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 millimeter. What pressure does the man experience?
[g=10 N/kg]
on each nail? 75*g/10,000mm^2
want it in N/m^2?
75g/10,000mm^2 * (1mm/.001m)^2
To calculate the pressure experienced by the man, we can use the formula:
Pressure = Force / Area
First, we need to calculate the force exerted by the man's weight on the bed of nails. We can use the formula:
Force = Mass * Acceleration due to gravity
Given that the mass of the man is 75 kg and the acceleration due to gravity is 10 N/kg, we can calculate the force:
Force = 75 kg * 10 N/kg = 750 N
Next, we need to calculate the total area of the nails in contact with the man's body. Since we are given that each nail has an area of 1.0 square millimeter, we need to convert this to square meters:
Area of one nail = 1.0 mm^2 = (1.0 * 10^-6) m^2
To find the total area, we multiply the area of one nail by the number of nails:
Total Area = Area of one nail * Number of nails = (1.0 * 10^-6) m^2 * 10,000
Finally, we can calculate the pressure using the formula:
Pressure = Force / Area
Substituting the values we have:
Pressure = 750 N / [ (1.0 * 10^-6) m^2 * 10,000 ]
Calculating the pressure will give us the answer.
To find the pressure experienced by the man, we need to divide the force exerted on the bed of nails by the total area of the nails in contact with the man's body.
First, we need to calculate the total force exerted on the bed of nails. The force can be calculated using the formula:
Force = mass x acceleration due to gravity
Given that the mass of the man is 75 kg and acceleration due to gravity is 10 N/kg (as given in the question), we can calculate the force as:
Force = 75 kg x 10 N/kg
= 750 N
Next, we need to calculate the total area of the nails in contact with the man's body. The area of each nail tip is given as 1.0 square millimeter. Since there are 10,000 nails, the total area of the nails in contact with the man's body can be calculated as:
Total Area = Area per nail x Number of nails
Total Area = 1.0 mm^2 x 10,000
= 10,000 mm^2
Since we need the answer in pressure units, we need to convert mm^2 to m^2. There are 1,000,000 mm^2 in 1 m^2, so the total area in m^2 can be calculated as:
Total Area = 10,000 mm^2 / 1,000,000
= 0.01 m^2
Now we can calculate the pressure experienced by the man by dividing the force by the total area:
Pressure = Force / Total Area
Pressure = 750 N / 0.01 m^2
= 75,000 N/m^2
Therefore, the man experiences a pressure of 75,000 N/m^2 when lying on the bed of nails.