Respuesta :
Answer:
Pressure exerted by the needle = 78.037 kPa
Explanation:
Pressure is defined as the force exerted on a surface per unit area. The SI unit of pressure is Pa (N.m⁻²).
The force exerted by the phonograph needle is equal to the gravitational force.
Thus,
F=m×g
Where,
F is the force
m is the mass of the body
g is the acceleration due to gravity
Also, g = 9.81 ms⁻²
Given, mass of the needle = 1.00 g
The conversion of g into kg is shown below:
1 g = 10⁻³ kg
Thus, mass of the needle = 1×10⁻³ kg
Thus, F= 1×10⁻³×9.81 N = 9.81×10⁻³ N
Ares of the circle = πr²
Given : Radius of tip of the needle = 0.200 mm
The conversion of mm into m is shown below:
1 mm = 10⁻³ m
Thus, mass of the needle = 0.2×10⁻³ m
Thus, Area of the tip of the needle = π×(0.2×10⁻³)² m² = 1.2571×10⁻⁷ m²
So, Pressure =F/A
P = (9.81×10⁻³)/1.2571×10⁻⁷ Pa = 7.8037×10⁴ Pa
The conversion of Pa into kPa is shown below:
1 Pa = 10⁻³ kPa
Thus, pressure exerted by the needle = 7.8037×10⁴×10⁻³ kPa = 78.037 kPa
