Question

It has been suggested that the pressure exerted on a skate blade is sufficient to melt the ice beneath it and form a thin film of water, which makes it easier for the blade to slide over the ice. Assume that a skater weighs \(120 \mathrm{lb}\) and the blade has an area of 0.10 in \(^{2}\). Calculate the pressure exerted on the blade \(\left(1\right.\) atm \(\left.=15 \mathrm{lb} / \mathrm{in}^{2}\right) .\) From information in the text, calculate the decrease in melting point at this pressure. Comment on the plausibility of this explanation and suggest another mechanism by which the water film might be formed.

Short answer

Question: Calculate the decrease in the melting point of ice due to the pressure exerted by a skater with a weight of 120 lb and a blade area of 0.1 in², and discuss the plausibility of this explanation for skating. Answer: The exact decrease in the melting point of ice due to the pressure exerted by the skater cannot be calculated without the specific relationship between pressure and melting point from the text. However, the pressure exerted on the ice by the skater can be found by using the formula Pressure = Force / Area, which equals (120 lb) / (0.10 in²). It is plausible that the pressure exerted by the skate blade could melt the ice, forming a thin film of water, making it easier to slide. An alternative mechanism that could contribute to this phenomenon is the heat generated by the friction between the ice and the skate blade, which might also play a role in facilitating sliding.

Step-by-step solution

Calculate the Pressure Exerted on the Ice

To calculate the pressure exerted on the ice, we will use the formula: Pressure = Force / Area Here, the skater's weight (force) is 120 lb, and the blade's area is 0.10 in². So, the pressure exerted on the ice can be found as follows: Pressure = (120 lb) / (0.10 in²)

Convert the Pressure into the Same Unit as the Given Reference Pressure

Given that 1 atm is equal to 15 lb/in², we will convert the pressure exerted on the ice (calculated in Step 1) to atm by dividing it by 15 lb/in². Pressure (in atm) = (Pressure calculated in Step 1) / 15

Calculate the Decrease in Melting Point

Since we are asked to calculate the decrease in melting point at this pressure from information in the text, we would need to know the specific relationship between pressure and melting point for that particular context. However, in general, when pressure increases, the melting point decreases. The exact values and relationship, unfortunately, cannot be provided here without the text's specific information.

Assess the Plausibility and Suggest an Alternative Mechanism

While it is possible that the pressure exerted by the skate blade is enough to melt the ice beneath it and form a thin film of water, making it easier for the blade to slide over the ice, it is not necessarily the only explanation. Another possibility could be that the friction between the ice and the skate blade generates heat, which in turn melts the ice, also creating a thin film of water. This mechanism might play a role alongside the pressure to facilitate the sliding of the skate blade over the ice.