#$&* course PHY 231 9/2 20:19 003. `Query 3
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Given Solution: The coordinates a point on the graph include a position and a clock time, which tells you where the object whose motion is represented by the graph is at a given instant. If you have two points on the graph, you know the position and clock time at two instants. Given two points on a graph you can find the rise between the points and the run. On a graph of position vs. clock time, the position is on the 'vertical' axis and the clock time on the 'horizontal' axis. • The rise between two points represents the change in the 'vertical' coordinate, so in this case the rise represents the change in position. • The run between two points represents the change in the 'horizontal' coordinate, so in this case the run represents the change in clock time. The slope between two points of a graph is the 'rise' from one point to the other, divided by the 'run' between the same two points. • The slope of a position vs. clock time graph therefore represents rise / run = (change in position) / (change in clock time). • By the definition of average velocity as the average rate of change of position with respect to clock time, we see that average velocity is vAve = (change in position) / (change in clock time). • Thus the slope of the position vs. clock time graph represents the average velocity for the interval between the two graph points. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: Pendulums of lengths 20 cm and 25 cm are counted for one minute. The counts are respectively 69 and 61. To how many significant figures do we know the difference between these counts? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your Solution: 69 - 61 = 8 One significant digit. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ********************************************* Question: What are some possible units for position? What are some possible units for clock time? What therefore are some possible units for rate of change of position with respect to clock time? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your Solution: Position units: Km, miles, m, cm, mm Time units: hours, minutes, seconds, milliseconds confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ********************************************* Question: `qQuery Principles of Physics and General College Physics: Summarize your solution to Problem 1.19 (1.80 m + 142.5 cm + 5.34 * 10^5 `micro m to appropriate # of significant figures) YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1.80m + (142.5cm ( 1m/ 100 cm)) + (5.34 *10^5 micro m (1 m / 1 * 10^6 micro m) 1.80m + 1.425m + .534m 3.76m confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 1.80 m has three significant figures (leading zeros don't count, neither to trailing zeros unless there is a decimal point; however zeros which are listed after the decimal point are significant; that's the only way we have of distinguishing, say, 1.80 meter (read to the nearest .01 m, i.e., nearest cm) and 1.000 meter (read to the nearest millimeter). Therefore no measurement smaller than .01 m can be distinguished. 142.5 cm is 1.425 m, good to within .00001 m. 5.34 * `micro m means 5.34 * 10^-6 m, so 5.34 * 10^5 micro m means (5.34 * 10^5) * 10^-6 meters = 5.34 + 10^-1 meter, or .534 meter, accurate to within .001 m. Then theses are added you get 3.759 m; however the 1.80 m is only good to within .01 m so the result is 3.76 m. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ********************************************* Question: For University Physics students: Summarize your solution to Problem 1.31 (10th edition 1.34) (4 km on line then 3.1 km after 45 deg turn by components, verify by scaled sketch). YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: First, I made my own diagram replicating the problem and connected the ending point to the beginning point of the route with a straight line. This represents the direct route needed to determine the magnitude of the displacement and direction. I used the 45 degree angle given in the upper right to find the 2nd parts of the Y and X axis distances. First, the Y Axis 2.6 km + (sin(45)*3.1km) 4.79 km X Axis 4.0km + (cos(45)*3.1km) 6.19km We then draw a triangle with a the lengths given above. We solve for the hypotenuse: x^2 = 6.19^2 +4.79^2 x = 7.83km The book shows the angle can be found using arctan (4.79km/6.19km) 38 degrees confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** THE FOLLOWING CORRECT SOLUTION WAS GIVEN BY A STUDENT: The components of vectors A (2.6km in the y direction) and B (4.0km in the x direction) are known. We find the components of vector C(of length 3.1km) by using the sin and cos functions. Cx was 3.1 km * cos(45 deg) = 2.19. Adding the x component of the second vector, 4.0, we get 6.19km. Cy was 2.19 and i added the 2.6 km y displacement of the first vector to get 4.79. So Rx = 6.19 km and Ry = 4.79 km. To get vector R, i used the pythagorean theorem to get the magnitude of vector R, which was sqrt( (6.29 km)^2 + (4.79 km)^2 ) = 7.9 km. The angle is theta = arctan(Ry / Rx) = arctan(4.79 / 6.19) = 37.7 degrees. