Understanding Elastic Spring Force: How It Works & What Affects It

AGrader Learning Centre
1 day ago
5 min read

Many students get tripped up because elastic spring force depends on just two things: how stiff the spring is (spring constant) and how much it is stretched or compressed (change in length). These work together in Hooke’s Law, causing misreads of graphs, wrong units, and lost marks. Whenever a spring “fights back” as you pull or push it, that’s the elastic spring force; in P6 Science it appears in clip-on masses, shock absorbers, and pop-up toys—and in exam diagrams that can be deceptively tricky. Master the two drivers—how stiff the spring is and how far it’s stretched or compressed—and most questions become straightforward.

This guide clarifies what elastic spring force is, how it behaves when a spring is stretched or compressed, why the negative sign appears in formulas, and how to avoid common mistakes with graphs and units. You’ll also learn the difference between elastic spring force and elastic potential energy, with PSLE-style examples to turn confusion into confidence

What Is the Elastic Spring Force? (And Where Does It Come From?)

When you compress a spring (push it) or stretch it (pull it), the spring deforms but tries to return to its original shape. The force you feel from the spring is a restoring force—it acts in the opposite direction to the displacement, pulling or pushing the elastic object back towards its equilibrium position (the position where the spring is neither stretched nor compressed).

This is precisely captured by Hooke’s Law, the law which states that the force exerted by a spring is proportional to how far it’s been stretched or compressed:

F = -(k)(x)

F is the elastic spring force (in newtons, N).
k is the spring constant (stiffness), in N/m.
x is the extension or compression from the equilibrium length (in m).
The negative sign shows the force acting is in the opposite direction to the displacement (a restoring force).

In simple language: the more you deform the spring, and the stiffer the spring, the larger the force it “pushes back” with.

The 2 Big Factors That Affect Elastic Spring Force

There are two and only two directly controlling factors in Hooke’s Law problems:

The Spring’s Stiffness

Firstly, the stiffness of a spring affects the amount of elastic spring force it exerts.

When different springs are compressed or stretched to the same length, a stiffer spring will exert a larger elastic spring force than a less stiff spring.

Spring A requires 2 kg, Spring B requires 3 kg, and Spring C requires 4 kg to be compressed to the same length. This shows that Spring A is the least stiff, so it exerts the smallest elastic spring force.

Spring B is stiffer than Spring A, so it exerts a larger elastic spring force than Spring A. Spring C requires the greatest mass to achieve the same compression, so it is the stiffest and exerts the largest elastic spring force.

The Extent of Stretch or Compression

Secondly, the extent of stretch or compression also affects the elastic spring force.

The greater the stretch or compression of a spring, the greater the elastic spring force it exerts on the object (provided the spring remains within its elastic limits).

Now, let’s look at two application questions that test these two factors.

This question examines the relationship between a spring’s stiffness and the elastic spring force it exerts. When 5 kg dumbbells are placed on Springs X and Y, Spring Y compresses more than Spring X. This indicates that Spring Y is less stiff than Spring X.

Because Spring X is stiffer, it exerts a larger elastic spring force on the left hand. Therefore, the left hand must push harder to compress Spring X, resulting in a greater push force.

Hence, option 2 is correct.

Let’s analyse this question part by part.

Part (a). The question asks for the force that propels the toy to jump out of the box. The spring is held down inside the box, so it is compressed and exerts an elastic spring force on the toy. When the hand lets go of the cover, the compressed spring exerts a push on the toy as it returns to its original shape, causing the toy to jump out of the box.

Part (b). Recall that the greater the compression, the larger the elastic spring force. If the box is replaced with a shorter one, the spring must be compressed more to fit the toy, so it exerts a greater elastic spring force and the toy jumps higher when released.

Part (c). The other factor is the stiffness of the spring (spring constant). Replacing the spring with a stiffer one means that, for the same compression, it exerts a larger elastic spring force, so the toy will jump higher when the cover is opened.

Elastic spring force is a restoring force described by Hooke’s Law. It depends on just two things: how stiff the spring is (its spring constant) and how far it’s stretched or compressed (its extension/compression). Greater stiffness or a larger stretch/compression produces a stronger “push back” (within the elastic limit), which is why stiffer springs or deeper compressions make toys jump higher and feel harder to press. This guide clarifies sign conventions, graphs, and units, and explains how force differs from elastic potential energy—using PSLE-style examples to build confidence.

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