Context You do an internship in a mechanical component characterization company for your engineering degree. You are currently working on determining the spring constant of industrial springs. To do this, you measure the elongation of springs placed on a graduated inclined plane, to which you attach masses. Constraints One end of the spring is attached to a hook at the top of the inclined plane and the other end is attached to a mass. The spring is parallel to the plane, and the force it exerts on the mass is also parallel to the plane. The angle of inclination of the plane is known, as well as its uncertainty. There is no friction between the plane and the mass. The natural length of the spring and its uncertainty are known. By hooking a known mass (m ± delta m), you measure that the spring now has a length (L ± delta L). We use the value g=(9.81 ± 0.01)m/s^2 for our calculations. Schematization Draw a diagram of the object that interests us. Draw your x and y axes. Draw and name each force experienced by the object that interests us. Modelization Build a model to find the spring constant of the spring (with its uncertainty) given the known parameters. Then test your model with the following values: Plane tilt angle: (11.4 ± 0.2) degrees Natural spring length: (0.145 ± 0.001) m Attached mass: (0.15 ± 0.001) kg Spring length with a mass attached: (0.17 ± 0.002) m
The spring constant
Context
You do an internship in a
Constraints
One end of the spring is attached to a hook at the top of the inclined plane and the other end is attached to a mass.
The spring is parallel to the plane, and the force it exerts on the mass is also parallel to the plane.
The angle of inclination of the plane is known, as well as its uncertainty.
There is no friction between the plane and the mass.
The natural length of the spring and its uncertainty are known.
By hooking a known mass (m ± delta m), you measure that the spring now has a length (L ± delta L).
We use the value g=(9.81 ± 0.01)m/s^2 for our calculations.
Schematization
Draw a diagram of the object that interests us. Draw your x and y axes. Draw and name each force experienced by the object that interests us.
Modelization
Build a model to find the spring constant of the spring (with its uncertainty) given the known parameters. Then test your model with the following values:
Plane tilt angle: (11.4 ± 0.2) degrees
Natural spring length: (0.145 ± 0.001) m
Attached mass: (0.15 ± 0.001) kg
Spring length with a mass attached: (0.17 ± 0.002) m
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