Question

Discuss Newton’s Second Law. (In equation and words.)

Describe the use of dynamics track & cart, pulley, string, mass, force sensor, and computer graphical interface to study motion. (Explain it in a way that someone who has not seen it can understand what was done.)

Describe how experimental and theoretical values for acceleration will be determined and compared to verify Newton’s Second Law.

Answer 1

Newtons Second Law:

In general we can state this law as net acceleration of a body is dependent up on two variables

1.Net force acting on a body.

2.Mass of the body.

To compute the formulation of newtons second law of motion we can tell that

Force acting on the body is directly proportional to the rate of change of momentum

dp/dt F_net -------------(1)

where p = momentum

dp/dt = mV-mU/t ------------(2)

m =mass of the object

V= final velocity of object

U= intial velocity of object

m(V-U)/t F_net--------------(3)

removing the proportionality constant we get the equation as

m[(V-U)/t ] = mak=F_net----------(4); taking the value of k =1

By applying the standard conditions of mass 1kg and acceleration = 1m/s² and F_net = 1 N

Hence newtons second law of motion can be stated in a single formula as below

F = ma-----(5)*

DYNMICS OF CART ADN TRACK: The below image is an experiment to understand the newtons second law of motion in a simpler way which uses a pulley, cart and track for it to move.

This complete experiment consists of three steps.

Sensor calibration , Recodring data and Analyzing data.

SENSOR CALIBRATION:

1. Mount the Smart Pulley at the end of the track (or the edge of the table).
2. Attach a string to the dynamics cart. Make the string long enough so that when the cart is next to the Smart Pulley and the string is over the pulley, the string reaches the ground.
3. Attach a mass hanger to the other end of the string.
4. Put the string that connects the cart and the mass hanger over the Smart Pulley. Adjust the Smart Pulley so that the string from the cart is parallel to the level track or the top of the table.
5. Place about 20 grams of mass on the mass hanger.
6. Add about 200 grams of mass to the top of the cart.
   • The applied net force is the weight of the hanger and masses (m x acceleration due to gravity) minus friction forces.
7. Measure and record the total mass of the cart (M).
8. Measure and record the total mass of the mass hanger and masses (m)

RECORDING DATA:

1. When you are ready to collect data, pull the cart away from the Smart Pulley until the mass hanger almost touches the pulley.
2. Turn the pulley so that the photogate beam of the Smart Pulley is "unblocked" (the light-emitting diode (LED) on the photogate is off).
3. Click the "REC" button to begin data recording.
4. Release the cart so it can be pulled by the falling mass hanger. Data recording will begin when the Smart Pulley photogate is first blocked.
5. Stop the data recording just before the mass hanger reaches the floor by clicking the "STOP" button.
   • WARNING: Do not let the cart hit the Smart Pulley!
6. In the Graph, click the "Statistics" button to open the Statistics area. Click the"Autoscale" button to resize the Graph to fit the data. Click the "Statistics Menu" button. Select "Curve Fit, Linear Fit" from the Statistics menu.
7. The "Statistics" area will show the y-intercept (a1), slope (a2), and the quality of the fit (chi^2).
8. Record the value of the slope of velocity versus time, which is the average acceleration of the cart.
9. Change the applied force (F = mg) by moving masses from the cart to the hanger. This changes the force without changing the total mass. Measure and record the new values for M (total mass of cart) and m (mass hanger and masses).
10. Repeat the data recording steps several times. Each time, move some of the mass from the cart to the mass hanger. Measure and record the values for M (cart) and m (mass hanger and masses). Record the value of the slope for each trial.

ANALYZING DATA:

1. Calculate the net force acting on the cart for each trial. The net force on the cart is the tension in the string minus the friction forces. If friction is neglected, the net force is:

   F_net = M_cart x Acceleration.

   Acceleration =

2. Also calculate the total mass that is accelerated in each trial.
3. Graph the acceleration versus the applied net force for cases having the same total mass.
4. Calculate the theoretical acceleration using Newton's Second Law (Fnet = ma). Record the theoretical acceleration in the Data Table.
5. Calculate the percentage difference between the actual and theoretical accelerations. Remember,

   Pecentage difference =

6. If you did the optional procedure, graph the acceleration versus the total mass for cases having the same applied net force.

COMPUTER SETUP : USED TO STUDY THE MOTION:

1. Connect the science workshop interface with your computer.
2. Open the Cart document or Cart and Track document in your handout folder.
3. This will open up with a document of velocity(m/s) and time (s).