lab report 8 - PHY2053L
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2053L
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Mechanical Engineering
Date
Dec 6, 2023
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docx
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Uploaded by inuyasha078
Cristian Acuna Vasquez
03/16/2020
PHY2053L
Title:
Energy in Simple harmonic Motion
Purpose:
The purpose of this experiment is to further understand and demonstrate simple
harmonic motion through a simulation experiment involving a spring and different masses.
Background Information:
Any motion that repeats itself at regular intervals is called periodic or harmonic motion.
Motion
is periodic about an equilibrium position.
The restoring forces are proportional to and oppositely
directed to a displacement from the equilibrium position.
It can be described for an oscillating
mass in terms of its position, velocity, and acceleration as a function of time.
energy is present in
three forms for the mass and spring system.
The mass , m, with velocity, can have kinetic energy
KE; which results in the formula
KE = ½ mv
2
.
The spring can hold potential energy
as well or
PE
elastic
,
which can be calculated by the formula PE
elastic
= ½ ky
2
.
k is the spring constant and y
is the extension or compression of the spring measured from the equilibrium position.
The
principle of this experiment,
if there are no other forces experienced by the system, is
conservation of energy ∆KE + ∆PE
elastic
= 0
Materials:
computer
Simulation software
PhET
Procedure:
Using the PhET simulation software, use
50 g to 200g masses and
mount them
into the spring.
As the mass moves up and down and it reaches equilibrium,
record the kinetic energy,
gravitational potential energy, elastic potential energy, thermal energy and total energy and
calculate the k constant of the spring.
Data:
Part I :
Preliminary data collection
Mass (kg)
Gravitational force
Force
(N)
Spring Displacement
(m)
0.05
9.8
0.49
0.07
0.1
9.8
0.98
0.14
0.15
9.8
1.47
0.21
0.2
9.8
1.96
0.28
0.25
9.8
2.45
0.35
Part II
: Determining spring constant
F= -kx
then
k= -F/x
Mass (kg)
Gravitational
force
Force
(N)
Spring Displacement
(m)
k constant (N/m)
0.05
9.8
0.49
0.07
-7.0
0.1
9.8
0.98
0.14
-7.0
0.15
9.8
1.47
0.21
-7.0
0.17
9.8
1.68
0.24
-7.0
0.2
9.8
1.96
0.28
-7.0
0.23
9.8
2.25
0.32
-7.03
0.25
9.8
2.45
0.35
-7.0
0.28
9.8
2.74
0.39
-7.03
0.30
9.8
2.94
0.42
-7.0
Part III : Energy in Simple harmonic motion
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Results/ Calculations:
Slope of force vs. position
7.016
N/m
Error Analysis:
In this lab, there are no errors because it was done by a simulation.
In real life, air resistance
could be a factor for different results
Conclusion:
In conclusion, we were able to calculate the spring constant k.
We observed that the relationship
between the slope of force vs. position graph results in the approximation of the value k of the
spring.
In simple harmonic motion, there is a continuous interchange of kinetic energy and
potential energy. At maximum displacement from the equilibrium point, potential energy is a
maximum while kinetic energy is zero. At the equilibrium point the potential energy is zero and
the kinetic energy is a maximum. At other points in the motion the oscillating body has differing
values of both kinetic and potential energy.
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Z///////
k
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F
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(c)
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