Physics: Energy Flow in Technological Systems PDF

PHYSICS Energy Flow in Technological Systems  Are we there yet?  Motion - Are we there yet? We can find out how far an object has gone (it’s motion) by comparing the object‘s position to another point. This point is called a reference point. 3 Moti...

PHYSICS Energy Flow in Technological Systems  Are we there yet?  Motion - Are we there yet? We can find out how far an object has gone (it’s motion) by comparing the object‘s position to another point. This point is called a reference point. 3 Motion - Are we there yet? Uniform motion is the simplest type of motion. It is a term used to describe an object that is traveling at a constant rate of motion in a straight line. 4  Many situations occur where an object appears to have uniform motion, but this type of motion is nearly impossible to maintain for long periods. For example, a car on a highway with the cruise control set at 100km/hr. Various forces act to slow the car down, such as friction of the tires on the road and wind resistance. 5  Average Speed Because uniform motion is difficult to maintain the term average speed is usually used. Average speed is uniform motion that involves traveling a distance in a specified time. 6  Average Speed The following equation is used to determine the average speed of an object: average speed = distance traveled time elapsed B.F.F. v = _Δd_ Δt 7 Example Problem B1: A person walks 10.0m away from a stop sign in 5.00s. What is the average speed of the person? Average speed v = _Δd_ Δt v = 10.0 m 5.00s v = 2.00 m/s The person walked at a speed of 2.00 m/s. 8  Practice Problems A bullet is shot from a rifle with a speed of 720 m/s. What time is required for the bullet to strike a target 28.60 m away? v = _Δd_ Δt 720m/s = _28.60 m_ 1 Δt Δt(720m/s) = 28.60 m 720m/s 720 m/s Δt = 0.0397 s It took 0.0397 s for the bullet to strike the target. 9  Plotting a Distance-Time Graph We use graphs to show relationships between two variables and to provide a visual representation of motion. 11  Plotting a Distance-Time Graph Suppose a motorboat is traveling at uniform speed. The boat passes marker buoys 5m apart. 1  Plotting a Distance-Time Graph Yes I am that bored!! As the boat passes the first marker, a person on shore starts to record the distance the boat travels away from the first marker every 2.0s. 1  Plotting a Distance-Time Graph The table shows the measurements taken by the person on shore. Distance Time t(s) d(m) 0 0 Time is the manipulated variable. The 2 10 person on shore recorded the distance 4 20 every 2 seconds, so she is manipulating this variable. This variable goes at the bottom, 6 30 on the x-axis. 8 40 10 50 1  Plotting a Distance-Time Graph Distance Time t(s) d(m) 0 0 The responding variable is the distance the boat goes. 2 10 It changes in response to the 4 20 manipulated variable. This 6 30 variable goes on the side, on the y-axis. 8 40 10 50 1  Plotting a Distance-Time Graph The table allows us to see the relationship between distance and time, but by reading the table, it is difficult to see the whole picture. Another way of looking at this relationship is to place the data on a graph. 1  Process of Graphing Data 1. Give the graph a title TITLE Distance versus Time GRAPH 1 Process of Graphing Data Distance versus Time GRAPH 2. Label the axes. Name (distance or time) and units (m or s). The manipulated variable goes on the horizontal or x-axis. X- AXIS Time t (s) NAME UNITS 1 Process of Graphing Data Distance versus Time GRAPH UNITS 2. Label the axes. Distance d (m) The responding NAME variable goes on the vertical or y axis. Y- AXIS Time t (s) 1  Process of Graphing Data 3. Decide on a suitable scale for the axes. (1, 2, 3, or 2, 4, 6, or 10, 20, 30, …) Distance versus Time GRAPH 30 35 25 Distance d 15 20(m) 40 45 50 0 5 10 0 1 2 3 4 5 6 7 8 9 10 Time t (s) 2 Process of Graphing Data 4. Plot the points. Distance versus Time GRAPH 30 35 20 25 Distance d 15 (m) 0 5 10 40 45 50 0 1 2 3 4 5 6 7 8 9 10 Time t (s) 2  Process of Graphing Data 5. Draw a line of best fit. Distance versus Time GRAPH 30 35 20 25 Distance d 15 (m) 40 45 50 0 5 10 0 1 2 3 4 5 6 7 8 9 10 Time t (s) 2  How to DRAW a LINE OF BEST FIT: A line of best fit goes through the middle of the plotted points with an equal number of points above and below the line. Draw line of best fit for these graphs: 2 Now draw the graph for the motorboat: 2  Since the graph is a straight line, it shows the boat has uniform motion. If the line of best fit were a curve of any type, this would mean the object would be speeding up or slowing down. 2  Calculating the Slope of a Line A graph is not always the best way to describe data. Sometimes an average of the data is better. One technique for averaging the data represented on a graph is to find the slope of the graph. 