIPTION SCORE/POINTS 1. NT FILL IN NOTE GUIDE SCORE /20 Graphing Foldable /10 2. TX PP. 122-135 WORKSHEET /53 3. MATH Math formula practice /56 4. MATH REVIEW AND PRACTICE MATH /40 5. MATH Holiday Math worksheet /24 6. Review Previous Units Review /12 Objectives: Explain the difference between speed, velocity, and acceleration. Explain the difference between distance and displacement Solve problems using the formulas: speed = distance Velocity = displacement time time Solve problems for average speed and average velocity Solve problems for Acceleration Describe production rate and solve problems using that formula. Solve for angular speed in revolutions per minute and radians per second. Analyze graphs of velocity and time, speed and time, and acceleration and time. Calculate the average velocity and average acceleration of a moving object using data obtained from measurements of position of the object at two or more times. Determine and compare the average and instantaneous velocity of an object from data showing its position at given times. Collect, graph, and interpret data for position vs. time to describe the motion of an object
2 1. In mechanical systems rates describe what? (1) 2. The speed of an object is what?(1) READING GUIDE pp. 122-135 3. When you plot constant speed on a graph, the slope of the line (the ratio of to the, is constant it is the same everywhere on the line. (2) 4. If you locate any two points A and B on the line the rise is the and the run is the. Therefore the speed equals the (3) 5. Write the formula to calculate speed. (1) 6. What is the difference between average speed and instantaneous speed? (2) 7. Read through the example 3.1 on p. 125. Then answer the following question. You take a trip in your car from Ogden south to Provo, a distance of 90 miles. It takes you 1.5 hours to get there. On the way back from Provo, there is a wreck on the freeway and it takes you 2 hours to get back. FIND: A Your average speed to Provo (2) B Your average speed back to Ogden. (2) C Your average speed for the entire trip. (2) 8. When we state the speed and direction of an object s motion, we are stating what? (1) 9. What is displacement? (1) 10. When an object travels from one point to another, What does average speed depend on? (1) What does average velocity depend on? (1) 11. What is acceleration? (1) 12. You can accelerate an object by changing what? (3) 13. What is the formula to find average acceleration? (1)
3 14. Look at example 3.3 on p. 130, then do the following problem. A pilot increases the takeoff speed of an airliner from 10 ft/s to 250 ft/s in 40 seconds. Find the average acceleration of the airliner. (4) 15. Negative acceleration means the object is We call this. (2) 16. What is angular speed? (1) 17. When you look at the motion of a bicycle, explain the difference between linear displacement and angular displacement. (2) 18. Write the formula to find angular speed using words and symbols. (2) 19. What is the Greek letter omega, and what does it stand for? (2) 20. The most common unit for angular speed is what? (1) 21. Angular displacement is measured in what? (1) 22. Look at example 3.4 on page 132. What does rpm stand for? (1) Show how to convert 1 rpm to rad/s. (2) 23. If a flywheel spins 40 revolutions in 2 minutes Find: Angular speed in rpm (2) Change this rpm to radians per second (rad/s) (2) 24. How do you find angular acceleration (write the formula). (2) 25. Look at Example 3.6, then solve the following. A car s brake is applied to a wheel for 10 seconds, reducing the wheel s speed from 300 rad/s to 200 rad/s. What is the angular acceleration (or deceleration). (4)
4 Practice Math Formulas Math Formulas Put letters in the formula box. Write the correct formulas: Average Speed = Total distance s = d d = t = total time t Velocity = Displacement V = d d = t = time t Acceleration = Final velocity (Vf) Initial Velocity (Vi) = Vf Vi Time t A = ΔV ΔV = t = t Write the correct formula (1pt) plug numbers and labels in (1pt) Get answer (1pt) and label (1pt) 1. Displacement = 30 feet, Time = 5 seconds, Solve for Velocity (4pts) 2. Speed = 60 mph, Time = 5 hours, Solve for distance traveled (4pts) 3. Speed = 50 mph, Distance = 250 miles; Solve for time. (4pts) 4. Velocity = 150 mph; Displacement = 300 miles; Solve for time (4pts) 5. Time = 10 minutes; Speed = 40 ft/min; Solve for distance (4pts) 6. Distance = 210 miles; time = 3 hours; Solve for average speed (4pts) 7. Starting Velocity = 0 Ending Velocity = 10 m/sec; Time = 2 seconds; Solve for acceleration (4pts) 8. Starting Velocity = 10 ft/sec Ending Velocity = 40 ft/sec; Time = 5 seconds; Solve for acceleration (4pts) 9. Change in Velocity (ΔV) = 50 m/sec, Acceleration = 5 m/sec 2 Solve for time. (4pts) 10. Acceleration = 20ft/sec 2 ; Time = 4 seconds; Solve for Change in Velocity. (4pts)
5 Production Rate = Number produced Time 11. Number produce = 500 items; Time = 5 hours; Solve for production rate (2pts) 12. Production rate = 60 items/minute; Minutes = 200; Solve for number produced (2pts) 13. Number produced = 45 items; Production rate = 3 items/min. Solve for time (2pts) Angular speed = angular displacement time = Revolutions OR radians Minutes seconds To change rpm to rad/sec: first change minutes to seconds (divide by 60) Then times by 6.28 to change rev to radians 14. Revolutions = 2000 minutes = 10 Find revolutions per minute (2pts) Change rpm to radians per second. (2pts) 15. Revolutions = 50 Minutes = 2 Find rpm (2pts) Change rpm to radians per second (2pts) 16. Speed = 30 rpm time = 10 minutes Find revolutions (2pts)
