Hooke's law - CCEA

• Hooke’s Law states that the extension of a spring is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.

• Hooke’s law gives the equation F = ke, where F is the applied force, e is the extension of the spring and k is called the spring constant.

• The gradient of the graph of force (y-axis) and extension (x-axis) is numerically equal to the spring constant.

To investigate experimentally the extension of a spring and how it is related to the applied force, and recall that the extension of a spring is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.

The main variables in a science experiment are the independent variable, the dependent variable and the control variables.

• The independent variable is what we change or control in the experiment.
• The dependent variable is what we are testing and will be measured in the experiment.
• The control variables are what we keep the same during the experiment to make sure it’s a fair test.

What are the variables?

In this experiment the:

• Independent variable is the stretching force F. This is the weight attached to the spring and is calculated using W = mg.
• Dependent variable is the extension of the spring e.
• Control variables are the material of the spring, and the cross section area of the spring. These are kept the same by not changing the spring during the experiment

Remember - these variables are controlled (or kept the same) because to make it a fair test, only 1 variable can be changed, which in this case is the stretching force (i.e. the weight attached to the spring).

What is the prediction?

• As the stretching force (i.e. the weight attached to the spring) increases, the extension of the spring will also increase.

What is the justification for the prediction?

• The greater the stretching force the greater the separation of the atoms of the spring. This will result in the spring having greater length and so greater extension

What safety guidelines should be followed?

• Safety goggles must be worn throughout the experiment.

• The spring is stretched and could fly off and hit someone in the eye.

• The retort stand must be secured to the bench with a clamp to prevent it from falling over and hurting someone or falling on their feet.

• Put a barrier in place to prevent feet being underneath the spring.

• This is to ensure that if weights fall off the spring they do not fall onto someone’s feet.

A steel spring, a 100g mass hanger, 12 x 100g masses, a retort stand, a boss and clamp, a clamp, a metre rule, an s-hook, a pointer, safety goggles, a slotted base.

1. Set up apparatus as shown in the diagram. Use a retort stand to secure the metre stick and ensure that it is vertical.

2. Attach the mass hanger s-hook and pointer to the lower end of the spring. The pointer should just touch the metre rule.

3. Read the pointer value from the metre rule. Record this length in a suitable table. This is the initial length of the spring for zero mass. We can neglect the mass of the hanger.

4. Add a 100g slotted mass to the hanger. Record the mass in kg in the table.

5. Read the new position of the pointer on metre rule. This is the stretched length of the spring. Record this length in the table.

6. Calculate the stretching force = weight of masses: W = mg.

7. Calculate: extension = stretched length – original length.

8. Repeat the procedure by adding 100g masses in steps of 100g up to 1200g. Record the new stretched length each time by reading the position of the pointer on the metre rule. Subtract the original length from the new stretched length to calculate each extension.

The main cause of error in this experiment is reading the stretched length of the spring.

The metre rule should be close to the spring.

The metre rule scale should be read at eye level directly opposite the pointer.

Use the retort stand to ensure that the metre rule is vertical.

Initial length of the spring = X cm.

Graph

Plot a graph of stretching force, F in N on the y-axis, against extension, e in cm on the x-axis.

Join the points with a line of best fit.

Forces may change the shape of an object.

The shape of an object might extend if forces act away from each other in a straight line.

The shape of an object might compress if forces act toward each other in a straight line.

An object, such as a spring, stores strain energy when stretched or squashed.

When an object, such as a spring, is stretched, the increased length is called its extension.

Key fact

Hooke's law: The extension of a spring is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.

The spring constant, k, is a measure of the stiffness of the spring.

It is different for different springs and materials.

The larger the spring constant, the stiffer the spring and the more difficult it is to stretch.

The spring constant shows how easy or hard it is to stretch a spring, for example a spring with a spring constant, k = 4 N/cm means a force of 4N is required to stretch the spring by 1 cm.

A different spring with a spring constant, k = 8 N/cm means double the force is required to stretch this spring by 1 cm.

The spring constant of a spring can be found by carrying out an experiment.

1. The unloaded length of a spring is measured.

2. Slotted masses are added to the spring.

3. Record each stretching force in N and the corresponding length of the spring.

4. The extension is the new length minus the unloaded length.

Key fact

The gradient of the graph of force F, (y-axis), and extension e, (x-axis), is equal to the spring constant k.

What happens when the limit of proportionality is reached?

Hooke’s Law is obeyed up to the limit of proportionality.

Beyond this point, stretching force and extension are no longer directly proportional and the graph begins to curve.

If a material is stretched further still, and beyond a point known as the elastic limit, it does not return to its original length when the force is removed.