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Waves - Hooke's Law and Spring Constant

Julia Wuestefeld

Design

Safety Precautions:

Beware of your feet because the stand or the weight might fall if it is not safely secured with tape.

Beware not to use a weight that is too heavy, so as not to stretch the spring beyond its capacity.

Aim: The aim of this investigation is to explore the validity of Hooke's Law and the relationship between a spring's force and the displacement of a mass.

Background: Hooke's Law states that there is a direct relationship between a spring's force and the displacement of the mass on it, as we can see in the formula:

F=-kx

Therefore, according to theory the more the mass is displaced, the more force the spring will have once it is released.

Research Question: Do springs in practice follow Hooke's law, such that there is a direct relationship between force and displacement?

Hypothesis: I believe that the springs will have a force directly proportional to the displacement of the mass attached to it.

Independent Variable: The displacement of the mass attached to the spring is the variable that will be changed in the experiment.

Dependent Variable: The force due to the spring is the variable that will change in this experiment due to the displacement of the mass attached to the spring.

Controlled Variables: The spring constant should remain constant throughout the experiment, for it is what is being calculated to find the direct relationship.

Materials:

Clamp stand

Weight (mass of 1N)

Five different kinds of spring scales

Measuring tape (30cm ± 0.1cm)

Masking Tape

Procedure:

Fix one of the spring scales to the clamp stand.

Attach the tape to one end so it is possible to measure the displacement of the scale.

Hang the 1N weight on the spring.

Pull the weight these specific distances from the equilibrium point and annotate the change in the force displayed in the scale in tables:

1 cm

0.5cm

1.5 cm

-0.5 cm

-1 cm

2 cm

Repeat procedures 1-4 utilizing different spring scales (remember to write down each trial on a separate table).

Data Collection

Table One. For each of the displacements, the change in force for the first spring scale was recorded, in order to then find k.

Displacement (x ± 0.1 cm)

ΔF (N± 0.1N)

1cm

0.5N

0.5cm

0.25N

1.5cm

0.75N

-0.5cm

-0.25N

-1cm

-0.5N

2cm

1N

Table Two. For each of the displacements, the change in force for the second spring scale was recorded, in order to then find k.

Displacement (x ± 0.1 cm)

ΔF (N± 0.1N)

1cm

0.4N

0.5cm

0.2N

1.5cm

0.60N

-0.5cm

-0.20N

-1cm

-0.40N

2cm

0.80N

Table Three. For each of the displacements, the change in force for the third spring scale was recorded, in order to then find k.

Displacement (x ± 0.1 cm)

...

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