A 10 -kg baby sits on a three-legged stool. The diameter of each of the stool's round feet is \(2.0 \mathrm{cm} .\) A \(60-\mathrm{kg}\) adult sits on a four-legged chair that has four circular feet, each with a diameter of $6.0 \mathrm{cm} .$ Who applies the greater pressure to the floor and by how much?

Weight is the force acting on an object due to gravity, and it's calculated as the mass of the object multiplied by the acceleration due to gravity (g = \(9.8 m/s^2\)). So, let's find the weight of the baby and adult. Weight of the baby = mass of baby × g Weight of the baby = 10 kg × 9.8 \(m/s^2\) = 98 N Weight of the adult = mass of adult × g Weight of the adult = 60 kg × 9.8 \(m/s^2\) = 588 N

The contact area for a single leg of both the stool and the chair will be the area of a circle with the diameter given in the problem. Let's first find the radius from the given diameter and then calculate the area for each. Radius of stool leg = diameter of stool leg / 2 Radius of stool leg = 1.0 cm = 0.01 m Radius of chair leg = diameter of chair leg / 2 Radius of chair leg = 3.0 cm = 0.03 m Now, we can calculate the area of a single stool and chair leg. Area of a single stool leg = \(\pi * (radius\ of\ stool\ leg)^2\) Area of a single stool leg = \(\pi * (0.01 m)^2\) = \(3.14 * 10^{-4} m^2\) Area of a single chair leg = \(\pi * (radius\ of\ chair\ leg)^2\) Area of a single chair leg = \(\pi * (0.03 m)^2\) = \(2.826 * 10^{-3} m^2\) Now, let's multiply these areas by the number of legs for each. Total contact area for stool = 3 * Area of a single stool leg Total contact area for stool = 3 * (\(3.14 * 10^{-4} m^2\)) = \(9.42 * 10^{-4} m^2\) Total contact area for chair = 4 * Area of a single chair leg Total contact area for chair = 4 * (\(2.826 * 10^{-3} m^2\)) = \(1.1304 * 10^{-2} m^2\)

Now we have all the information necessary to calculate the pressure exerted by both the baby and the adult. Pressure exerted by the baby = Weight of the baby / Total contact area for stool Pressure exerted by the baby = 98 N / (\(9.42 * 10^{-4} m^2\)) = \(104044.59 N/m^2\) Pressure exerted by the adult = Weight of the adult / Total contact area for chair Pressure exerted by the adult = 588 N / (\(1.1304 * 10^{-2} m^2\)) = \(52000 N/m^2\)

Comparing the pressures calculated in Step 3, we find that: Pressure exerted by the baby > Pressure exerted by the adult \(104044.59 N/m^2\) > \(52000 N/m^2\) The baby exerts more pressure on the floor than the adult, and the difference in pressure is: Difference in pressure = Pressure exerted by the baby - Pressure exerted by the adult Difference in pressure = \(104044.59 N/m^2 - 52000 N/m^2 = 52044.59 N/m^2\) So, the baby applies greater pressure to the floor by \(52044.59 N/m^2\).