Question:Exercise 1 Motion on a Ramp In this exercise you will roll a marble down a ramp and calculate its...

Exercise 1 Motion on a Ramp In this exercise you will roll a marble down a ramp and calculate its linear acceleration and velocity. You will then create graphs to illustrate the motion of the marble.

Part 1: Angle of Inclination Gather the wooden board with central groove, marble, stopwatch, tape measure, tape, several textbooks, protractor, plumb bob weight with string, and safety goggles. Put on your safety goggles. Measure the length of the wooden board to 0.001 m and record in Data Table 1. Construct an angle measuring tool as shown in Figure 10. Build a plumb line by tying a short length of string, around 10-15 cm, around the plumb bob weight. Tape the other end of the string to the middle of the flat side of the protractor so that when held horizontally, the string passes directly over the 90-degree marking on the curved part of the protractor. A hand holds a clear plastic protractor with the flat side horizontal and the curves side down. A piece of string is taped over the flat side, so that it hangs down covering the hole in the center of the flat side of the protractor. A lead weight hangs from the end of the string below the bottom of the curved side of the protractor. The string crosses the 90 degree mark on the curved side of the protractor. Figure 10. Angle measuring tool constructed using the protractor and plumb bob. Support one end of the wooden board with a single textbook. Measure the angle of incline of the wooden board using the angle measuring tool as demonstrated in Figure 11. Record the measurement to 0.1 degrees in Data Table 1. The grooved wooden board is propped up by three textbooks on one end. A hand holds a clear plastic protractor with the flat side aligned with the top of the board. A string attached to the protractor at the top of the flat side, just above the circular hole, has a lead weight attached to the other end of the string. The string hangs down just below the bottom of the curved part of the protractor so that the string indicates an angle of 20 degrees. Figure 11. Using the angle measuring tool to measure 20 angle. Hold the marble at the top of the ramp, resting in the groove. Release the marble and start the stopwatch simultaneously. Note: Gently release the marble. Do not throw or push the marble in any direction. Release quickly. Stop the stopwatch as the marble reaches the end of the ramp. Record the time to the nearest 0.01 seconds in Data Table 1. Repeat steps 7-10 four more times for a total of five trials. Add a second textbook under the ramp and measure and record the angle of incline to 0.1 degrees in Data Table 1. Repeat steps 7-11 for the ramp supported by two books. Add a third textbook under the ramp and measure and record the angle of incline to 0.1 degrees in Data Table 1. Repeat steps 7-11 for the ramp supported by three books. Calculate the average time taken by the marble to roll down the incline for each inclination angle and record in Data Table 1. Use Equation 1 as illustrated in the background to solve for the acceleration of the marble for each inclination angle and record to .01 m/s2 in Data Table 1. Equation 1: a = 2 x / t 2 Use Equation 2 as illustrated in the background to solve for the velocity of the marble at the bottom of the ramp and record to 0.01 m/s in Data Table 1. Equation 2: v = a t Part 2: Constant Acceleration Measure and mark with tape flags distances of 15, 25, and 35 cm on the wooden board as shown in Figure 12. The grooved wooden board is propped up with the groove facing up by one textbook on one end. Fifteen centimeters from the propped up end of the board, a green piece of tape is attached to the thin side of the board and labeled 15 cm with an arrow pointing to the left side of the tape. Twenty-five centimeters from the propped up end of the board, a green piece of tape is attached to the thin side of the board and labeled 25 cm with an arrow pointing to the left side of the tape. Thirty-five centimeters from the propped up end of the board, a green piece of tape is attached to the thin side of the board and labeled 35 cm with an arrow pointing to the left side of the tape. Figure 12. Wooden board on incline with tape flags indicating 15, 25, and 35 cm. Rest the end of the board where you started your distance measurements on a single textbook (smallest angle of incline). Measure the angle using the angle measurement device and record to 0.1 degrees in Data Table 2. Rest the marble in the central groove at the top of the ramp. Release the marble and simultaneously start the stopwatch. Stop the stopwatch when the marble passes the 15 cm mark. Record the time to 0.01 seconds in Data Table 2. Repeat steps 22-24 four more times for a total of five trials. Release the marble from the central groove at the top of the ramp and simultaneously start the stopwatch. Stop the stopwatch when the marble passes the 25 cm mark. Record the time to 0.01 seconds in Data Table 2. Repeat steps 26 and 27 for the 25 cm distance four more times for a total of five trials. Release the marble from the central groove at the top of the ramp and simultaneously start the stopwatch. Stop the stopwatch when the marble passes the 35 cm mark. Record the time time to 0.01 seconds in Data Table 2. Repeat steps 29 and 30 four more times for a total of five trials. Calculate the average time taken by the marble to travel 15, 25, and 35 cm. Record these times in Data Table 2. Calculate the acceleration and velocity of the marble at each of these distances using the equations listed in steps 17 and 18. Record these values in Data Table 2. Draw a motion diagram on a sheet of paper for the marble when it travels 35 cm. Include your name and the date on the page. See Figure 13 for an example diagram. Note: Include enough points to clearly show the motion. Choose a reasonable time interval in order to do this, possibly 0.1 or 0.2 seconds. Include velocity arrows and velocity change arrows in your diagram. Clearly label each point. A black pen drawing has four evenly spaced dots in a horizontal line with arrows pointing from each dot on the left to the subsequent dot to its right. Above the first arrow to the left is the text v1, above the second arrow is the text v2, above the third arrow is the text v3 and