The metal bar falls to the ground and hits an obstacle inelastically. the speed of the metal bar before impact is 28 m / s

The metal bar falls to the ground and hits an obstacle inelastically. the speed of the metal bar before impact is 28 m / s. the temperature of the metal bar before the impact was 40 degrees Celsius. to what temperature will the metal bar heat up if we assume that the entire amount of heat released upon impact is absorbed by the metal bar? and the specific heat of the material from which the bar is made is 280 J / kg * C.

Given:

v = 28 m / s – the speed of the metal bar before hitting an obstacle;

t0 = 40 ° Celsius – the initial temperature of the bar;

c = 280 J / (kg * C) – specific heat capacity of the metal from which the bar is made.

It is required to determine t (degree Celsius) – to what temperature the metal bar will be heated as a result of the impact.

According to the condition of the problem, the entire amount of heat upon impact is absorbed by the bar. Then, according to the law of conservation of energy:

Ekin = Q, where Ekin is the kinetic energy of the bar before the impact;

m * v ^ 2/2 = m * c * (t – t0);

v ^ 2/2 = c * (t – t0);

t – t0 = v2 / (2 * c);

t = t0 + v ^ 2 / (2 * c) = 40 + 28 ^ 2 / (2 * 280) = 40 + 28 / (2 * 10) = 40 + 28/20 = 40 + 1.4 = 41, 4 ° Celsius.

Answer: The bar will heat up to a temperature of 41.4 ° Celsius.