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Chapter 10: Problem 39

Why does an ice skater exert more pressure on ice when wearing newly sharpened skates than when wearing skates with dull blades?

Short Answer

Expert verified
Answer: An ice skater would exert more pressure on the ice when wearing newly sharpened skates than when wearing skates with dull blades. This is because the contact area between the skate and the ice surface is smaller for newly sharpened skates than for dull blades, while the force exerted by the skater remains constant. As pressure is calculated as the force applied divided by the contact area (P = F/A), a smaller contact area results in a higher pressure exerted on the ice surface.

Step by step solution

01

Understand the Concept of Pressure

Pressure is defined as the force per unit area that is applied on an object. The formula for pressure is given by: P = F / A, where P is the pressure, F is the applied force, and A is the contact area.
02

Compare the Contact Area of Newly Sharpened Skates and Dull Blades

Newly sharpened skates have a smaller contact area with the ice surface compared to skates with dull blades. This is because the sharp edges on the newly sharpened skates minimize the area of contact, while dull blades have a wider and less defined edge, resulting in a larger contact area.
03

Analyze the Force Exerted by the Skater on the Ice

The force exerted by the skater on the ice remains constant, assuming the skater's weight and the gravitational force acting on them do not change. The force can be represented by the skater's weight, which is the mass (m) of the skater multiplied by the acceleration due to gravity (g), i.e., F = mg.
04

Calculate Pressure Exerted by Newly Sharpened Skates and Skates with Dull Blades

As we know the formula for pressure is P = F / A, we can now compare the pressure exerted by the newly sharpened skates and the skates with dull blades. For newly sharpened skates: - The contact area (A1) is smaller. - The force exerted (F) is constant. - The pressure (P1) is P1 = F / A1. For dull blades: - The contact area (A2) is larger. - The force exerted (F) is constant. - The pressure (P2) is P2 = F / A2.
05

Conclusion

Since the contact area (A1) for newly sharpened skates is smaller than the contact area (A2) for dull blades, and the force (F) exerted by the skater is constant, the pressure (P) exerted by newly sharpened skates will be greater than the pressure exerted by dull blades. Therefore, an ice skater exerts more pressure on ice when wearing newly sharpened skates than when wearing skates with dull blades.

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