I think this is the solution:
1: U-1, F,-4
2: Na-6, Mo-1, O-4
3: Bi-1, O-1, C-1, I-1
4: In-9, N-1
5: N-2, H-4, S-1, C-1
6: Ge- 15, N-4
7: N-1, H-4, C-1, I-1, O-3
8: H-7, F-1
9: N-1, O-5, H-1, S-1
10: H-8
11: Nb-1, O-1, C-1, I-3
12: C-3, F-3, S-1, O-3, H-1
13: Ag-1, C-1, N-1, O-1
14: Pb-6, H-1, As-1, O-4
Based on the law of conservation of energy, we know that we can't create energy, machines can only convert one type of energy into another. So, if we want to improve a machines's ability then we need to reduce it's loss energy (part of energy which is useless). Out of all the options only Option C fits best with it.
In short, Your Answer would be Option C
Hope this helps!
Answer:
-2.3 × 10^-9 Coulombs(C).
Explanation:
So, we are given the following data or information or parameters that is going to help us to solve the problem effectively and efficiently;
=> " the shuttle's potential is typically changed by -1.4 V during one revolution. "
=> " Assuming the shuttle is a conducting sphere of radius 15 m".
So, in order to estimate the value for the charge we will be making use of the equation below:
Charge, C =( radius × voltage or potential difference) ÷ Coulomb's law constant.
Note that the value of Coulomb's law constant = 9 x 10^9 Nm^2 / C^2.
So, charge = { 15 × (- 1.4)} / 9 x 10^9 Nm^2 / C^2.
= -2.3 × 10^-9 Coulombs(C).
Answer:
part (a) ![a_1\ =\ 2.9\ kg](https://tex.z-dn.net/?f=a_1%5C%20%3D%5C%202.9%5C%20kg)
Part (b) ![a_2\ =\ 6.25\ kg](https://tex.z-dn.net/?f=a_2%5C%20%3D%5C%206.25%5C%20kg)
Explanation:
Given,
- mass of the smaller disk =
![M_1\ =\ 0.900\ kg](https://tex.z-dn.net/?f=M_1%5C%20%3D%5C%200.900%5C%20kg)
- Radius of the smaller disk =
![R_1\ =\ 2.45\ cm\ =\ 0.0245\ m](https://tex.z-dn.net/?f=R_1%5C%20%3D%5C%202.45%5C%20cm%5C%20%3D%5C%200.0245%5C%20m)
- mass of the larger disk =
![M_2\ =\ 1.6\ kg](https://tex.z-dn.net/?f=M_2%5C%20%3D%5C%201.6%5C%20kg)
- Radius of the larger disk =
![R_2\ =\ 5.0\ cm\ =\ 0.05\ m](https://tex.z-dn.net/?f=R_2%5C%20%3D%5C%205.0%5C%20cm%5C%20%3D%5C%200.05%5C%20m)
- mass of the hanging block = m = 1.60 kg
Let I be the moment of inertia of the both disk after the welding,![\therefore I\ =\ I_1\ +\ I_2\\\Rightarrow I\ =\ \dfrac{1}{2}(M_1R_1^2\ +\ M_2R_2^2)\\\Rightarrow I\ =\ 0.5\times (0.9\times 0.0245^2\ +\ 1.6\times 0.05^2)\\\Rightarrow I\ =\ 2.27\times 10^{-3}\ kgm^2](https://tex.z-dn.net/?f=%5Ctherefore%20I%5C%20%3D%5C%20I_1%5C%20%2B%5C%20I_2%5C%5C%5CRightarrow%20I%5C%20%3D%5C%20%5Cdfrac%7B1%7D%7B2%7D%28M_1R_1%5E2%5C%20%2B%5C%20M_2R_2%5E2%29%5C%5C%5CRightarrow%20I%5C%20%3D%5C%200.5%5Ctimes%20%280.9%5Ctimes%200.0245%5E2%5C%20%2B%5C%201.6%5Ctimes%200.05%5E2%29%5C%5C%5CRightarrow%20I%5C%20%3D%5C%202.27%5Ctimes%2010%5E%7B-3%7D%5C%20kgm%5E2)
part (a)
A block of mass m is hanging on the smaller disk,
From the f.b.d. of the block,
Let 'a' be the acceleration of the block and 'T' be the tension in the string.
