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AimThe aim of this experiment is to find the force constant of a helical spring by plotting a graph between load and extension.
Apparatus RequiredA helical spring
A set of weights
A ruler or meter scale
A clamp stand
A load hanger
A stopwatch or timer
TheoryThe force constant of a spring is a measure of its stiffness or the amount of force required to produce a given extension or compression. It is defined as the ratio of the applied force to the resulting extension or compression. Mathematically, it is given by:
k = F / Δx
where k is the force constant of the spring, F is the applied force, and Δx is the resulting extension or compression of the spring.
In this experiment, we will apply a gradually increasing load to the spring and measure the corresponding extension of the spring. We will then plot a graph of load against extension and use the slope of the graph to determine the force constant of the spring.
ProcedureSet up the clamp stand and attach the spring to it using the load hanger.
Measure the initial length of the spring using the ruler or meter scale.
Hang a known weight on the spring and measure the corresponding extension of the spring.
Record the data in a table and calculate the force and extension using the following equations:
Force (F) = mass x gravitational acceleration (g) Extension (Δx) = final length – initial length
Repeat steps 3-4 for different loads.
Using the data obtained, plot a graph of load against extension (Δx).
Draw the best-fit straight line through the graph.
Measure the slope of the graph. The slope of the graph represents the value of the force constant (k) of the spring.
Observation and ResultResult: The result of the experiment is the force constant of the helical spring. We will obtain a graph that represents the relationship between load and extension (Δx) of the spring.
Observation: During the experiment, we observe that as the load applied to the spring increases, the extension of the spring also increases. By plotting the values of load and extension on a graph, we observe a linear relationship between these variables. The slope of this line can be used to determine the value of the force constant of the spring.
We also observe that the spring exhibits elastic behavior up to a certain point, after which it undergoes plastic deformation. The elastic limit is the maximum stress or force that a material can withstand without undergoing permanent deformation. In this experiment, we must ensure that we do not exceed the elastic limit of the spring, as this would result in permanent deformation and inaccurate results.
This experiment demonstrates the concept of force constant and the behavior of springs under load. It also highlights the importance of ensuring that we operate within the elastic limit of a spring when measuring its mechanical properties.