Forces in Action
Stretching and Deformation
To stretch, bend or compress an object, more than one force must be applied. A single force would simply cause the object to accelerate (Newton's Second Law). Two opposing forces are needed for deformation — for example, a weight pulling a spring down while the support holds it up.
When forces are applied to a spring, it can undergo two types of deformation:
• Elastic deformation — the object returns to its original shape and size when the force is removed. The spring "bounces back."
• Plastic deformation — the object is permanently deformed and does not return to its original shape. The spring has been stretched beyond its limit.
Hooke's Law
Hooke's Law states that the extension of a spring is directly proportional to the force applied, as long as the elastic limit is not exceeded. The equation is:
$$F = k \times e$$
Where \(F\) is force (N), \(k\) is the spring constant (N/m), and \(e\) is extension (m). A larger spring constant means a stiffer spring that is harder to stretch. Extension means the change in length — so \(e = \text{stretched length} - \text{original length}\).
On a force-extension graph, the linear (proportional) region appears as a straight line through the origin. The gradient of this straight line equals the spring constant \(k\). Beyond the elastic limit, the line bends towards the extension axis — the gradient falls because each extra newton now stretches the spring more. This is the non-linear region where Hooke's Law no longer applies and the spring is undergoing plastic deformation.
Hooke's Law: \(F = ke\). The force-extension graph is a straight line through the origin up to the elastic limit. Beyond this, deformation becomes plastic (permanent).
Clamp a spring vertically from a stand. Measure and record the original length using a ruler. Add known masses one at a time, recording the new length each time. Calculate the extension for each mass (\(e = \text{new length} - \text{original length}\)). Plot force (y-axis) against extension (x-axis). The straight-line section confirms Hooke's Law. The point where the line begins to curve marks the elastic limit. To improve accuracy, take three readings at each force and calculate the mean, check for parallax by reading the ruler at eye level, and ensure the spring hangs freely without touching the stand.
When a spring is stretched, energy is stored as elastic potential energy. This can be calculated using:
$$E_e = \frac{1}{2} \times k \times e^2$$
Where \(E_e\) is elastic potential energy (J), \(k\) is the spring constant (N/m), and \(e\) is the extension (m). This equation only works within the elastic limit (the linear region). On a force-extension graph, the elastic potential energy equals the area under the straight-line section (which forms a triangle: \(\frac{1}{2} \times F \times e\)). When the spring is released, this stored energy is transferred to kinetic energy or other forms.
Gravity and Weight
All matter has a gravitational field that attracts other masses. Every object with mass creates a gravitational field around it, but the field is only noticeable for very massive objects like planets, moons and stars. The gravitational field strength at the Earth's surface is \(g = 10 \text{ N/kg}\), meaning every kilogram of mass experiences a gravitational force of 10 N.
Weight is the force of gravity on an object: \(W = m \times g\). It is measured using a newton meter (spring balance) and always acts downwards towards the centre of the Earth. The acceleration due to gravity in free fall equals \(g = 10 \text{ m/s}^2\) — numerically the same as gravitational field strength but with different units.
Gravitational Potential Energy
When an object is raised above the ground, work is done against gravity and energy is stored as gravitational potential energy (GPE):
$$E_p = m \times g \times h$$
Where \(E_p\) is GPE (J), \(m\) is mass (kg), \(g\) is gravitational field strength (N/kg), and \(h\) is height (m). If the object falls, this GPE is converted to kinetic energy (assuming no air resistance). At the top of a roller coaster, GPE is at its maximum; at the bottom, it has all been transferred to kinetic energy.
Work done equals the energy transferred when a force moves an object through a distance. The equation is:
$$W = F \times d$$
Where \(W\) is work done (J), \(F\) is force (N), and \(d\) is distance along the line of action of the force (m). One joule of work is done when a force of one newton moves an object one metre. Work done and energy transferred are always equal — 1 J = 1 N m. The distance must be measured in the same direction as the force. If you carry a box horizontally, you do no work against gravity because the force (weight) acts downwards, perpendicular to your motion.
Work done \(W = Fd\) = energy transferred. Gravitational PE \(E_p = mgh\). Elastic PE \(E_e = \frac{1}{2}ke^2\). All measured in joules (J).
Power
Power is the rate of doing work or transferring energy:
$$P = \frac{W}{t}$$
Where \(P\) is power (W), \(W\) is work done or energy transferred (J), and \(t\) is time (s). One watt equals one joule per second. A 60 W light bulb transfers 60 J of energy every second. A more powerful engine can do the same amount of work in less time — or more work in the same time — compared to a less powerful one. For example, two students who both climb the same flight of stairs do the same work against gravity (\(W = mgh\)), but the student who climbs faster has a greater power output.