__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/s^{2}**.** In American Consistent System,
F is in
pound-force (lbf), M is in slugs, and
a is in ft/s^{2}**.**

__
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 = m_{2}g)
that causes motion must be equal to the mass
of the system (m_{1}+m_{2}) multiplied by the acceleration of
the system, a**.** Writing this statement mathematically, we have

Σ F =
(m_{1} + m_{2})a,
or,

m_{2}g = (m_{1}
+ m_{2})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 = (v_{f}
- v_{i})/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 Equations: { a
= (v Equations in (2) are to be used to measure
t, v |

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 V_{o} and
V_{f }. Determine the elapsed
time (t) between
V_{o}
and V_{f }. With
the V_{o}, V_{f }, 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 20**0**gr 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 30**0**gr 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 40**0**gr, 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 50**0**gr, 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 V_{o
}, V_{f },
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/s^{2}**.**

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

Part A**:** Part B**: ** Part
C**: **

__
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**.**