Question

a carbon steel ball with a 30mm diameter is pressed against a flat carbon steel plate with a force of 20n. calculate the diameter of the circular contact area and the maximum pressure that occurs at the center of the contact area

Answer 1

The diameter of the circular contact area is 30 mm and the maximum pressure at the center of the contact area is approximately 0.14 N/mm^2.

Step-by-step explanation:

To calculate the diameter of the circular contact area, we need to determine the radius of the contact area first. The radius can be found by dividing the diameter of the ball by 2. In this case, the radius is 15 mm.

The area of the circular contact area can be calculated using the formula A = πr^2, where A is the area and r is the radius. The maximum pressure at the center of the contact area can be found by dividing the force applied on the plate by the area of the contact area.

Using these formulas, the diameter of the circular contact area is 30 mm and the maximum pressure at the center of the contact area is approximately 0.14 N/mm^2.

Answer 2

28,288.54N/m²

Step-by-step explanation:

Given the diameter of the carbon steel = 30mm

If the carbon steel is pressed against a flat carbon steel plate with a force of 20N, the diameter of the circular contact area will be the same i.e the diameter of the carbon steel that came in contact with the area will imprint the same diameter of 30mm on the circular area.

The pressure exerted on the center on the contact area can be calculated using the formula;

Pressure = Force/Area

Where applies force = 20N

Area = πd²/4 where d = 30mm

d = 30/1000 = 0.03m(converted to meters)

Area = π(0.03)²/4

Area of the circular disc = 0.000707m²

Pressure applied = 20N/0.000707m²

Pressure applied = 28,288.54N/m²