![mg\ -\ T\ =\ mg\\\Rightarrow T\ =\ mg\ -\ ma\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,eqn (1)](https://tex.z-dn.net/?f=mg%5C%20-%5C%20T%5C%20%3D%5C%20mg%5C%5C%5CRightarrow%20T%5C%20%3D%5C%20mg%5C%20-%5C%20ma%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2Ceqn%20%281%29)
Net torque on the smaller disk,
![\therefore \tau\ =\ I\alpha\\\Rightarrow TR_1\ =\ \dfrac{Ia}{R_1}\\\Rightarrow T\ =\ \dfrac{Ia}{R_1^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,enq (2)](https://tex.z-dn.net/?f=%5Ctherefore%20%5Ctau%5C%20%3D%5C%20I%5Calpha%5C%5C%5CRightarrow%20TR_1%5C%20%3D%5C%20%5Cdfrac%7BIa%7D%7BR_1%7D%5C%5C%5CRightarrow%20T%5C%20%3D%5C%20%5Cdfrac%7BIa%7D%7BR_1%5E2%7D%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2Cenq%20%282%29)
From eqn (1) and (2), we get,
![mg\ -\ ma\ =\ \dfrac{Ia}{R_1^2}\\\Rightarrow a\ =\ \dfrac{mg}{\dfrac{I}{R_1^2}\ +\ m}\\\Rightarrow a\ =\ \dfrac{1.60\times 9.81}{\dfrac{2.27\times 10^{-3}}{0.027^2}\ +\ 1.60}\\\Rightarrow a\ =\ 2.91\ m/s^2](https://tex.z-dn.net/?f=mg%5C%20-%5C%20ma%5C%20%3D%5C%20%5Cdfrac%7BIa%7D%7BR_1%5E2%7D%5C%5C%5CRightarrow%20a%5C%20%3D%5C%20%5Cdfrac%7Bmg%7D%7B%5Cdfrac%7BI%7D%7BR_1%5E2%7D%5C%20%2B%5C%20m%7D%5C%5C%5CRightarrow%20a%5C%20%3D%5C%20%5Cdfrac%7B1.60%5Ctimes%209.81%7D%7B%5Cdfrac%7B2.27%5Ctimes%2010%5E%7B-3%7D%7D%7B0.027%5E2%7D%5C%20%2B%5C%201.60%7D%5C%5C%5CRightarrow%20a%5C%20%3D%5C%202.91%5C%20m%2Fs%5E2)
part (b)
In this case the mass is rapped on the larger disk,
From the above expression of the acceleration of the block, acceleration is only depended on the radius of the rotating disk,
Let '
' be the acceleration of the block in the second case,
From the above expression,
![\therefore a\ =\ \dfrac{mg}{\dfrac{I}{R_1^2}\ +\ m}\\\Rightarrow a\ =\ \dfrac{1.60\times 9.81}{\dfrac{2.27\times 10^{-3}}{0.05^2}\ +\ 1.60}\\\Rightarrow a\ =\ 6.25\ m/s^2](https://tex.z-dn.net/?f=%5Ctherefore%20a%5C%20%3D%5C%20%5Cdfrac%7Bmg%7D%7B%5Cdfrac%7BI%7D%7BR_1%5E2%7D%5C%20%2B%5C%20m%7D%5C%5C%5CRightarrow%20a%5C%20%3D%5C%20%5Cdfrac%7B1.60%5Ctimes%209.81%7D%7B%5Cdfrac%7B2.27%5Ctimes%2010%5E%7B-3%7D%7D%7B0.05%5E2%7D%5C%20%2B%5C%201.60%7D%5C%5C%5CRightarrow%20a%5C%20%3D%5C%206.25%5C%20m%2Fs%5E2)
Complete Question:
A 59.1 g sample of iron is put into a calorimeter (see sketch attached) that contains 100.0 g of water. The iron sample starts off at 85.0 °C and the temperature of the water starts off at 23.0 °C. When the temperature of the water stops changing it's 27.6 °C. The pressure remains constant at 1 atm.
Calculate the specific heat capacity of iron according to this experiment. Be sure your answer is rounded to the correct number of significant digits
(Question attached)
Answer:
![c_{iron}=0.568 J/kg.\°C](https://tex.z-dn.net/?f=c_%7Biron%7D%3D0.568%20J%2Fkg.%5C%C2%B0C)
(rounded to 1 decimal place)
Explanation:
A calorimeter is used to measure the heat of chemical or physical reactions. The example given in the question is using the calorimeter to determine the specific heat capacity of iron.
When the system reaches equilibrium the iron and water will be the same temperature,
. The energy lost from the iron will be equal to the energy gained by the water. It is assumed that the only heat exchange is between the iron and water and no exchange with the surroundings.
(Eq 1)
(Eq 2)
Water:
![m_{water}=100.0 g, c_{water}=4.186 J/kg.\°C, T_{initial,water}=23 \°C, T_{e}=27.6 \°C](https://tex.z-dn.net/?f=m_%7Bwater%7D%3D100.0%20g%2C%20c_%7Bwater%7D%3D4.186%20J%2Fkg.%5C%C2%B0C%2C%20T_%7Binitial%2Cwater%7D%3D23%20%5C%C2%B0C%2C%20T_%7Be%7D%3D27.6%20%5C%C2%B0C)
Iron:
![m_{iron}=59.1 g, c_{iron} = ? J/kg.\°C, T_{initial,iron}=85 \°C, T_{e}=27.6 \°C](https://tex.z-dn.net/?f=m_%7Biron%7D%3D59.1%20g%2C%20c_%7Biron%7D%20%3D%20%3F%20J%2Fkg.%5C%C2%B0C%2C%20T_%7Binitial%2Ciron%7D%3D85%20%5C%C2%B0C%2C%20T_%7Be%7D%3D27.6%20%5C%C2%B0C)
Substituting Eq 1 into Eq 2 and details extracted from the question:
![-m_{iron}c_{iron}(T_{iron,e}-T_{initial})=m_{water}c_{water}(T_{water,e}-T_{initial})](https://tex.z-dn.net/?f=-m_%7Biron%7Dc_%7Biron%7D%28T_%7Biron%2Ce%7D-T_%7Binitial%7D%29%3Dm_%7Bwater%7Dc_%7Bwater%7D%28T_%7Bwater%2Ce%7D-T_%7Binitial%7D%29)
![-59.1*c_{iron}(27.6-85)=100.0*4.186(27.6-23)](https://tex.z-dn.net/?f=-59.1%2Ac_%7Biron%7D%2827.6-85%29%3D100.0%2A4.186%2827.6-23%29)
![c_{iron}=0.568 J/kg.\°C](https://tex.z-dn.net/?f=c_%7Biron%7D%3D0.568%20J%2Fkg.%5C%C2%B0C)
![c_{iron}=0.6 J/kg.\°C](https://tex.z-dn.net/?f=c_%7Biron%7D%3D0.6%20J%2Fkg.%5C%C2%B0C)