2  Calculating the Slope of a Line The formula for slope Slope = rise rise is: run run Slope = change in distance = Δd = speed (v)change in time Δt 2  The slope of a distance-time graph is a visual representation of the speed of an object. A faster greater or steeper slope indicates a faster speed and a lesser slope indicates a slower speed. slower 2 Find the slope of the following graph: Slope = dfinal - dinitial tfinal- tinitial Speed of Motor Boat 50 Slope = 30 m – 10 m 40 6.0 s – 2.0 s Distance d (m) 30 Slope = 20 m 20 4.0 s 10 0 Slope = 5.0 m/s 0 2 4 6 8 10 Time t (s) Therefore, the average speed, v, is 5.0 m/s. 3  Graphing and Slope Practice Time Distance Speed of Electric Train t(s) d(m) 0 0.0 Distance d (m) 5 2.0 21 18 10 4.0 15 15 8.0 12 20 12.0 9 6 25 15.0 3 30 17.0 0 0 10 20 30 40 35 19.0 Time t (s) 40 21.0 3  2. The information in the table is for a jet traveling at a uniform speed. a. Draw a distance-time graph for the data in the table. b. Determine the slope of the line. c. What value does the slope of the graph represent? 3  2. The information in the table is for a jet traveling at a uniform speed. a. Draw a distance-time graph for the data in the table. Time Distance Speed of Jet 2500 t(s) d(m) 0.0 0 2000 Distance d (m) 1.0 490 1500 2.0 1020 3.0 1490 1000 4.0 2010 500 5.0 2480 0 0 1 2 3 4 5 Time t (s) 3  2. The information in the table is for a jet traveling at a uniform speed. b. Determine the slope of the line. Speed of Jet 2500 2000 Distance d (m) 1500 Slope = dfinal - dinitial tfinal- tinitial 1000 500 0 Slope = 2500 m – 0.0 m 5.0 s – 0.0 s 0 1 2 3 4 5 Time t (s) Slope = 2500 m 5.0 s Slope = 500.0 m/s 3  Plotting a Speed-Time Graph The speed of a moving object is the distance it travels per unit time. Suppose a motor boat is traveling past marker buoys. A person on shore uses a radar gun to record the speed of the motorboat every 2.0s. The data is shown in the table. Plot the graph and find the slope. 3  Suppose a motor boat is traveling past marker buoys. A person on shore uses a radar gun to record the speed of the motorboat every 2.0s. The data is shown in the table. Plot the graph and find the slope. Speed versus Time Time Speed 5 t(s) v(m/s) 4 Speed v(m/s) 0.0 5.00 3 2.0 5.00 4.0 5.00 2 6.0 5.00 1 8.0 5.00 0 0 2 4 6 8 10 Time t (s) 3  Suppose a motor boat is traveling past marker buoys. A person on shore uses a radar gun to record the speed of the motorboat every 2.0s. The data is shown in the table. Plot the graph and find the slope. The slope of the line is: Speed versus Time Slope = rise 5 run 4 Speed v(m/s) Slope = 5 m/s – 5.0 m/s 3 8.0 s – 0.0 s 2 Slope = 0 m/s 8.0 s 1 Slope = 0.0 m/s2 0 0 2 4 6 8 10 Time t (s) 3  A slope of 0.0 m/s2 (units for acceleration) confirms that the motion is uniform. There is no acceleration. You can determine the DISTANCE the boat traveled by calculating the AREA under the line of the speed – time graph. 3  Area = area of a rectangle area = length x width Speed of Motor Boat area = (v)(Δ t) 5 4 area = (5.00m/s)(8.0s) Speed v(m/s) 3 area = 5 x 8 2 area = 40m 1 0 The distance the boat 0 2 4 6 8 10 traveled in 8 seconds is Time t (s) 40 m. 4  Since the speed formula v =Δd Δt can be rearranged to vxΔt=Δd the area under the line is the same as Δ d. Thus, the area under the line of the speed-time graph indicates the distance traveled in the time period. 4  If the line of best fit were a straight line with a slope other than zero, then the speed of the object is increasing or decreasing: Speed-Time Graph of Two Objects 50 Speed is increasing 40 Speed is decreasing Speed v 30 (m/s) 20 10 0 0 2 4 6 8 10 Time t (s) 4 SIGNIFICANT DIGITS All non-zero numbers are significant. Start counting from the first non-zero number (on the left). All numbers to the right of that number are significant. Example 0.031 The first non-zero number is 3. There are 2 significant digits. 4 4  Motion, Work and Energy st In the 1 century A.D., A Greek engineer named hero of Alexandria designed the first heat engine. 4