Physics Olympiad - Basic To Advanced Exercises by The Committee of Japan Physics Olympiad

Author:The Committee of Japan Physics Olympiad
Language: eng
Format: epub
Published: 2018-08-22T16:00:00+00:00

Problem 5.2. Potential energy and heat

A bag containing copper particles of 1kg is dropped at initial speed zero from a fixed point P to a rigid floor (the height of P is 1.5 m above the floor). This bag does not bound at all when it drops on and collides with the floor. By this collision, 70% of the kinetic energy of the particles within the bag is given to the particles as heat. How many times should you drop this bag in order to raise the temperature of particles by 5 K. Choose the most favorable answer.

The acceleration of gravity is 9.8 m/s 2. The specific heat of copper is 0.38 J/(g ⋅ K). Since the heat conduction of copper is well, you can assume that the heat given to the particles is uniformly delivered to all the particles without delay.

(a) 90 times (b) 130 times (c) 190 times (d) 1800 times

(the 1st Challenge)

Answer (c)

Solution

A matter with mass m at height h has a potential energy, mgh. This potential energy changes into the kinetic energy by falling to the ground. The kinetic energy changes into molecule’s vibration energy by collisions, which is the thermal energy of molecules.

Let n be the number of collisions. The energy given to molecules is E = n × 1 × 9.8 × 1.5 × 0.70 J. The quantity of heat required for raising the temperature by 5°C is Q = 0.38 × 1000 × 5J. Equating E to Q, we obtain n = 185 ≈ 190 times

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