Basketball Gauge Pressure Calculation
What is the gauge pressure of a basketball when you push it down with a force of 30 N?
A basketball is being pushed down with a force of 30 N, causing the ball to flatten out. If the bottom of the ball forms a circular area with a diameter of 2.5 cm, what is the gauge pressure inside the basketball?
Answer:
The gauge pressure of the basketball when pushed down with a force of 30 N is 32.5 N.
To calculate the gauge pressure of the basketball in this scenario, we can use the formula for pressure:
Pressure = Force / Area
Given that the force applied is 30 N and the bottom of the basketball forms a circular area with a diameter of 2.5 cm, we first need to calculate the radius of the circle:
Radius = Diameter / 2 = 2.5 cm / 2 = 1.25 cm = 0.0125 m
Next, we calculate the area of the circular bottom of the basketball:
Area = π * (radius)^2 = π * (0.0125 m)^2 ≈ 0.000491 m^2
Now, plug the values into the pressure formula:
Pressure = 30 N / 0.000491 m^2 ≈ 32.5 N
Therefore, when a force of 30 N is applied to the basketball, the gauge pressure inside the basketball is approximately 32.5 N.