Question

The pressure exerted by a phonograph needle on a record is surprisingly large. If the equivalent of 0.900 g is supported by a needle, the tip of which is a circle 0.200 mm in radius, what pressure is exerted on the record in N/m2?

Answer 1

70223 Pa

Step-by-step explanation:

The pressure can be calculated as the force divided by the area. In this case, the force is the weight supported by the needle and the area is the area of the tip.

The weight can be calculated as:

F = mg

F = (0.0009 kg)(9.8 m/s²)

F = 0.00882 N

Because the mass m = 0.9 g is equal to m = 0.0009 kg.

On the other hand, the radius r = 0.200 mm is equal to r = 0.0002 m, so the area can be calculated as

`\begin{gathered} A=\pi r^2 \\ A=(3.14)(0.0002\text{ m\rparen}^2 \\ A=1.256*10^(-7)\text{ m}^2 \end{gathered}`

Then, the pressure is equal to

`P=\frac{0.00882\text{ N}}{1.256*10^(-7)\text{ m}^2}=70223\text{ Pa}`

Therefore, the answer is 70223 Pa