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physics1007

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## Homework Statement

A solid aluminum sphere has a radius of 2.34 m and a temperature of 89.0 °C. The sphere is then completely immersed in a pool of water whose temperature is 22.3 °C. The sphere cools, while the water temperature remains nearly at 22.3 °C, because the pool is very large. The sphere is weighed in the water immediately after being submerged (before it begins to cool) and then again after cooling to 22.3 °C. Use Archimedes' principle to find the magnitude of the difference between the weights.

## Homework Equations

Weight of sphere in water before cooling W1 = W - ρ * g * V1 ρ = density of water

where W = actual weight of sphere and V1 the volume before cooling

Also, W2 = W - ρ * g * V2 Then W2 - W1 = -(V2 - V1 ) * ρ * g

V1 = 4/3 * π * r^3 V2 = 4/3 * π * (r + Δr)^3

Expanding (r + Δr)^3 and dropping any terms with Δr^3 or Δr^2 since these are very small

V2 = 4/3 * π * (r^3 + 3 * r * Δr)

V2 - V1 = 4 * π * r^2 * Δr

Δr = k * r * ΔT where k = coefficient of linear expansion for Al and ΔT the temperature change

This gives V2 - V1 = 4 * π * r^3 * k * ΔT

W2 - W1 = -4 * π * r^3 * k * ρ * g * ΔT

## The Attempt at a Solution

i get -2420.678 and that's not right. any suggestions?