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Lab-Report
1) Title Page :
EMANUELA SAGONTI
8/02/2014
The second law of dynamics: analysis of the dependence between force an acceleration
using a cart running on a law friction rail.
2) Abstract
With this experiment we want to prove the direct proportionality between force and
acceleration as stated by Newton’s second law of dynamics. We used a cart of constant mass
pulled by different forces and we measured the different lapses of time the cart needed to
run a constant distance. The collected data were represented on a graph to prove the direct
dependence.
3) Introduction: (theoretical principles and background)
Newton’s second law states that when a force acts on an object, it will cause the object to
accelerate . The larger the force applied on the object, the greater the acceleration of the object.
This law may be written as
F = m * a, where F indicates the force which causes motion, m
indicates the mass of the object and a indicates the acceleration.
The two physical quantities F and a are directly proportional, which means that if the force is
doubled the acceleration is also doubled, if the force increases or decreases, the acceleration
increases or decreases in the same ratio. If we draw a graph representing the dependence
between the two quantities we obtain a straight line passing through the origin of the Cartesian
plane. The slope of the line represents the constant ratio between the two quantities. The general
form a direct proportional relationship between two items y and x is y=k*x.
1
2
The displacement/time law for the constant acceleration motion states that s=s0+v0t+ 𝑎𝑡 2 .
The applied pulling force is the weight of the free falling masses hooked to the cart with the
light rope (as you can see in the picture). We obtain it as the product of mass and gravity
(g=9.81m/s2).
4) Materials (or Equipment)
1.
2.
3.
4.
5.
A low friction rail
A cart
Two photoelectric cells
An electromagnet
Different masses (10g each)
5) Instruments
1. A ruler (range: 60cm, scale: 1mm)
2. An electric timer (scale: 0,01 s)
6) PICTURE of the equipment
7) Experimental Procedure
First we checked if the rail was exactly horizontal.
We set the two photoelectric cells at a distance s =50cm. We placed the cart on the rail and
hooked it to the first mass using a light rope. We switched the electromagnet off: the cart was
free to move under the influence of the pulling force caused by the free falling mass. Passing in
front of the photocells the cart made them start and stop timing.
We set the first photocell at the starting point of the cart so that the initial position so and the
initial velocity v0 were equal to zero. Using the value of the interval of time and rearranging the
2𝑠
displacement/time formula we found the value for the acceleration of the cart a= 2
𝑡
We repeated the procedure changing the pulling force: we doubled the mass, tripled it,
multiplied it 4 and 5 times.
To dim the experimental errors we repeated the experiment three times and calculated the mean
elapsed time.
8) Results
We collected the following data:
9) Graph
10) Conclusion
As we expected the ratio between applied force and acceleration is constant, the graph we
obtained using the collected data is a straight line passing through the origin, so we can conclude
that there is a directly proportional dependence between force and acceleration as stated by
Newton’s second law of dynamics.