6 REVIEW AND PRACTICE MATH QUESTIONS 1. Explain the difference between speed and velocity. (2pts) 2. Explain the difference between velocity and acceleration.(2pts) 3. What are the SI units for speed? What are the SI units for acceleration? (2pts) 4. In qualifying a car completes one lap around a 1.5 mile track in 34.6 seconds. a. What is the car s average speed in miles/second? (4pts; formula, work, answer, label) b. What is the car s average velocity for the one lap? (1pt) Explain your answer. (1pt) 5. A company has a robot part-delivery system that moves at a speed of 3 ft/sec. The path that the robot follows from the stock room through the assembly area is 570 feet in length. How much time is required for the robot to travel this path? (4 pts ; formula, work, answer, label) 6. A student walks 3 miles south at a speed of 4 mph. Then he turns west and walks 4 miles at a speed 4 mph. a. How long did it take him to walk the entire distance? (4 pts ; formula, work, answer, label) 3 miles???? (displacement) a 2 + b 2 = c 2 b. What was his average velocity? (4 pts ; formula, work, answer, label) 4 miles 7. Speedlite Air Charter sends one of its airplanes from San Antonio to New Orleans to pick up Sam and take him to Memphis, Tennessee for a repair job. The plane flies 500 miles east to New Orleans in 1.81 hours. After picking up Sam, the plane flies 370 miles north to Memphis in 1.41 hours. a. What is the speed of the plane from San Antonio to New Orleans? (4 pts ; formula, work, answer, label) b. What is the speed of the plane from New Orleans to Memphis? (4 pts ; formula, work, answer, label) c. What is the speed of the plane for the combined flying time? (Ignore any time on the ground in New Orleans. (4 pts ; formula, work, answer, label) d. What is the velocity of the plane for the entire trip (Ignore any time on the ground in New Orleans. (4 pts ; formula, work, answer, label)
7 HOLIDAY MATH 1. You drive to visit a friend for Christmas break. You travel 205 miles in 3 hours. Then you run into a traffic jam because of a snow storm and travel another 40 miles in 1.5 hours. What is your average speed for the entire trip? (2 pts answer, label) 2. You go to Disneyland for Christmas and ride on Space Mountain. This rollercoaster travels 3,450-feet in 2 minutes and 45 seconds. What is the average speed in feet per second? (2 pts answer, label) 3. You are going to have a big New Years Eve party and need 6 dozen cookies. If it takes you 1 hour to make the 6 dozen cookies, what is your production rate in cookies per minute? (2 pts answer, label) 4. Chris went snowboarding over Christmas vacation. He went down a 1500 foot hill in 40 seconds. What was his average speed? (2 pts answer, label) 5. You travel to visit Grandma for Christmas. You fly on an airplane a distance of 820 miles in 3.5 hours. What was the average speed for the plane? (2 pts answer, label) 6. Santa s elves are busy making toy horses for Christmas. It takes each elf 10 minutes to make one horse. There are 5 elves working on the horses. What would be the elves production rate for one hour? (2 pts answer, label) 7. Santa s reindeer are flying at 200 meters/second. They need to land on a roof top and come to a stop in 6 seconds. What is their deceleration? (2 pts answer, label) 8. Santa s reindeer take off from the North Pole. The sleigh is really loaded down, so it slides on the snow for a while reaching a speed of 50 m/sec. Then the reindeer start to fly and reach a speed of 400 m/sec in 5 seconds. What was their acceleration while flying? (2 pts answer, label) 9. Santa s elves have gotten really good at making radio controlled cars. They can make 100 cars in a 12 hour shift. What is their production rate per hour? (2 pts answer, label) 10. You go Ice skating at the ice sheet. You glide across the ice a distance of 100 feet in 15 seconds. What is your average speed? (2 pts answer, label) 11. You use a snow blower to clear snow off your driveway. The blade turns 500 times in 10 minutes to clear the snow. What is its angular rate in rpms and rad/sec. (Remember there are 6.28 rad in one revolution) (4pts total 2pts for rpm and 2 pts for rad/sec)
8 PREVIOUS UNITS REVIEW 1. A satellite is in orbit around the earth. If its orbit moves 3 times farther away from the earth, how is the gravitational force between the earth and the satellite affected? (1 pt) 2. If the distance between two masses decreases by 3 times (they are 3 times closer), what happens to the total gravitational force between them? (1 pt) 3. Look at the picture on. the right to use for the following questions +3 charge on ball (rod) -1 distance between = 2 units A. If the distance between the charges decreases to 1 unit, how many times closer is this? (1pt) B. What happens to the total electrical force between the ball and the post? (1 pt) C. If the distance goes up from 2 units to 8 units apart? How many times farther is this? (1pt) D. What happens to the total Electrical force between the ball and the post? (1pt) 4. The property of an object to resist changes in motion is called (1pt) 5. If the net force is not zero, the applied forces are what? (balanced or unbalanced?) (1pt) 6. What is the English unit for force? (1pt) 7. If two forces of the same magnitude act on an object along the same line - but in opposite directions, the object is said to be (balanced or unbalanced?) (1pt) 8. What is the difference between a vector and a scalar? (2pts)