A man of mass 75 kg lies on a bed of 10 000 nails. The tip of each nail has an area of 1.0 square millimetre.
What pressure does the man experience?
[g = 10 N/kg]
A. 7.5\times 10^6 Pa
B. 7.5 \times 10^4 Pa
C. 7.5 \times 10^3 Pa
D. 7.5 \times 10^7 Pa
E. 7.5\times 10^5 Pa
For this question, we can use the formula:
Pressure ( Pa ) = {\frac{Force(N)}{Area(m^2)}}
Let’s divide the workload. First, we can find the force exerted-
Since we have Mass in Kilograms, we need to convert it into Force or Weight in Newton. We do this using the formula:
Weight= {{Mass}\times{Gravity}}= {75 kg \times \frac{10N}{kg}}= 750 N
Next, we find the total area of the bed of nails, so we must pay attention to find the area of the tip of one nail in the correct SI unit {(m^2)}, then use that to calculate the total of 10,000 nails.
We can start by converting the area of one tip from {mm^2} to {m^2}.
To convert mm to m, we divide by 1000. So, it is easy to conclude that to convert from {mm^2} to {m^2}, we divide by {1000^2}.
It is however easier to format this as number {10^{-6}}, for the sake of the question.
This would make the area of the tip of one nail {1\times 10^{-6}} {m^2}.
Now we can multiply this value over the 10,000 nails: {(1\times 10^{-6}) \times 10,000}= 0.01 {m^2} (This is our total Area.)
Finally, we can construct our final equation:
Pressure ( Pa ) = {\frac{Force(N)}{Area(m^2)}}= {\frac{750N}{0.01 m^2}}= {7.5 \times 10^4} Pa
Thus, making our answer B.