Final answer:
To find the inverse relationship between pressure and area for the steak knife, we multiply the given pressure (10 kg/mm²) by the given area (2 mm²) resulting in a numerator of 20 kg for the equation pa = 20 kg/a.
Step-by-step explanation:
When discussing the sharpness of a knife in relation to the pressure it can exert, it's important to understand that pressure is calculated as the force applied over a certain area. This is typically represented by the formula P = F/A where P is pressure, F is force, and A is area. The question at hand is a practical application of this formula, showing an inverse relationship between pressure (P) and the contact area (A).
Inversely proportional means that as the area increases, the pressure decreases, and vice versa, when considering a constant force being applied. The provided information states that the pressure of the knife is 10 kg/mm² when its area is 2 mm². The question asks us to find the numerator for an equation that shows this inverse relationship in the form pa = ?/a.
To find the missing numerator, we simply multiply the initial pressure by the initial area:
- Initial Pressure (pa) = 10 kg/mm²
- Initial Area (a) = 2 mm²
- Numerator (?) = pa * a = 10 kg/mm² * 2 mm²
The calculated numerator is 20 kg which means that the full equation expressing the inverse relationship would be pa = 20 kg/a. This equation shows that for any given area 'a', you can find the pressure 'pa' the knife will exert by dividing 20 kg by the area 'a'.