Force, Pressure, Tractions, and Stress Answer the following questions completely

Question

Force, Pressure, Tractions, and Stress

Answer the following questions completely and show ALL of your work.

1) The traction exerted by a 1 km high column of granite on one square meter is only about 3 to 5 times greater
than the traction exerted by a person standing on your fingernail. You will demonstrate this and calculate a more
exact relationship for the two tractions.

a) After several hot dogs at the WVU football game, Ben weighs around 170 pounds at sea level. Calculate
the traction associated with Dr. Shackleton stepping on your fingernail, assuming your fingernail is about
1 cm2 Use SI units and report your answers in MPa.

b) Now calculate the traction due to the 1 km high column of granite. Take the average unit weight of
granite as 2.667 x 104
N

Explanation / Answer

Pressure is force per unit area. Smaller the area greater would be the force to compensate the same pressure.

a) Ben weights 170 pounds which is equal to 77.11 kg because one kg is 2.2046 pounds.

so 170/2.2046 = 77.11kg

Traction is F1/A1 = mg / A1 = (77.11kg ) (9.8) / 1x10^-4 m^2 = 7.557x10^6 Pa

    =7.557 MPa

b) Granite

Traction is F2/A2 = mg / A2 = (2.667x10^4 N ) (1000 m) / 1 m^2 = 26.67x10^6 Pa

   = 26.67 MPa

c) Traction of granite / traction of ben = 26.67 / 7.557 = 3.53 times

d) the pressure exerted by the granite is 3.53 times greater than the pressure exerted by Ben on 1cm^2.

When area of cross section increases, the weght to hold traction can increase so that pressure (traction) is constant or vice versa.

We can increase pressure with decrease in area and increase in weight.

2)

a) The force of gravity at sea level is approximately 9.8 m/s2.  

b) In practice, force is often expressed in terms of kg m /s2 or Newtons.

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