An object has a density of 1250 kg/m^3 at 10 degree C and a coefficient of linea

Question

An object has a density of 1250 kg/m^3 at 10 degree C and a coefficient of linear expansion of alpha = 2.5 times 10^-5 1/K. What is the objects density when the temperature is 25 degree C? A 5.0kg cube of metal has a density of 3000 kg/m^3 and is held by a vertical string while immersed in water which has a density of 1000 kg/m^3. Assume that the cube is oriented so that all the faces are either vertical or horizontal. (a) What is the length of each side of the cube? (b) What is the difference in pressure between the top of the cube and the bottom? (c) What are the vertical components of force due to water pressure on the top and bottom of the cube? (d) Assuming that the cube is in equilibrium, what is the tension in the string? A large cylinder (shaped like a tuna can) has top and bottom area A and height h, and is made of a uniform material of density rho_c. It is floating on a liquid of density rho_f. Assume that Squareroot A > h so the cylinder doesnt tip while the top is facing upwards, and assume that rho_c

Explanation / Answer

(Since nothing is stated, I will be solving only the forst question according to Chegg's guidelines)

Volume of the object changes with temperature according to the equation,

V2 = V1(1 + 3T)

Now, density of the object, D = M/V

=> D2 = M/V2

=> D2 = M / [V1(1 + 3T)]

=> D2 = (M/V1) * [1/(1 + 3T)]

=> D2 = D1 * [1/(1 + 3T)]

=> D2 = 1250 * {1 / {1 + [3 * (2.5 * 10-5) * (25 - 10)]}}

=> D2 = 1248.6 kg/m3

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