A piece of aluminum metal at an initial temperature of 97.3°C was placed in a calorimeter containing 49.0g of water at an initial temperature of 22.0°C. The two were allowed to come to thermal equilibrium and the final temperature was 24.1°C. The specific heats of water and aluminum are 4.184 J/g °C and 0.902 J/g °C, respectively. What was the mass of the Al piece that was added?

0.153 g

Explanation:

Because the aluminum metal was at a higher temperature, it loses heat while the water gains heat. By the principle of mixtures, heat lost by hot material is the same heat gained by colder material, assuming there is no heat loss to the environment.

We work under the assumption that the heat gained by the calorimeter is negligible.

Heat lost by metal

where m, c and Δθ are the mass, specific heat  and change in temperature of the aluminum.

Heat gained by water

Equating both energy equations,

the independent variable, or the one that is intentionally manipulated is the speed.

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.