IB Physics HL A.2.9 Springs and Elastic Forces

Practise calculating maximum spring force from oscillation amplitude and angular frequency.

Exam points

apply F=-kx to extension or compression and include the restoring direction
use spring force and extension data to determine elastic energy or oscillation quantities
relate maximum displacement or amplitude to maximum restoring force and acceleration

[Maximum number: 2]

An object attached to a spring oscillates with simple harmonic motion in a horizontal plane. The graph shows how the kinetic energy of the object varies with the displacement x.

Figure for Question A.2.9—Hooke’s law restoring force question 1 — IB Physics HL

The mass of the object is 0.15 kg .

Calculate the maximum force exerted on the object by the spring.

ALTERNATIVE 1
$\begin{aligned} & a_{\max }=8.6^{2} \times 0.060 \text { OR }\left(\frac{2 \pi}{0.73}\right)^{2} \times 0.060<=4.44 \mathrm{~m} \mathrm{~s}^{-2}> & F_{\max }=0.15 \times 4.44=0.67<\mathrm{N} \gg \end{aligned}$

ALTERNATIVE 2
$\begin{aligned} & k=8.6^{2} \times 0.15 \text { OR }\left(\frac{2 \pi}{0.73}\right)^{2} \times 0.15<=11.1 \mathrm{~N} \mathrm{~m}^{-1}> & F_{\max }=11.1 \times 0.060=0.67<\mathrm{N}> & \end{aligned}$

MP1 find a or k MP2 F=m a / F=k x

Award [2] for BCA

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A.2.9—Hooke’s law restoring force question 1