Newton s Second Law Thou rulest the power of the sea: and appeasest the motion of the waves thereof. Psalms 88:10

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1 Newton s Second Law Thou rulest the power of the sea: and appeasest the motion of the waves thereof. Psalms 88:10 Introduction Newton developed a second law that further clarified the force, mass and acceleration in relationship to motion. Newton s Second Law of Motion loosely stated is: Acceleration of an object increases proportionately as the net force acting on the object increases, and; acceleration decreases proportionately as the mass of the object increases. This is stated mathematically as: Force = (mass) x (acceleration). Newton s Second Law describes motion of objects for which the forces are not balanced. The net force causes the object to accelerate, either going faster or slower. The acceleration depends inversely upon the mass of the object the greater the mass, the lower the acceleration. Newton s Second Law will be examined using a fixed pulley system. A fixed pulley is a grooved wheel that turns freely and changes the direction of a force. In this experiment you will time the downward displacement of a set of washers on a pulley. Knowing time and the amount of displacement, you will calculate predicted and actual acceleration. This acceleration increases as the force acting upon it increases. The greater the mass of an object, the lower the acceleration. Learning Objectives: Explore the relationship between net force, mass, acceleration and force-reaction pairs. Materials Required: From Physics Kit Safety Glasses Washers Average mass of 7.2 g each Pulley String Student Supplied Measuring tape Timer Masking tape Safety Objects will be moving vertically and horizontally. Ensure that the work area is free and clear. Experiment: Newton s Second Law Regarding the Pully System: Find a place (table, dresser, hook, curtain or shower rod) to attach a pulley so that the objects on either side can both freely move and can reach the floor. Note: The higher the pulley, the greater the time intervals, the better able you will be to measure the time it takes the weights to reach the floor. It is best to have an assistant for these steps. Regarding the Trials: You will perform a total of four trials with the number of washers for the heavy side (M1) and the number for the lighter side (M2) as shown in Table A. An average of 7.2 g per washer has been used to estimate the masses of M1 and M2. The estimated total masses for M1 and M2 have been calculated and placed in Table A for you Catholic Initiatives in Math and Science, LLC All Rights Reserved 1

1. Set up the Pully System: Attach pulley to the side by tying a string around one hook and using masking tape so that it is secure (see figure). Thread string over the groove of the pulley.

2 1. Set up the Pully System: Attach pulley to the side by tying a string around one hook and using masking tape so that it is secure (see figure). Thread string over the groove of the pulley. Mass 1 (M1) will be on one side and Mass 2 (M2) will be on the other side. For purpose of uniformity, M1 will always be the heavier mass. The string should be long enough so that M2 can be near the pulley and M1 should just be touching the floor. 2. Set up the masses for Trial 1: On one side of the string, tie or paperclip 5 washers. This is M1. On the other side of the string, tie or paperclip 4 washers. This is M2. 3. Measure the height (the displacement): Pull M2 gently until it is just touching the ground. Mark START location for heavier M1 near the pully: o The heavier M1 mass will always start at the pully and end at the floor o With masking tape, mark on some convenient location, where M1 bottom touches o You will START at this location for each trial Using measuring tape, measure the distance from the START to the bottom edge of M2. Place the measurement in Table A. This will be height (h, or displacement) for all trials. 4. Perform Trial 1 (best performed with 2 people): Place the heavier M2 near the pulley Bottom of the mass should be in line with the START mark on the masking tape Person 1: o Hold M2 in place o When ready to drop the mass, count down and release the mass at the count of 1 Person 2: o At the moment 1 is said, Person 2 will start the stopwatch o This countdown minimizes reaction time errors o Stop the timer when M1 reaches the floor Record the time on a sheet of paper Repeat the measurement twice more Average the 3 readings Record the average in Table A in the column, Timeavg (s) 5. Trial 2 There are now 6 washers on M2 and 3 on M1 (See Table A) Run the Trial 2 experiment by repeating Step 4 above 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 2

3 6. Trial 3 There are now 7 washers on M2 and 2 on M1 (See Table A) Run the Trial 3 experiment by repeating Step 4 above 7. Trial 4 There are now 8 washers on M2 and1 on M1 (See Table A) Run the Trial 4 experiment by repeating Step 4 above Perform Data Calculations: With the M1, M2, height and average time data, you will first calculate the predicted and actual acceleration using equations for a stationary pulley. Next, you will use the actual acceleration and Newton s Law (Force = mass*acceleration) to find the Force used in each mass pair. 8. Find Predicted Acceleration and record in Table B This is Equation 1 Where: o g = gravity = 9.81 m/s 2 o M1 = heavier mass acceleration = [ M1 M2 M1 + M2 ] x g o M2 = lighter mass 9. Find your actual Measured Acceleration and record in Table B acceleration = 2h t 2 This is Equation 2 Where: o h = height in meters o t = time in seconds 10. Find Percent Error and record in Table B Percent Error = [ This is Equation 3 predicted value measured value predicted value ] x 100% 11. Find Force for each Mass pair and record in Table C Force = (mass) x (acceleration) This is Equation 4 Acceleration = Measured Acceleration obtained in Table B (place it in Table C) 12. Graph Measured Acceleration vs. Mass Difference (M1 M2) using provided graph paper 13. Perform Data Analysis and Conclusions 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 3

4 Lab Report for Data Tables: Table A Newton s Second Law Experiment Height or Displacement (d): Trial Mass 1 (M 1,g) Mass 2 (M 2,g) M1-M2 (g) Timeavg (s) M1+M2 (g) (5 washers) 28.8 (4 washers) (6 washers) 21.6 (3 washers) (7 washers) 14.4 (2 washers) (8 washers) 7.2 (1 washers) Trial Table B Newton s Second Law Experiment Predicted a m/s 2 (Eq. 1) Measured a m/s 2 (Eq. 2) Percent Error (Eq. 3) Trial Table C Newton s Second Law Experiment M1-M2 (g) Measured a m/s 2 (Eq. 2) Net Force (Newtons) Graph your data with Measured Acceleration on the y-axis and Mass Difference (M1-M2) on the x-axis. Use the graph paper that follows Table B. LABEL! 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 4

Conclusions and Evaluations for Newton s Second Law Experiment Now that you have organized the data and performed certain analyses on it, let us draw some conclusions. 1.

5 Conclusions and Evaluations for Newton s Second Law Experiment Now that you have organized the data and performed certain analyses on it, let us draw some conclusions. 1. Newton s Law predicts, but does not prove, that acceleration is proportional to the difference between masses on a fixed pulley. This is because of the increasing pull of gravity on the increasing mass. Does your graph above of Measured Acceleration vs Mass Difference support or refute this? Explain 2. Compare how changing your mass pairs affected the Net Force. Plot M1-M2 vs. Net Force (y-axis) on the graph below. LABEL! Do the results obey Newton s Second Law? Explain. 3. How well did your acceleration compare with the predicted acceleration? What are some sources of error? 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 5

Part 1: Relationship of Radius and Time Period. PHY Lab 10: Circular Motion

Part 1: Relationship of Radius and Time Period. PHY Lab 10: Circular Motion Circular Motion The wind goes towards the south, and turns towards the north; it turns about continually, and the wind returns again to its circuits. Ecclesiastes 1:6 Introduction Most have been on a Ferris