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A student of mass 67 kg wants to walk beyond the edge of a cliff on a heavy beam

ID: 1408685 • Letter: A

Question

A student of mass 67 kg wants to walk beyond the edge of a cliff on a heavy beam of mass 200 kg and length 7.8 m. The beam is not attached to the cliff in any way, it simply lies on the horizontal surface of the clifftop, with one end sticking out beyond the clilf's edge: How far from the edge of the ledge can the beam extend if it sticks out as far as possible beyond the edge, but the student can walk to the beam's end without falling down? A solid metal sphere of volume 1.36 m^3 is lowered to a depth in the ocean where the water pressure is equal to 1.74 Times 10^7 N/m^2. What is the change in the volume of the sphere? The atmospheric pressure is 1.013 Times 10^5 Pa and the bulk modulus of the metal from which the sphere is made is 8.58 Times 109 N/m^2. 1.4 m^3 of concrete weighs 52000 N. What is the height of the tallest cylindrical pillar, made from this amount of concrete, that will not collapse under its own weight? The compression strength of concrete is 2 Times 10^7 N/m^2.

Explanation / Answer

a)

balancing torque,

200 x 9.8 x (3.9 - d) = 67 x 9.8 x d

d = 780/267 = 2.92135 m

b)

bulk modulus = VdP/dV

8.58 x 109 = 1.36 x (174 - 1.013) x 105/dV

dV = 2.742 x 10-3 m3

c)

let h be the height

then

area = 1.4/h m2

pressure = 52000/area = 2 x 107

area = 26 x 10-4 = 1.4/h

h = 538.46 m