A baby bouncer is a harness attached to a spring that hangs from a door frame - AQA - GCSE Physics - Question 7 - 2023 - Paper 1

In position A, the baby has gravitational potential energy due to its height. As the baby moves downwards to position B, this gravitational potential energy is transformed into kinetic energy of the baby. Once the baby reaches position B, all the energy is transferred into elastic potential energy in the spring.

First, convert the extension from cm to m: 8.0 cm = 0.080 m.

Using the formula for elastic potential energy: $E_p = \frac{1}{2} k e^2$

Where:

• $E_p = 4.0 J$
• $e = 0.080 m$

Rearranging the equation to find $k$ gives:

$k = \frac{2 E_p}{e^2} = \frac{2 \times 4.0}{(0.080)^2} \\ = \frac{8.0}{0.0064} \\ = 1250 \, N/m$

Thus, the spring constant is $1250 \, N/m$.