Question

A block of aluminum is attached to a nylon string that has a diameter of 4. 0cm. The block is fully immersed and suspended by the string in a container filled with oil. The density of the oil is 650.0kg/m3, the density of the aluminum block is 2700.0kg/m3, the volume of the aluminum block is 0.0700m3, the Young’s Modulus of nylon is 3.00x109Pa.

a) Calculate the tension in the string holding the aluminum block when the block is fully immersed? Answer --> [1.4x103N]

b) Calculate the fractional change in the length of the string due to the tension in part (a). Answer --> [3.7x10-4]

c) Calculate the acceleration of the aluminum block within the oil if the string is cut. Answer --> [7.5m/s2]

d) What density of fluid allows the aluminum block to float with 30.0% of the volume of the aluminum block immersed in the fluid?
Answer --> [9.0x103kg/m3]

Answer 1

pal = 2700 kg/m^3
poil = 650 kg/m^3
Val = 0.07 m^3
Y = 3.0 * 10^9 Pa

We know,
Density = Mass/Volume

T = m*g - Fb
T = pal*val*g - poil*g*val
T = (2700 - 650) * 9.8 * 0.07 N
T = 1.4 * 10^3 N

(b)
Stress = Force/Area
Strain = ΔL/L
Y = Stress/Strain
3.0 * 10^9 = [(1.4 * 10^3) / (1/4 *π *0.04^2 ) ]/ [ΔL/L]
[ΔL/L] = 3.7 * 10^-4

(c)
We know,
F = m*a
m*a = 1.4 * 10^3
2700 * 0.07 * a =1.4 * 10^3
a = 7.5 m/s^2

(d)
Let the density be p.
m*g = p*0.3*val*g
2700 * 0.07 = p*0.3*0.07
p = 9000 kg /m^3
p = 9.0 * 10^3 kg/m^3