To investigate Hooke’s law by estimating the spring constant of a spring.
Hooke’s law is a law in physics named after Robert Hooke, a British physicist who lived in the 17th century and is said to have been the first to pose the idea of this law.(wikipedia,2010) Hooke’s law states that the Force with which a spring pushes back is linearly proportional to the distance from its equilibrium (wikepedia,2010) , this can be simplified by saying that the force acting on a spring/material is directly proportional to the extension(which is how long the spring/material has become/stretched since the force was applied) of the string/material (Breithaupt, 2010). This can be expressed as an equation. F= -ke
Where F represents the Force (in N), e represents the extension (in m) and k is referred to as the spring constant (which is the stiffness of the spring and is unique for each spring) in N/m (Breithaupt, 2010). Many materials obey this law as long as the load applied on the material does not cause the material to exceed its elastic limit causing the material to loose its elasticity and become deformed even after the load applied has been removed. As the material exceeds its elastic limit the string begins to display a behaviour called “Plastic behaviour”, in some materials like glass, once it reaches its elastic limit it breaks. When represented on a graph it is seen that the after the elastic limit has been exceeded the material stops obeying Hooke’s law.
Extension (m) Fig. 1: Showing the behaviour of a material when its elastic limit has been exceeded.
Materials that obey Hooke’s law are referred to as “Hookean” Materials. However not all materials obey this law and they are referred to as “non-Hookean” materials, Rubber is a good example of a Non-Hookean material because its extension is dependent on stress, temperature and loading rate. (Wikipedia, 2010). This experiment was designed to calculate the spring constant of a spring by measuring the extension of the spring for several weights hung on the spring and it was predicted that the spring constant “k” will be constant for all the values. The independent variable in the experiment was the force applied on the spring while the dependent variable was the extension of the spring for each weight applied.
The apparatus was set up as shown below:
Hanger with mass (50g)
Masses (50g and 20g)
Fig. 2: Apparatus setup
The spring was hung on the retort stand and the pointer was attached to the end of the spring. The metre rule was placed as shown on Fig.1; the metre rule was used to read the equilibrium position of the spring i.e. with no weight attached, and the reading was recorded. The hanger with a mass of 50g was then attached to the pointer as shown in Fig.2; the reading of the new position of the spring on addition of the hanger was recorded. A weight of 50g was added on the hanger and the new position of the spring was recorded. Another weight of 50g was then added on top of the 50g weight on the hanger and the new position of the spring was recorded. The new positions of the spring on addition of several weights of 50g until the mass on the spring was up to 400g was recorded. Weights of 70g (50g and 20g) and 90g (50g and two 20g) were also added to the hanger individually and the new position of the spring for each of them was recorded.
The readings recorded are tabulated in the Tables below.
TABLE 1: shows the values of the mass (g), the calculated Force (N), the positions of the spring (cm) and the calculated extension (cm) readings collected....