Problem 25P

A cube of ice is taken from the freezer at −8.5°C and placed in a 95-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0°C. The final situation is observed to be all water at 17.0°C. What was the mass of the ice cube?

Solution(a).The oscillating mass is in simple harmonic motion. The position of the oscillating mass isgiven by (t) = (0.10 rad) cos(5.0 t), where t is in seconds.Compare this equation with the position of simple harmonic equation x = A cos(2 ft)Then amplitude is A = 0.10 rad.(b).The frequency is given by 2f = 5 f = 5/2 f = 0.80 Hz(c).Frequency of oscillation is given by f = 1/2 g/L Squaring on both sides 2 2 L = g/4 f L = (9.8 m/s )/4 (0.80) 2 L = 0.38m~38 cm(d).The angle at t = 2.0 s (2) = (0.10 rad) cos(5 × 2 s) = 0.084 rad