Figure 8 shows some springs inside a mattress - AQA - GCSE Physics Combined Science - Question 5 - 2019 - Paper 2

To calculate the mass of the person, we use the formula:

$F = m imes g$

Where:

• $F$ is the total force acting on the springs,
• $m$ is the mass of the person,
• $g$ is the gravitational field strength (9.8 N/kg).

The total force on the springs can be found by multiplying the mean force on each spring by the number of springs:

$F = 0.49 ext{ N/spring} imes 1200 ext{ springs} = 588 ext{ N}$

Now substituting this value back into the formula:

$588 = m imes 9.8$

Rearranging gives:

$m = \frac{588}{9.8} = 60 ext{ kg}$

The spring constant ($k$) can be calculated using Hooke's Law:

$F = k imes x$

Where:

• $F$ is the force on the spring (0.49 N),
• $k$ is the spring constant,
• $x$ is the compression of the spring (3.5 × 10^-3 m).

Rearranging gives us:

$k = \frac{F}{x} = \frac{0.49 ext{ N}}{3.5 imes 10^{-3} ext{ m}} = 140 ext{ N/m}$

Springs with a low spring constant will make the mattress soft. This is because a low spring constant signifies that the springs can compress significantly under a small force, providing a softer and more comfortable feel. These springs can absorb more energy, allowing for more significant compression and comfort.