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: A ball rolls from rest down a book, off that book and onto another book, where it picks up additional speed before rolling off the end of that book. Suppose you know all the following information: • How far the ball rolled along each book. • The time interval the ball requires to roll from one end of each book to the other. • How fast the ball is moving at each end of each book. How would you use your information to determine the clock time at each of the three points, if we assume the clock started when the ball was released at the 'top' of the first book? Start with time zero, and then add the time it takes to reach the end of the first book, then add the time interval for the second book to the sum, and finally add the last time interval (third book) to the previous sum. This will give us an initial starting point and three other time and position measurements. How would you use your information to sketch a graph of the ball's position vs. clock time? I would graph: (0,0) (Time 1 from above , Length of book 1) (Time 2 from above , Length of book 1+2) (Time 3 from above , Length of book 1+2+3) (This question is more challenging that the others): How would you use your information to sketch a graph of the ball's speed vs. clock time, and how would this graph differ from the graph of the position? Using the points above we can find the average velocity (slope) for certain points. It would be best to use the data we have above as we would just be predicting values along a best fit line otherwise. Velocities (slopes) = Change in distance traveled/change in time. As we have four points on the position vs. time graph we should be able to measure three average velocities and then plot them on a second graph versus the times found such as the following example: (T0 + ((T1-T0)/2) confidence rating #$&*: 3, I realized the average velocities were given, yet this way made more sense to be because the answer to the initial question which all the others build off of depends on how you envision the experiment being setup. Is there a large drop between the books? Are they side by side where the ball continues rolling from one to another with no drop? (The latter is more the way I had already envisioned it before thinking about the other possibilities - but I think this was the implied idea.) The way I answered the question makes sure that consistency is maintained; yet, I could have left out the part about calculating the avg. velocities. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: A ball rolls from rest down a book, off that book and onto another book, where it picks up additional speed before rolling off the end of that book. Suppose you know all the following information: • How far the ball rolled along each book. • The time interval the ball requires to roll from one end of each book to the other. • How fast the ball is moving at each end of each book. How would you use your information to determine the clock time at each of the three points, if we assume the clock started when the ball was released at the 'top' of the first book? Start with time zero, and then add the time it takes to reach the end of the first book, then add the time interval for the second book to the sum, and finally add the last time interval (third book) to the previous sum. This will give us an initial starting point and three other time and position measurements. How would you use your information to sketch a graph of the ball's position vs. clock time? I would graph: (0,0) (Time 1 from above , Length of book 1) (Time 2 from above , Length of book 1+2) (Time 3 from above , Length of book 1+2+3) (This question is more challenging that the others): How would you use your information to sketch a graph of the ball's speed vs. clock time, and how would this graph differ from the graph of the position? Using the points above we can find the average velocity (slope) for certain points. It would be best to use the data we have above as we would just be predicting values along a best fit line otherwise. Velocities (slopes) = Change in distance traveled/change in time. As we have four points on the position vs. time graph we should be able to measure three average velocities and then plot them on a second graph versus the times found such as the following example: (T0 + ((T1-T0)/2) confidence rating #$&*: 3, I realized the average velocities were given, yet this way made more sense to be because the answer to the initial question which all the others build off of depends on how you envision the experiment being setup. Is there a large drop between the books? Are they side by side where the ball continues rolling from one to another with no drop? (The latter is more the way I had already envisioned it before thinking about the other possibilities - but I think this was the implied idea.) The way I answered the question makes sure that consistency is maintained; yet, I could have left out the part about calculating the avg. velocities. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!