If an adult has 3 times the weight of a child, the adult's foot will be twice as long and twice as wide as the child's foot. What is the ratio of force per unit area (pressure P) exerted on the feet of the child compared to the force exerted on the adult's feet?

Question

Quizplus · Accepted Answer

The pressure (P) exerted is given by the force (F) divided by the area (A) over which the force is distributed, P = F/A. If the adult weighs 3 times as much as the child, the force (weight) exerted by the adult is 3 times that of the child. If the adult's foot is twice as long and twice as wide, the area of the adult's foot is 4 times that of the child's foot (since area scales with the square of the dimensions). Therefore, the pressure exerted by the child is (F_child/A_child) and that by the adult is (3F_child/4A_child) = (3/4)(F_child/A_child). To find the ratio of the child's pressure to the adult's pressure, we divide the child's pressure by the adult's pressure: (F_child/A_child) / (3/4)(F_child/A_child) = 4/3.

If an Adult Has 3 Times the Weight of a Child