above the fourth arrow is the text v4. Below the first dot on the left is 1, below the second dot is 2, below the third dot is 3 and below the fourth dot is 4. Below the first dot on the left is the text delta t = 0.1 s, and below this is the text delta v = 0. Figure 13. Sample motion diagram for motion with constant velocity. Velocity change arrow has a length of 0. Time interval is 0.1 seconds. Take a photo of the motion diagram and upload the image to Photo 1. Using graphing software, create two graphs: distance versus time and velocity versus time for the data collected in Data Table 2. Clearly label each graph and the axes, including units. Add trendlines to these graphs and include the equation of the lines chosen on the graphs. Upload an image of each graph into Graph 1 and Graph 2. Use the equation of the trendline found for the velocity vs. time graph to determine the acceleration of the marble and record this value in Data Table 2. Part 3: Constant Velocity Use the wooden ruler with grooved center to build a ramp with a small angle, ending at the base of the wooden board. The wooden board should lie flat on a flat surface. Support the base of the ruler with one or two small note pads so that the groove of the ruler just aligns with the groove of the wooden board as shown in Figure 14. Wooden ruler with groove side up enters the frame of the image from the left, and appears to be supported at an angle out of the frame. The base of the ruler is resting on top of two small sticky-note pads so that the top of the ruler just aligns with the top of the wooden board. The grooved wooden board is aligned in a straight line with the ruler starting in the middle of the frame and ends outside the frame on the right. A green tape marking with the text 15 cm is just visible on the right side of the wooden board. The grooves of the ruler and the wooden board are aligned. Figure 14. Base of ruler supported by small note pads to align ruler groove with groove in wooden board. Use the markings on the ruler to determine a release point for the marble approximately 10 cm from the base of the ruler. Record the distance to 0.001 meters in Data Table 3. Gently release the marble and simultaneously start the stopwatch. Stop the stopwatch when the marble reaches the bottom of the ruler. Record the time in Data Table 3. Repeat steps 43 and 44 four more times for a total of five trials. Calculate the average time for the marble to travel down the ruler and record in Data Table 3. Calculate the velocity of the marble at the bottom of the ruler using the equation v = 2x/t and record this value in Data Table 3. Note: This velocity will be your v0 for the remainder of this experiment. Release the marble from the 10 cm point used previously, starting the stopwatch when the marble just reaches the flat wooden board. Stop the stopwatch as the marble passes the 15 cm mark on the board. Record the time to 0.01 seconds in Data Table 3. Repeat steps 48 and 49 four more times for a total of five trials. Release the marble from the 10 cm point used previously, starting the stopwatch when the marble just reaches the flat wooden board. Stop the stopwatch as the marble passes the 25 cm mark on the board. Record the time to 0.01 seconds in Data Table 3. Repeat steps 51 and 52 for the 25 cm mark four more times for a total of five trials. Release the marble from the 10 cm point used previously, starting the stopwatch when the marble just reaches the flat wooden board. Stop the stopwatch as the marble passes the 35 cm mark on the board. Record the time to 0.01 seconds in Data Table 3. Repeat steps 54 and 55 for the 35 cm mark four more times for a total of five trials. Calculate the velocity and acceleration at each distance marker using the equations below and record the values in Data Table 3. v = v 0 + a t a = 2 ( x v 0 t ) / t 2 Using graphing software, create a graph of distance versus time for the flat board and a graph of velocity versus time for the flat board. Properly label each graph including axes and units. Add trendlines and show equations on the graph. Note: Include data for Time 0 on your graphs. Upload an image of each graph into Graph 3 and Graph 4. Use the trendline equations to calculate the acceleration and velocity of the marble on the flat board and record these values in Data Table 3. Cleanup: Return all HOL provided items to the kit for use in future experiments. Exercise 1 - Questions 1. Explain the mathematical and graphical relationship between velocity and acceleration using your own words. 0 Words 2. Explain the mathematical and graphical relationship between velocity and position using your own words. 0 Words 3. How does the angle of inclination affect the velocity of the marble? The acceleration? 0 Words 4. Compare calculated velocity and acceleration to velocity and acceleration determined from graphs. Do the values match? If not, which value is more accurate and why? 0 Words 5. Describe the motion of an object with positive velocity and negative acceleration. Describe the motion of an object with negative velocity and positive acceleration. Describe the motion of an object with negative velocity and negative acceleration. 0 Words 6. Describe the motion depicted by the following motion diagram. Then, sketch a velocity versus time graph for this motion diagram and insert the image into Graph 5: Motion diagram with five black dots in a horizontal line decreasing in space between them from left to right with green arrows pointing from the left dots to the dot immediately to the right, followed by three evenly spaced black dots with green arrows pointing from the left dot to the dot immediately to its right, followed by three dots with increasing space between them with green arrows pointing from the left dot to the dot immediately to its right. Text above the first dot on the left reads t = 0 sec, text below the third dot from the left reads t = 2 sec, text above the fifth dot reads t = 4 sec, text below the seventh dot reads t = 6 sec, text above the ninth dot reads t = 8 sec, and text below the eleventh and last dot reads t = 10 sec. 0 Words 7. Relate the velocity and position versus time graphs you made in Part 2 and Part 3 to one another. 0 Words 8. How does the distance traveled with constant incline (Part 2) affect the velocity? What about the acceleration? 0 Words