Answer:
173.45 K
Explanation:
This an Adiabatic process because no energy is lost by thermal conduction on expansion. We will be using this Adiabatic condition and ideal gas equation to solve the question.
From idea gas equation;
PV = nRT
-----(1)
where
P is pressure of the gas
V is volume of the gas
n is number of moles
R is gas constant 8.31441 J K-1 mol-1.
T is temperature in Kelvin
For Adiabatic Condition;
----(2)
Substituting equation(1) into equation(2)
![\frac {nRT_{1}V_{1}^{k}}{V_{1}} = \frac{nRT_{2}V_{2}^{k}}{V_{2}}](https://tex.z-dn.net/?f=%5Cfrac%20%7BnRT_%7B1%7DV_%7B1%7D%5E%7Bk%7D%7D%7BV_%7B1%7D%7D%20%3D%20%5Cfrac%7BnRT_%7B2%7DV_%7B2%7D%5E%7Bk%7D%7D%7BV_%7B2%7D%7D)
Eliminating the constants and simplify with exponent
Making T₂ the subject of the formula;
![T_{2} = \frac {T_{1}V_{1}^{(k-1)}}{V_{2}^{(k-1)}}](https://tex.z-dn.net/?f=%20T_%7B2%7D%20%3D%20%5Cfrac%20%7BT_%7B1%7DV_%7B1%7D%5E%7B%28k-1%29%7D%7D%7BV_%7B2%7D%5E%7B%28k-1%29%7D%7D)
The temperature when the initial volume has quadrupled ⇒ V₂ = 4V₁
⇒ ![\frac{V_{1}}{V_{2}} = 4](https://tex.z-dn.net/?f=%5Cfrac%7BV_%7B1%7D%7D%7BV_%7B2%7D%7D%20%3D%204)
Since air is diatomic, we assume k = 1.4
∴ ![T_{2} = T_{1} \frac {V_{1}}{V_{4}}^{(k-1)}](https://tex.z-dn.net/?f=%20T_%7B2%7D%20%3D%20T_%7B1%7D%20%5Cfrac%20%7BV_%7B1%7D%7D%7BV_%7B4%7D%7D%5E%7B%28k-1%29%7D)
![T_{2} = 302 K \frac {1}{4}^{(1.4-1)}](https://tex.z-dn.net/?f=%20T_%7B2%7D%20%3D%20302%20K%20%5Cfrac%20%7B1%7D%7B4%7D%5E%7B%281.4-1%29%7D)
![T_{2} = 302 K \frac {1}{4}^{(0.4)}](https://tex.z-dn.net/?f=%20T_%7B2%7D%20%3D%20302%20K%20%5Cfrac%20%7B1%7D%7B4%7D%5E%7B%280.4%29%7D)
T₂ = 173.45 K
Answer:
d) The total mechanical energy is constant.
Explanation:
The total mechanical energy of a pendulum is given by:
![E=KE+PE](https://tex.z-dn.net/?f=E%3DKE%2BPE)
where
KE is the kinetic energy (the energy of motion), given by
![KE=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=KE%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
where
m is the mass of the pendulum
v is its speed
PE is the potential energy of the pendulum (the energy due to its position), given by
![PE=mgh](https://tex.z-dn.net/?f=PE%3Dmgh)
where
g is the acceleration due to gravity
h is the height of the pendulum relative to the ground
In absence of air resistance, the total mechanical energy of the pendulum is constant. This means that there is a continuous conversion of energy between kinetic and potential. In particular:
- When the pendulum is at its highest position (maximum displacement), the potential energy is maximum while the kinetic energy is minimum)
- When the pendulum crosses its equilibrium position, the kinetic energy is maximum (maximum speed) while the potential energy is minimum
Answer:
Newton states his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes or F = m*a. The change in momentum is the difference between the final and initial values of momentum. ... It is equal to the change in momentum.
Explanation:
Potential energy is measured using formula Ep=mgh
m=mass (kg)
g= acceleration due to gravity (which is 9.8 on earth)
h= height in metres above ground
For this question
m=0.1
g=9.8
h=1
So Ep=0.1(9.8)(1)
Ep=0.98 Joules
When it is dropped all of this potential energy is converted into kinetic energy which can be measured using formula
Ek=1/2m(v^2) (v=final velocity)
Since all potential energy in this q is converted to kinetic we know Ek=0.98Joules and our mass is the same (0.1kg)
So when we sub everything in we get
0.98=1/2(0.1)(v^2)
0.98=0.05(v^2)||divide both side by 0.05
19.6=v^2 ||square root both sides
v=4.4 m/s