ANALYSIS Another topic that we have tackled in Physics is Newton’s Second Law of Motion. In this experiment we will focus on Newton’s Second Law of Motion which states that a net force is required for a body to have an acceleration. And if a net force is applied on the object, the object will accelerate in the direction of the net force. The acceleration of the object is also directly proportional to the net force but inversely proportional to its mass. We will verify the relationships between a body’s acceleration and net force, and between acceleration and mass. The theory behind Newton’s Second Law of Motion is that first Newton defined momentum or P as the product of mass and velocity. The change in momentum or △P is brought about by the impulse ( J=F net △t ) acting on the body and will result with our first equation which is , F net △t=△P And if we let △t as it approaches zero, the instantaneous rate of change of momentum is, F net =lim ∆t→ 0 ∆P ∆t = dP dt = d ( mv ) dt
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ANALYSIS
Another topic that we have tackled in Physics is Newton’s Second Law of
Motion. In this experiment we will focus on Newton’s Second Law of Motion
which states that a net force is required for a body to have an acceleration. And if a
net force is applied on the object, the object will accelerate in the direction of the
net force. The acceleration of the object is also directly proportional to the net
force but inversely proportional to its mass. We will verify the relationships
between a body’s acceleration and net force, and between acceleration and mass.
The theory behind Newton’s Second Law of Motion is that first Newton
defined momentum or P as the product of mass and velocity. The change in
momentum or △P is brought about by the impulse (J=Fnet △ t ) acting on the body
and will result with our first equation which is ,
Fnet△ t=△P
And if we let △ t as it approaches zero, the instantaneous rate of change of
momentum is,
Fnet= lim∆t → 0
∆ P∆ t
=dPdt
=d (mv )
dt
Since for most objects, the mass is constant the equation will be
Fnet=mdvdt
And Newton’s Law of motion is mathematically expressed as
Fnet=ma
For this experiment, the materials that we will use are one dynamics track
with a pulley, one dynamics cart, 1.5m of string, 2 pieces of photogates, 1 smart
timer, 1 set of weights, and a weight hanger. We are asked first asked to clean the
surface of the dynamics track by wiping it with tissue to remove dust and other
particles. We should also put extra care on the super pulley and the photogates to
avoid damage. We should also be sure to use 220V-AC source to power the smart
timer.
The first part of this experiment is “Constant Mass, Changing Net Forcer”
wherein the mass of the cart is constant and the mass of the pulley is changing. The
first procedure of this experiment is to first setup the dynamics track. For our
group, we set-up the dynamics track on our laboratory table. We make sure that the
track doesn’t move. The next thing we did was to get the mass of the dynamics cart
which is at 0.51724 kg. The next thing we did was to set the first photogate at the
20-cm mark of the dynamics track and the second photogate at the 50-cm mark.
We then plugged the photogates into the smart timer and set it at “Time:Two
Gates”. Then we set one end of the string to the cart and the other on the weight
hanger over the pulley. On our first trial, we used 20g on our hanging weight. We
then repeated this again while using 40g, 60g, 80g, and 100g for each trial. We
then computer for the accepted value of acceleration as well as the experimental
and the percentage error each trial. We got these results:
CONSTANT MASS, CHANGING NET FORCE
Mass of Cart, m1 = 0.51724 kg
Distance Traveled, s = 0.5 m
TRIAL Total
hanging
mass, m2
Net force,
m2g
Acceleration
(accepted
value), a
Time
of
travel, t
Acceleratio
n
(exp.
value), a
%
Error
1 0.02 kg 0.196 N 0.365 m/s2 1.6389
s
0.372 m/s2 1.92%
2 0.04 kg 0.392 N 0.703 m/s2 1.2030
s
0.691 m/s2 1.71%
3 0.06 kg 0.588 N 1.019 m/s2 0.9587s 1.088 m/s2 0.98%
4 0.08 kg 0.784 N 1.313 m/s2 0.9398
s
1.134 m/s2 13.63%
5 0.10 kg 0.980 N 1.588 m/s2 0.8066
s
1.537 m/s2 3.21%
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Constant Mass, Changing Net Force
Net Force (N)
Acce
lera
tion
(m/s
2)
From this table and graph, we found that the dynamics cart’s acceleration
will increase as the net force increases.
For the second part of our experiment entitled “Changing Mass, Constant
Net Force”, we first used the same set-up as the first part. We repeated the same
experiment but instead of changing the mass of the pulley we only set it at 100
grams. Then for trials 2-5, we increased the mass of the dynamics cart by 100g
each trials. We then calculated the accepted value, experimental value, and the
percentage error of the experiment.
CHANGING MASS, CONSTANT NET FORCE
Total hanging mass, m2 = 0.1 kg Net Force, m2g = 0.98 N
Distance Traveled, s = 0.5 m
TRIAL Mass of cart +
mass added, m1
Acceleration
(accepted
value), a
Time of
travel, t
Acceleration
(exp. value),
a
%
Error
1 0.51724 kg 1.5877 m/s2 0.7620 s 1.722 m/s2 8.51%
2 0.61724 kg 1.3663 m/s2 0.8169 s 1.494 m/s2 9.74%
3 0.71724 kg 1.1992 m/s2 0.9426 s 1.125 m/s2 6.17%
4 0.81724 kg 1.0684 m/s2 0.9974 s 1.005 m/s2 5.90%
5 0.91724 kg 0.9634 m/s2 1.0814 s 0.855 m/s2 11.21%