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Chapter 14: Problem 8

An experiment is conducted with a basic Joule apparatus, where a mass is allowed to descend by \(1.25 \mathrm{m}\) and rotate paddles within an insulated container of water. There are several different sizes of descending masses to choose among. If the investigator wishes to deliver \(1.00 \mathrm{kJ}\) to the water within the insulated container after 30.0 descents, what descending mass value should be used?

Short Answer

Expert verified
Answer: Approximately 3.38 kg.

Step by step solution

01

Calculate the total energy to be delivered to the water

Since we want the mass to deliver 1.00 kJ of energy to the water after 30 descents, we first calculate the total energy it needs to deliver. It is given in kJ, so we'll convert it into Joules (J) as follows: \(1.00\,\text{kj} = 1.00 \times 10^3\, \text{Joules}\)
02

Calculate the energy delivered per descent

Now, we must find out the energy delivered in each descent. To do this, we will divide the total energy by the total number of descents: \(E_\text{per descent} = \frac{1.00 \times 10^3\, \text{J}}{30}\)
03

Find the mass value

We will now use the potential energy formula to find the mass value: \(E_\text{per descent} = mgh\) We know the values of \(E_\text{per descent}\), \(g\), and \(h\). Rearranging the equation, we can calculate the mass: \(m = \frac{E_\text{per descent}}{gh}\) Plugging the values and calculations into the equation, we can find the descending mass value: \(m = \frac{1.00 \times 10^3\, \text{J}/30}{(9.81\, \text{m/s}^2)(1.25\, \text{m})}\) Upon solving, we get the mass value that should be used: \(m \approx 3.38\, \text{kg}\) So, the descending mass value to be used is approximately 3.38 kg.

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