Lab 6 - Atwoods Machine and N2 Instructions

Figure 2 – The free-body diagram of m 1 and m 2 , assuming m 2 is pulling the system downward. T represents the tension in the string and the bottom force is the weight, or mg of each mass. The tension of the string is the same throughout, therefore the tension T in the free-body diagram for m 1 is the same as the tension in the free-body diagram for m 2 . The free body diagram gives the net force for each mass T − m 1 g = m 1 a and m 2 g − T = m 2 a (2) One can add the two equations simultaneously to eliminate the Tension variable (also unknown in the experiment) and to combine the equations into one m 2 g − m 1 g = m 2 a + m 1 a (3) The expression can be reduced down to ( m 2 − m 1 ) g = ( m 2 + m 1 ) a (4) Written this way, the expression models Newtons Second Law. The Net Force on the left is the difference in weight and on the right, the m is replaced by the combined masses ( m 2 + m 1 ) and a remains the net acceleration of the system. In the lab setting the masses can be measured with a triple beam balance or scale, and the acceleration can be measured either using kinematics or through Vernier Smart Pulley photogate measurement. The pulley will impart some friction on the system. We can rewrite equation 4 to incorporate the friction on the system with ( m 2 − m 1 ) g − f = ( m 2 + m 1 ) a (5) The friction can be added to the right side of the equation to model a linear relationship similar to y=mx + b. In this case, the y-axis will be the Net force, ( m 2 − m 1 ) g , the x-axis will be a . This leaves the slope as the ( m 2 + m 1 ) or the total mass of the system and the y-intercept will represent the frictional force implied on the system. ( m 2 − m 1 ) g = ( m 2 + m 1 ) a + f (6) The acceleration in this lab will be measured two ways. The first way is through the kinematic equation

2. Using the Velocity vs. Time graph, highlight the section of the graph that represents a straight line. Ignore any other shapes the graph might make. Since there are two lines, you may do this one at a time, or do them both at once. 3. Select the “Linear Fit” Icon at the top of the screen to find the slope of the graph. 4. Select both Run 1 and Lastest. 5. Record the slope of the graph in Trial 1 and Trial 2 of Table 5. 6. Repeat for each file for each mass difference. 7. Calculate the average acceleration for the two values. 8. Calculate the net force of the system using the same equation as step 8 in Method 1. They are the same net force. 9. Graph the Net force on the y-axis and the Acceleration on the x-axis. Label this graph as Method 2 Fnet vs Acc. 10. Determine the graphical information listed on Table 6 similar to Method 1. Analysis Questions 1. What is the evidence for Newtons Second Law in a Net Force vs Acceleration graph? Do your graphs support the theory for Newtons Second Law in Method 1 and Method 2? CER 2. Which method was more accurate and why? CER 3. Friction becomes important when the percentage between friction and the net force are greater than 25%. Usually if the percentage were less than 5%, then the friction would be negligible and not a factor to consider when evaluating data. The frictional force comes from the y-intercept of your graph. The net force comes from the y-values of the graph. a. For each applied force, divide the frictional force to get a percentage for each method % Friction = friction force Net Force ∗ 100% Mass Diff (g) Net Force Percentage of friction Method 1 4 8 12 16 20 24