Experiment 7

Newton’s Second Law of Motion

Objective:

The objective is to experimentally verify Newton’s Second Law, a relation between force, mass, and acceleration.

Equipment:

A car and track system, a spark generator, a weight hanger, a set of weights, electric wire, a few meters of spark-sensitive tape, a Metric ruler, and a scientific calculator

Theory:

According to Newton’s Second Law, the resultant force on an object is directly proportional to the mass of the object and the acceleration that the object undergoes.  Mathematically, this is expressed as ΣF = Ma where, in SI units, F is in Newtons (N), M is in kilograms (kg), and a is in m/s2.  In American Consistent System, F is in pound-force (lbf), M is in slugs, and a is in ft/s2.

Procedure:

General:  Set up the car and track system as in Fig. 1.  Do not connect it to the spark generator yet.  Use the leveling screws and adjust the track such that the car can move down the track at a constant velocity after being given a slight push.  At constant velocity, the slope force equals the friction force.  This eliminates the effects of friction and simplifies your calculations.

Adjust the spark-sensitive tape such that sparks (dots) are made only on one edge of the tape.  A tape may be used for 3 runs (once at each edge and once at the middle).  The weight hanger should hit the floor when the car is about 3/4 of the way down the track.  Dots beyond this point are not valid.  Mark this point on your tape.  Connect the spark generator and set it to 60 sparks per second.

WARNING:  When the spark generator is on, the entire apparatus is electrified.  Any contact must be through an insulator to avoid electric shock.  Turn the spark timer off immediately after each run.

If Newton’s Second Law (Σ F = ma) is true, the driving force (F = m2g) that causes motion must be equal to the mass of the system (m1+m2) multiplied by the acceleration of the system, a.   Writing this statement mathematically, we have

Σ F = (m1 + m2)a, or,

m2g = (m1 + m2)a.    (1)

All quantities are known except a that can be solved for.

In each run, the theoretical (accepted) value of acceleration can be calculated from this kinetic formula: Σ F = ma.

The experimental (measured) value of acceleration can be found from one of the kinematics equations: a = (vf - vi)/t .

Calculate a percent error between the theoretical and the experimental values in each run and record it in a table that you will arrange.

 A brief on Kinematics and Kinetics:If the net force ΣF is known and acceleration is found from it by using ΣF = ma, as in (1) the study is called "kinetics."   When force is not used, and instead distance, x, velocity, v, and time, t are used to solve for acceleration (Chapter 2 equations), the study of motion is called kinematics. Equations: { a = (vf - vi)/t ,  x = (1/2)at2 + vit , and  v = Δx/Δt }are three kinematics equations none of which involves force.  (2) Equations in (2) are to be used to measure t, vi , and vf  from the dots on the spark tape from which the experimental (measured) value of the acceleration a can be found.

Part A:  Constant force, varying mass

For each run, use a set of five good dots at the beginning of the tape and a set of five good dots at its end to calculate Vo and Vf .  Determine the elapsed time (t) between Vo and Vf .  With the Vo, Vf , and t that you measure, the experimental value of acceleration can be calculated for each run.  If necessary, see the experiment on  " The Acceleration of Gravity.

Run 1—The car is packed with four weights.  Place 200gr on the weight hanger.  Turn the timer on and release the car.  When the weight hanger hits the floor, turn the spark timer off.  Draw a small circle around each dot in Run 1.

Run 2—Remove one of the weights from the car.  Be sure to record its mass.  Move the spark-sensitive tape over a little so that a new line of dots can be obtained When you are ready, turn the spark timer on and release the car as in the first run.  Draw a small square around each dot in Run 2.

Run 3—Remove another weight, record its mass, and make another run.  Draw a small triangle around each dot in Run 3.

Part B:   Constant mass, varying force

Run 1-- Leave all four weights in the car.  Add 300gr to the weight hanger.  Turn the spark timer on and release the car.  Draw small circles around the dots.

Run 2— Increase the weight on the weight hanger to 400gr, shift the tape slightly, make a new run, and draw small squares around the dots.

Run 3—Increase the weight on the weight hanger to 500gr, shift the tape slightly, make a new run, and draw small triangles around the dots.

As in Part A, for each run, record data, calculate Vo , Vf , and t, and using these values, calculate the experimental value of acceleration.

Calculate the theoretical values of acceleration in each run and a corresponding percent error.

Part C:  Graph of F versus a

Use the data in Part B to graph F versus a.  For each run there will be one point on the graph. Each point will consist of an acceleration value and its corresponding force value.  The slope of the graph is m, the mass of the system (m=ΣF/a).  Find the slope of the graph with its correct unit.

Data:

Given:            g = 9.8 m/s2.

Measured:     For each part, on a separate sheet, arrange an appropriate  table.

Part A:                         Part B                         Part C

### Provide the necessary calculations.

Comparison of the results:

Provide the percent error formula used as well as the calculated of percent errors.

Conclusion:

State your conclusions of the experiment.

Discussion:

Provide a discussion if necessary.