How many times will a person’s pressure on the ice change if he puts on skates.

How many times will a person’s pressure on the ice change if he puts on skates. The area of the soles of the boots. in contact with ice is 300 cm². The length of the skate blade is 20 cm, and its width is 4 mm.

To determine how many times the pressure of a person weighing m on the ice will change if he puts on skates, it is necessary to find the ratio of the pressure created by the blades of the skates p₁ to the pressure created by the soles of the boots p₂. The force of pressure is created by the weight of a person: F = m ∙ g, where the coefficient g = 9.8 N / kg.

The area of ​​the soles of boots in contact with the ice is S₂ = 300 cm² = 0.03 m², then р₂ = m ∙ g / S₂.

The length of the skate blade is a = 20 cm = 0.2 m, and its width b = 4 mm = 0.004 m, the pressing surface of the two blades will be equal to S 2 = 2 ∙ a ∙ b, which means p₁ = m ∙ g / S₁ or p₁ = m ∙ g / (2 ∙ a ∙ b).

We get: р₁: р₂ = (m ∙ g / (2 ∙ а ∙ b)): (m ∙ g / S₂); р₁: р₂ = S₂ / (2 ∙ a ∙ b); р₁: р₂ = 0.03 m²: (2 ∙ 0.2 m ∙ 0.004 m); p₁: p₂ = 18.75 (times).

Answer: at 18.75, a person’s pressure on the ice will increase if he puts on skates.