The document describes an experiment to measure torque on a thin rod. A force sensor was used to measure the force applied at different distances along the rod. The collected data showed a linear relationship between force and distance. An equation was derived from a line of best fit to the data points: F = -3.597x + 5.3602. This equation represents the mathematical model of the relationship between force and distance for torque on the thin rod.
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Objective
The aim of this experiment is to collect and use data obtained from the experiment on forces acting on a
thin rod to develop mathematical models representing relationship between the dependent and
independent variables.
Equipment and tools
Bench clamps, Bench rods, Force sensor, Magnetic angle measurer, Meter stick, Pendulum clamp, Right
angle clamp, Scissors, Short rod, string, Threaded rod.
Theory
Torque is the rotational force applied to an object. Net torque will cause an object to rotate with
an angular acceleration. The size of a torque depends on, the size of the force applied and its
perpendicular distance from the axis of rotation which depends both on the direction of the force
plus its physical distance from the axis of rotation. An object is considered to behave like a point
particle when forces are applied to it in such that it moves but does not rotate.
Procedure
A thin rod was hung horizontally as in figure below.
A force was applied to the system and corresponding data was collected.
Figure 1. Experiment set up.
The position of the force sensor was varied along the length of the thin rod.
The value of the force measured was determined using the Capstone software
Data collection
The force on the rod was recorded at different distance along the rod and recorded in the table
below.
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Distance Force
0.905 2.12
0.89 2.14
0.865 2.27
0.86 2.3
0.853 2.31
0.83 2.35
0.8 2.45
0.766 2.52
0.75 2.64
0.737 2.67
0.721 2.9
0.678 2.94
0.632 3.07
Figure 2. Data collected for force and distance.
Results
From the data collected a graph of force versus distance is developed. From the graph a linear
relationship is established and an equation for the graph is obtained
𝐹 = −3.597𝑥 + 5.3602
From the equation linearized data is obtained and used to draw a linear graph.
y = -3.597x + 5.3602
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1
Force
Distance
Graph of force against distance
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Distance Force Linealized
0.905 2.12 2.104915
0.89 2.14 2.15887
0.865 2.27 2.248795
0.86 2.3 2.26678
0.853 2.31 2.291959
0.83 2.35 2.37469
0.8 2.45 2.4826
0.766 2.52 2.604898
0.75 2.64 2.66245
From the graphs the y intercept is 5.3602 and the gradient of the graph is -3.597.
Conclusion
y = -3.597x + 5.3602
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1
Force
Distance
Graph of linearized force versus distance
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Data obtained from testing torque on a thin rod is used to develop mathematical models. The
data is represented graphically by drawing a curve from the data. A line of best ft is
approximated from the data and used to obtain linearized data. The linearized data is used to
provide an equation for the graph. In this experiment the equation of the graph is obtained as
𝐹 = −3.597𝑥 + 5.3602
Having a gradient of -3.597 and you intercept of 5.2602.
