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

To calculate the mass, we start with the formula for force:

$F = m imes g$

Where:

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

Given that the mean force on each spring is 0.49 N and there are 1200 springs:

$F = 0.49 ext{ N} imes 1200 = 588 ext{ N}$

Now rearranging the formula gives:

$m = \frac{F}{g} = \frac{588 ext{ N}}{9.8 ext{ N/kg}} = 60 ext{ kg}$

Thus, the mass of the person is 60 kg.

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

$F = k imes x$

Where:

• $F$ is the force applied (0.49 N per spring),
• $x$ is the compression of each spring (3.5 × 10^{-3} m).

Rearranging the formula, we get:

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

Thus, the spring constant of each spring is 140 N/m.

Springs with a low spring constant can compress by a larger amount for the same applied force. This property leads to a softer mattress, allowing it to adapt better to the weight of a person, thereby providing comfort.