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 using two Photogates and computer software for timing 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 2 Galileo assumed that the acceleration is constant for free falling objects and for balls Phy 211 General Physics I Lab PCC Cascade Fall 2006 page 2 of 4 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 I 2 Position the 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 I to the Channel 1 of the LabPro and Photogate 2 to the Channel 2 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 ban does not strike the sides of the Photogates Reposition the Photogates 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 From the Physics with Computers experiment files of Logger Pro 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 Record the distance between the Photogates in the table Carefully measure the distance from the beam of Photogate I to the beam of Photogate 2 It may be easier to measure from the leading edge of Photogate 1 to the leading edge of Photogate 2 To obtain accurate results you must enter an accurate measurement 6 Click Collect Roll the ball from rest from the first Photogate and record the time in the table displayed in the column Time from Gate 1 to Gate 2 7 Move the second Photogate to a different distance and record the distance in the table Repeat steps 5 6 8 Repeat the experiment for a total of 10 different distances 9 Using Graphical Analysis plot the distance vs time graph Open Program Files Vernier Software Graphical Analysis Double click on the header of the x column to edit the name of the column and the units Repeat the procedure for the y column enter your values for x and time in the cells Phy 211 General Physics I Lab PCC Cascade Fall 2006 page 3 of 4 Table I 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 Hint write the equation of the accelerated motion and compare it to the fit equation dx dt LoggerPro can calculate the velocity for you in a new column 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 To 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 Click between the two arrows on the y axis label and select velocity The graph of the velocity will be displayed What is the shape of the graph What type of motion is the motion 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 Phy 211 General Physics I Lab PCC Cascade Fall 2006 page 4 of 4 Slope 7 Is there any relationship between the slope of the velocity graph and the coefficient a in step 4 Explain 8 Did you prove that the acceleration is constant How does your data support this affirmation