I got part a and b, but not c. We are trying to find delta T in part c, but I'm still confused on where to start even with the help.
(a) An iron block of the mass 1.2 kg is suspended on a spring of the spring constant 140 N/m, and merged into a vessel with 5 liters of water. The mass is displaced by 10 cm from its equilibrium position, and released. How much energy in J has been dissipated by the time the mass comes to a rest?
E = 0.7 J
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(b) What is the mass of water in the container in kg ?
m(water) = 5 kg
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(c) Assuming that the water with the block are thermally isolated from their surroundings, by how much will their temperature increase? Express your answer in C. You will need the values of the heat capacity:
cwater = 4186 J/kg*C
ciron = 448 J/kg*C
Delta T = ? C
HELP: All the energy from part (a) will be converted to heat.
HELP: If we want to increase the temperature of water by Delta T, we have to increase its thermal energy by
Ewater = cwater*mwater*(Delta T)
The same equation holds for iron if the label water is replaced by iron. But Delta T stays the same, because the temperature of the iron and of the water are the same both at the beginning and at the end.
This hint tells you that the energy from part (a) is equal to
Ewater + Eiron.
So, you can substitute for Ewater and Eiron, and get an equation of the form
Epart (a) = something * (Delta T)
For part c, you use the help Ewater+Eiron=the answer from part a. So this would be the set up:
(4186*5*delta T)+(448*1.2*delta T)=0.7
20930delta T + 537.6delta T = 0.7
21467.6delta T = 0.7
delta T= 3.26E-5
To find delta T in part c, we can start by using the equation mentioned in the hint:
E(a) = Ewater + Eiron
We already know the value of E(a) from part (a), which is 0.7 J.
Next, let's substitute the expressions for Ewater and Eiron using the equation:
Ewater = cwater * mwater * (Delta T)
Eiron = ciron * miron * (Delta T)
Since the temperature of the iron and water are the same both at the beginning and at the end, we can use the same Delta T for both.
Now, let's substitute the expressions for Ewater and Eiron into the equation:
E(a) = cwater * mwater * (Delta T) + ciron * miron * (Delta T)
To solve for Delta T, we need to isolate it on one side of the equation. We can factor out Delta T:
E(a) = (cwater * mwater + ciron * miron) * (Delta T)
Now, we can divide both sides of the equation by (cwater * mwater + ciron * miron) to solve for Delta T:
Delta T = E(a) / (cwater * mwater + ciron * miron)
By substituting the known values for E(a), cwater, mwater, ciron, and miron, you can calculate the value of Delta T, which represents the temperature increase.