Download The Rolling Ball - Aerospace 3: Introduction to Dynamics and Systems | ASEN 2003 and more Lab Reports Dynamics in PDF only on Docsity! ASEN 2003 Introduction to Dynamics and Systems Spring 2004 1 Lab #9: The Rolling Ball DUE BY 3 PM, APRIL 30, ECAE 177 OBJECTIVES • Use energy methods to analyze the motion of a sphere. • Identify failures of a model and investigate improvements. OVERVIEW This lab investigates the motion of a ball on the ITLL ball machine. You will use a simple model to predict the ball’s velocity and then adjust the parameters of the model to see if the fit to the data improves. Figure 1 shows a front view of a ball on the ball track. The track separation values are given for two different types of track: narrow and wide. Figure 1: Front view of a ball on the ball machine track. Using energy methods and the assumption that the ball is rolling without slipping, it can be shown that the ball speed, v is v2 = vo 2 + 2lr2 g sinb - Fr m Ê Ë Á Á ˆ ¯ ˜ ˜ r2 + 2 5 R2 (1) where v0 = initial velocity l = distance along ramp b = slope of ramp (given below) ASEN 2003 Introduction to Dynamics and Systems Spring 2004 2 Fr =some unknown retarding force in direction of the track r = rolling radius R = radius of ball m = mass of the ball, 35 grams g = 981 cm/sec/sec The rolling radius r is r2 = R2 - w 2 + t 2 Ê Ë Á ˆ ¯ ˜ R R + 0.5t Ê Ë Á ˆ ¯ ˜ È Î Í ˘ ˚ ˙ 2 (2) where w = the track width t = thickness of track gauge (0.5 cm) Sensors have been placed along the track to measure velocity. These sensors are electronic gates through which the balls pass. Inside each sensor is a LED and a photo-sensitive diode. As the ball passes through the sensor, the beam of light from the LED is temporarily broken. All the sensors are synchronized to a computer clock, so the instantaneous velocity of the ball can be determined at each sensor by dividing the diameter of the ball by the pulse-width. Although the apparatus also calculates the time the ball goes through the sensor, we will not be using this information in this lab. The simple track is a narrow track with sensors positioned as shown in Figure 2. The distances of the sensors from the start marker are as follows: S1 = 14.3 cm, S2 = 54.5 cm, S3 = 90.8 cm Figure 2: The simple track. For the compound track, the distances of the sensors from the start marker are as follows: S1 = 4.2 cm, S2 = 28.3cm, S3 = 40.4 cm, S4 = 69.8 cm, S5 = 84.4 cm
