a rectangular box of mass 400g has a diameter 20cm by 10cm by 5cm compute the pressure it exerts on each face of the box when it rests on a table take g=10m/s2
Pressure P= mg/S
P₁ = mg/s₁ =0.4•10/0.2•0.2 =100 Pa
P₂ = mg/s₂ =0.4•10/0.1•0.1 =400 Pa
P₃= mg/s₃ =0.4•10/0.05•0.05 =1600 Pa
Genie
To compute the pressure that the rectangular box exerts on each face when it rests on a table, we need to use the formula:
Pressure = Force / Area
First, we need to calculate the force exerted by the box. The force is equal to the weight of the box, which is given by the formula:
Force = mass * gravity
Given that the mass of the box is 400 grams, we need to convert it to kilograms by dividing by 1000:
mass = 400 grams / 1000 = 0.4 kg
The acceleration due to gravity is given as 10 m/s^2.
Force = 0.4 kg * 10 m/s^2 = 4 N
Now, let's calculate the area of each face of the box. The area of a rectangle is given by the formula:
Area = length * width
For the top and bottom faces of the box, the length is 20 cm and the width is 10 cm:
Area_top/bottom = 20 cm * 10 cm = 200 cm^2
To compute the pressure, we need to convert the area from square centimeters to square meters:
Area_top/bottom = 200 cm^2 / (100 cm/m)^2 = 0.02 m^2
For the side faces of the box, the length is 20 cm and the width is 5 cm:
Area_sides = 20 cm * 5 cm = 100 cm^2
Convert the area to square meters:
Area_sides = 100 cm^2 / (100 cm/m)^2 = 0.01 m^2
Finally, we can compute the pressure on each face using the formula:
Pressure = Force / Area
Pressure_top/bottom = 4 N / 0.02 m^2 = 200 N/m^2 = 200 Pa
Pressure_sides = 4 N / 0.01 m^2 = 400 N/m^2 = 400 Pa
Therefore, when the rectangular box of mass 400g rests on a table, it exerts a pressure of 200 Pa on each of the top and bottom faces, and a pressure of 400 Pa on each of the side faces.