PHY 211 General Physics I Lab Instructor Tony Zable page 1 of 4 Experiment Atwood Machine OBJECTIVES 1 To measure the acceleration in 2 different cases 2 To analyze the relationship between F and a 3 To study a two body system 4 To determine the acceleration due to gravity g 5 To estimate the friction force for an Atwood Machine MATERIALS LoggerPro slotted weights Force Sensor Smart Pulley Accelerometer photo gate Dynamics cart lab stand C clamp According to Newton s Second Law the acceleration of an object depends on the net force acting on it and on its mass All the forces acting on an object can be represented on a freebody diagram Examples of forces are gravity friction tension in a string etc During the first part of this lab you will prove Newton s Second law by measuring the net force acting on a cart and its resulting acceleration During the second part you will study a 2 body system known as Atwood Machine By measuring the acceleration of the system you will determine the free fall acceleration g and the friction force present in the system PRELIMINARY QUESTIONS 1 A variable force in the range 0 to 50 N is applied to an object of mass m 1Kg Predict and sketch the acceleration vs force graph 2 How would your graph change if the mass of the object is now 5 Kg What is the significance of the slope of the graph 3 For the system represented in the figure below a Draw the free body diagram for each object considering the mass of the pulley and the mass of the string to be zero m1 b m2 Calculate the acceleration of the system in terms of m 1 m2 and f the friction force Part I Newton s Second Law PHY 211 General Physics I Lab Instructor Tony Zable page 2 of 4 PROCEDURE 1 Attach the accelerometer to the dynamics cart so as the arrow will point in the direction of the motion Attach the Force Sensor to the same cart with the hook toward outside so you can hold the hook 2 Connect the Low g Accelerometer to the Ch 1 and the Dual Range Force Sensor to the Ch2 of the LabPro interface 3 Open the experiment 09 Newton s Second Law from the Physics with Computers directory 4 Click on the Zero icon to zero both sensors and then push Collect 5 Grab the hook of the Force Sensor and move the cart back and forth for 10 seconds The force applied to the hook and the acceleration of the cart will be recorded ANALYSIS QUESTIONS 1 Examine the Force vs time and acceleration vs time graph using the Examine option under the Analyze pull down menu When is the force maximum What is the value of the acceleration when the force is maximum What is the maximum value of the acceleration 2 What is the shape of the Force vs acceleration graph Find the best fit 3 Cut and paste the graph including the best fit information into Word 4 What is the significance of the slope of the Force vs acceleration graph What are the units 5 Disconnect the sensors from the interface and find the total mass of the object cart sensors using the digital scale Enter your result below Total mass 6 Compare the mass to the slope of the graph determined in step 3 Write a conclusion regarding the relationship between force mass and acceleration below Part II Atwood Machine PHY 211 General Physics I Lab Instructor Tony Zable page 3 of 4 For the system described in the Preliminary Question the acceleration depends on the masses of the 2 objects and the friction force 1 a m1g m2g f m1 m2 During this experiment the sum m1 m2 will remain constant but the difference m1 m2 will be varied The acceleration vs m 1 m2 graph will be used to determine g from the slope and f y intercept PROCEDURE 1 Attach the Smart Pulley to the Photogate using the included rod Thread the string around the pulley Connect the Smart Pulley to the Dig Sonic1 port of the Lab Pro interface 2 Attach the rod to a lab stand and secure the lab stand to the table with a C clamp 3 Start LoggerPro and open Experiment Probes and Sensors Photogate Pulley cmbl 4 Attach 2 hangers on the 2 ends of the string Add slotted weights 450 g on each hanger using many small weights 2 g on one of the hangers During the experiment the total mass will remain constant but the mass difference m 1 m2 will be changed by moving small weights from one hanger to the other 5 Since there are 450 g on each hanger your system is now in equilibrium To estimate the friction force move small weights from one hanger to the other until the system barely starts moving Record the mass difference at which the system starts moving This difference in weight represents the force needed to overcome the friction Record this value below f N 6 Restore the equilibrium 450 g on each hanger Move 4 g from one hanger to the other but keep the system from moving The mass difference is now 8g Record the mass difference in the table 9including units Push the Collect button and release the system 7 Find a linear fit for the velocity graph What is the significance of the slope of this graph Record the value of the acceleration including units in the table 8 Repeat steps 6 7 for 8 more values of the mass difference m 1 m2 9 After all the values have been recorded plot acceleration vs m 1 m2 graph using Graphical Analysis Find a best fit equation for your graph 10 Cut and paste the graph including the best fit information into Word Print out the graphs PHY 211 General Physics I Lab Instructor Tony Zable page 4 of 4 Data Table Trial m1 m2 a ANALYSIS QUESTIONS Refer to equation 1 to answer the following questions 1 What is the significance of the slope of the acceleration vs m 1 m2 graph What are its units 2 From the slope of the acceleration vs m1 m2 graph determine the acceleration due to gravity g don t forget to take into account the mass of the hanger Enter your result below g 3 Compare your value above to the accepted value and calculate the difference List several reasons for the difference 4 Does the friction force account for the difference calculated above Why or why not Be specific 5 What is the physical significance of the y intercept b of your fit equation Calculate the friction force f using this coefficient and enter your result below f 6 Compare your answer in 5 to the measured value of the friction force recorded above and calculate the difference List several reasons for the difference you observed