A boy with a mass of 45 kg stands on a square wooden block of 50 cm. How do you calculate the pressure exerted by the boy?

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

By definition, the pressure is the force divided by the area, on which force acts. In SI it is measured in pascals (`N/m^2` ).

In our case area is `50cm*50cm = 0.5m*0.5m = 0.25m^2` .

The force is the gravity one (probably we ignore the buoyancy force of air). This force is equal to m*g, where m is mass and g is gravity acceleration, `g=9.8m/s^2` .

So the pressure is

`45*9.8/0.25` = 1764(Pa).

Sources:
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vlmsthn | eNotes Newbie

Posted on

We know that 

                   Pressure =   Force / Area

 Step 1: Calculation of Force  

  We know that Force = ma 

                               = mass x acceleration due to gravity

  Given that mass of the boy = 45 kg

 we know that acceleration due to gravity = 9.8 m/s^2

Hence, Force = mass x acceleration due to gravity

                   = 45 kg x 9.8 m/s^2 

                   =  441 N ( Newton, N= kg . m/s^2) 

Step 2: Calculation of Area 

Since boy is standing on the square wooden block , we have to calculate the area of the square wooden block .

Given that side of square wooden block = 50 cm

                                                        = 50 x 0.01 m (1 cm = 0.01 m)

                                                        = 0.5 m

               Area of the square block =  side x side  ( area of square = side x side)

                                                   = 0.5 m x 0.5 m

                                                   = 0.25 m^2

 Therefore, Area of square block = = 0.25 m^2

Step 3: Calculation of Pressure

 Pressure =  Force / Area

From step 1,  Force =  441 N

From Step 2, Area = 0.25 m^2

Therefore,

               Pressure = Force / Area

                            =  441 N/ 0.25 m^2

                            = 1764 N/ m^2

                            =  1764 Pa ( Pascal, Pa = N/m^2)

                           = 0.017 atm

                {We know that 1 atm  = 101325 Pa

           Hence , 1764 Pa =  0.017 atm   [(1764 Pa/ 101325 Pa) x 1atm ] = 0.017 atm) }

Therefore, 

pressure exerted by the boy on the pole = 0.017 atm

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