Phy 211 General Physics I Lab PCC Cascade Fall 2006 page 1 of 4 Experiment 2 Accelerated Motion You have probably watched a ball roll off an incline During the first part of the 17 th century Galileo experimentally determined the concept of acceleration using inclines If the angle of the incline is small a ball rolling down an incline moves slowly and can be accurately timed In the first part of this experiment you will roll a ball down a ramp and determine the ball s velocity with a pair of photogates The photogates can record the time when the ball passes through them breaking an infrared beam and then the LoggerPro software can calculate the time it took the ball to travel between the 2 photogates Using the time and the distance you will then graph distance vs time and acceleration vs time graphs This example will allow you to better understand the concept of acceleration and the kinematic equations ball photogates Figure 1 Experimental set up OBJECTIVES Measure the travel time for a ball traveling in accelerated motion Construct a mathematical model for the observed accelerated motion Compare the mathematical model with the kinematic equations for the accelerated motion Determine the significance of the model constants and their role in the kinematic equations MATERIALS Windows based computer 2 Vemier Photogates 1 2 ringstands w clamps a small ball 1to 5 cm diameter LabPro Interface Logger Pro ramp software PRELIMINARY QUESTIONS 1 If you were to drop a ball releasing it from rest what information would be needed to predict how much time it would take for the ball to hit the floor What assumptions must you make Phy 211 General Physics I Lab PCC Cascade Fall 2006 page 2 of 4 2 Galileo assumed that the acceleration is constant for free falling objects and for balls rolling down an incline What shape of the velocity vs time graph would prove that the acceleration is constant Explain 3 For Galileo measuring speed was very difficult inaccurate time measuring devices so he had to rely on distance and time measurements Since he assumed that the acceleration is constant for a rolling ball what type of distance vs time graph did he expect to obtain PROCEDURE 1 Set up a low ramp on the table so that a ball can roll down the ramp as shown in Figure 1 2 Position two photogates so the ball rolls through each of the photogates while rolling on the ramp surface Record the distance between the photogates in the table Approximately center the detection line of each photogate on the middle of the ball Connect Photogate 1 to DIG1 of the LabPro and Photogate 2 to DIG2 To prevent accidental movement of the Photogates use tape to secure the ring stands in place 3 Roll the ball down the ramp starting at the first photogate from rest Make sure that the ball does not strike the sides of the photogates reposition them if necessary If the red LED comes on when the ball passes through the Photogate the experimental set up works properly 4 Prepare the computer for data collection by opening Exp 08 in the Physics with Computers experiment files for LoggerPro A data table and two graphs are displayed one graph will show the time required for the ball to pass through the Photogates for each trial 5 Carefully measure the distance from the beam of Photogate 1 to the beam of Photogate 2 To obtain accurate results you must enter an accurate measurement Record the distance between the photogates in the table 6 Start data collection then roll the ball from rest down the ramp through both photogates Record the measured time in the data table Time from Gate 1 to Gate 2 7 Move Photogate 2 to a different distance from Photogate 1 Repeat steps 5 6 8 Repeat steps 5 7 of the experiment for a total of 6 different distances 9 Using the Graphical Analysis software plot the distance vs time graph Be sure to label the data columns appropriately Phy 211 General Physics I Lab PCC Cascade Fall 2006 page 3 of 4 Table 1 Time s Distance m 1 2 3 4 5 Average Analysis Questions 1 Look at the distance vs time graph What is the shape of the graph What type of motion is the motion down the ramp 2 Click and drag on the graph and select the appropriate fit from Analyze Curve Fit What kind of curve fit best matched the graph Print the graph 3 What is the physical significance of the coefficients a b and c for the fit Hint write the equation of the accelerated motion and compare it to the fit equation dx dt LoggerPro can calculate the velocity for you From the Data menu select New Calculated Column In the pop up window enter the name of the new column velocity and the short name v Define the new function select derivative from Functions Calculus Enter the argument of the derivative function x from the Variable menu The definition is now derivative x Click Done and the new column will appear in your data table 4 The velocity is the derivative of the distance traveled v 5 Create a velocity vs time graph What is the shape of the graph What type of motion best describes the travel of the ball 6 Click and drag on the graph and then try a linear fit What is physical significance of the slope of this graph Print the graph Slope Phy 211 General Physics I Lab PCC Cascade Fall 2006 page 4 of 4 7 Is there any relationship between the slope of the velocity graph and the coefficient a in step 3 Explain 8 Does your experiment prove that the acceleration for the ball is constant How does your data support your answer