Question

experiment 6 verification of newton's second law of motion

Answer 1

Newton’s Second

Objective: To study accelerated motion under an applied force to test Newton’s Second Law of Motion.

Pre-lab Discussion

In this experiment we will measure the acceleration of a cart subject to an applied force and test the theoretical predictions of Newton’s Second Law. A general diagram for this experiment is illustrated here:

Treating the two masses as a single system with the pulley only serving to change the direction of the applied force, we see that the applied force is equal to m2g. So F = ma becomes m2g= (m1 + m2)a . In

this experiment we will first vary the applied force (while keeping the total mass constant) and then vary the total mass (while keeping the applied force constant). We will be measuring accelerations in each case.

Procedure

Part I: Acceleration With Fixed Total Mass

1. Obtain a dynamics cart, smart pulley, and mass set. Set up your kinematics track as shown below.

Level the track as carefully as possible.

2. Configure Capstone to use a Photogate with Pulley (Smart Pulley). Display a velocity graph so that you can measure accelerations by finding the slope of the graph.

3. Attach a string to the cart and a mass hanger (for m2) to the string. Use a string that is long enough so that when the cart is next to the smart pulley and the string is over the pulley, the string touches the ground. Weigh your dynamics cart. Place an extra 20 g on the mass hanger (so that m2 = 25 g), and100 g of mass on the cart.

4. Pull the cart back so that mass m2 is as high off the floor as possible. Release the cart from a stationary position and let it travel as far as it is able, while still accelerating. Do not let the cart hit the pulley! Don’t let the mass hanger crash into the floor!

5. Obtain a “good” run and use your onscreen graph to measure its acceleration. Record all acceleration values in your lab notebook in a data table that has three columns, m2 (kg), m2g (N),   and a (m/s2).

6. Repeat this procedure for a hanging mass of 50 g, 75 g, 100 g, and 125 g. In each case, make sure the total of the hanging mass and the mass on the cart is 125 g so that m1 + m2 = the cart mass + 0.125 kg.

7. Print a graph for each person in your group, showing the five runs you made.

Part II: Acceleration With Constant Driving Force

1.   In this part of the experiment we will vary the total mass of the system, keeping the driving mass fixed. Use a mass of 50 g for m2. Do not place any masses on the cart. Measure the acceleration like you did in Part I.

2.    Record your data in a table with columns for (m1 + m2) (kg), 1/(m1+m2)(1/kg), and a (m/s ).

3.   Next, repeat the procedure with runs where you add 100 g, 200 g, and 300 g to your cart. Record all results. Print a graph showing your four runs for each group member.

Data Analysis

1.   Use Pasco Capstone to plot your results on a graph. To create User-Entered Data, add a Table to a new Capstone page, click on the column header and select on of the User-Entered Data options in the “Create New” menu. Then add a graph to your page and choose the data you just entered to be displayed on the axes of the graph.

2.    For Part I, plot m2g on the horizontal axis and acceleration on the vertical axis (a vs. m2g). Use proper

labels and units for your graph. Perform a linear regression on your data to determine the slope.

3.    We know that the equation that describes this experimental system is m2g=(m1+m2)a . Re-arranging

        This so as to be in the form y= mx+b, we get a = (1/(m1+m2)).(m2g) the slope of the line should therefore be equal to 1/(m2+m2).

4. Compare your measured slope with the theoretical slope 1/(m1+m2) and calculate the percentage error.

And calculate the error = ((measured-theoretical)/theoretical)X100

5.    Print one copy of the graph for each person in your group to be included in your lab report.

6.     Use your data from part II to make a graph a vs. 1/(m1+m2) . the equation a = (1/(m1+m2) ).m2g still applies, but now the independent variable is 1/(m1+m2) and the theoretical slope is m2g, which we held constant during part II . Measure the your slope and calculate a percentage error.