Final answer:
Without the coefficient of linear expansion for aluminum or the final temperature, we cannot calculate the exact change in length of the aluminum bar due to thermal expansion from heating with the information provided. Moreover, the mass of the bar would contribute to calculating temperature change, not the length change, which depends on material properties and temperature difference.
Step-by-step explanation:
To calculate the change in length of an aluminum bar when heated, we first need to know the coefficient of linear expansion for aluminum (α), which typically is about 23 × 10-6 /°C. The question, however, does not provide this figure or the final temperature reached by the aluminum bar after heating, which would allow us to calculate the exact change in length. It is also worth mentioning that the mass of the aluminum bar, given as 350 g, is not directly required to calculate the change in length due to thermal expansion unless we are to calculate the change in temperature first using the specific heat capacity of aluminum, which is 900 J/kg°C.
We do know the energy added, 10,500 J, which would change the temperature and consequently cause the bar to expand. To find the change in length, we use the formula: ΔL = α × L0 × ΔT, where ΔL is the change in length, L0 is the original length, and ΔT is the change in temperature. Missing values in the provided information make it impossible to calculate the change in length with the given data.
As for the idea of a weapon inventor using thermal expansion, it is important to consider that different materials have different thermal expansion coefficients; invar, for example, has a very low thermal expansion coefficient compared to aluminum. This mismatch could lead to stresses and potential damage or failure of the mechanism under high temperatures, a factor the inventor might be overlooking.