Answer:
m_added = 2 kg
Explanation:
From the question, we are told that the cylinder is allowed to fall 800 m in height. Thus, the potential energy will be converted into heat energy which will increase the temperature of water .
Now, let the mass of the falling cylinder be denoted by "m1" and let h be the height of fall.
Thus;
Formula for potential energy = mgh
Thus, as said earlier it's converted to heat generated. So heat generated = m1gh
Now let's calculate the heat absorbed;
heat absorbed = (m2)cΔt
Where;
ΔT is change in temperature
c is specific heat of water .
m2 is mass of water
Heat absorbed = heat generated
Thus;
(m2)cΔt = m1gh
Δt = m1gh/(m2•c)
Now, in both cases of the water and cylinder, m1, g , h and c are constant
Thus, we have;
Δt = (m1gh/m2) × 1/c
Where;
(m1gh/m2) is denoted as a constant k.
Thus;
Δt = K/m
For the first experiment, we have;
m = 2 kg
Δt = 2.4
Thus;
2.4 = K/2
Multiply both sides by 2 to get;
K = 4.8
For the second experiment, we have;
Δt = 1.2
Also,we have seen that K = 4.8
Thus;
Δt = K/m
Thus;
1.2 = 4.8/m
m = 1.2
m = 4 kg
Thus,mass added is;
m_added = 4 - 2
m_added = 2 kg
