homework problem

Question

A 3-kilogram [kg] projectile traveling at 100 meters per second [m/s] is stopped by being shot into an insulated tank containing 100 kilograms [kg] of water. If the kinetic energy of the projectile is completely converted into thermal energy with no energy lost, how much will the water increase in temperature in units of degrees Celsius [degrees Upper C]? The specific heat of water is 1 calorie per gram per degree Celsius [cal/(g degrees Upper C)].

The temperature will increase by.................celsius. (Round your answer to three significant digits.)

Answer 1

Apply conservation of energy.  Set the inbound kinetic energy of the projectile equal to the thermal energy rise of the water, and then solve for the temperature rise of the water.

 

m = mass of projectile = 3 kg

v = inbound speed of projectile = 100 m/s

M = mass of water = 100 kg

c = specific heat of water ≅ 4186 J/(kg ºC)  [Work the problem in these units.]

ΔT = temperature rise of the water

 

mv²/2 = McΔT

 

ΔT = mv² / (2Mc) = (3)(100)² / [2(100)(4186)] °C ≅ 0.0358 °C