A pressure sensor inside of a mixing tank is designed to turn red when the pressure inside the tank exceeds 1.9 kPa. If the sensor is a square, 10 cm on each side, how great a force must be exerted on the sensor in order for it to turn red?

19 N

Explanation:

From the question given above, the following data were obtained:

Pressure (P) = 1.9 kPa

Length (L) = 10 cm

Force (F) =?

Next, we shall convert 1.9 KPa to N/m². This can be obtained as follow:

1 KPa = 1000 N/m²

Therefore,

1.9 KPa = 1.9 KPa × 1000 N/m² / 1 KPa

1.9 KPa = 1900 N/m²

Thus, 1.9 KPa is equivalent to 1900 N/m².

Next, we shall convert 10 cm to m. This can be obtained as follow:

100 cm = 1 m

Therefore,

10 cm = 10 cm × 1 m / 100 cm

10 cm = 0.1 m

Thus, 10 cm is equivalent to 0.1 m

Next, we shall determine the area of the square. This can be obtained as follow:

Length (L) = 0.1 m

Area of square (A) =?

A = L²

A = 0.1²

A = 0.01 m²

Thus, the area of the square is 0.01 m².

Finally, we shall determine the force that must be exerted on the sensor in order for it to turn red. This can be obtained as follow:

Pressure (P) = 1900 N/m²

Area (A) = 0.01 m²

Force (F) =?

P = F/A

1900 = F / 0.01

Cross multiply

F = 1900 × 0.01

F = 19 N

Therefore, a force of 19 N must be exerted on the sensor in order for it to turn red.

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