Answer:
4.7 m³
Explanation:
We'll use the gas law P1 • V1 / T1 = P2 • V2 / T2
* Givens :
P1 = 101 kPa , V1 = 2 m³ , T1 = 300.15 K , P2 = 40 kPa , T2 = 283.15 K
( We must always convert the temperature unit to Kelvin "K")
* What we want to find :
V2 = ?
* Solution :
101 × 2 / 300.15 = 40 × V2 / 283.15
V2 × 40 / 283.15 ≈ 0.67
V2 = 0.67 × 283.15 / 40
V2 ≈ 4.7 m³
Explanation:
It is given that,
Mass of person, m = 70 kg
Radius of merry go round, r = 2.9 m
The moment of inertia, ![I_1=900\ kg.m^2](https://tex.z-dn.net/?f=I_1%3D900%5C%20kg.m%5E2)
Initial angular velocity of the platform, ![\omega=0.95\ rad/s](https://tex.z-dn.net/?f=%5Comega%3D0.95%5C%20rad%2Fs)
Part A,
Let
is the angular velocity when the person reaches the edge. We need to find it. It can be calculated using the conservation of angular momentum as :
![I_1\omega_1=I_2\omega_2](https://tex.z-dn.net/?f=I_1%5Comega_1%3DI_2%5Comega_2)
Here, ![I_2=I_1+mr^2](https://tex.z-dn.net/?f=I_2%3DI_1%2Bmr%5E2)
![I_1\omega_1=(I_1+mr^2)\omega_2](https://tex.z-dn.net/?f=I_1%5Comega_1%3D%28I_1%2Bmr%5E2%29%5Comega_2)
![900\times 0.95=(900+70\times (2.9)^2)\omega_2](https://tex.z-dn.net/?f=900%5Ctimes%200.95%3D%28900%2B70%5Ctimes%20%282.9%29%5E2%29%5Comega_2)
Solving the above equation, we get the value as :
![\omega_2=0.574\ rad/s](https://tex.z-dn.net/?f=%5Comega_2%3D0.574%5C%20rad%2Fs)
Part B,
The initial rotational kinetic energy is given by :
![k_i=\dfrac{1}{2}I_1\omega_1^2](https://tex.z-dn.net/?f=k_i%3D%5Cdfrac%7B1%7D%7B2%7DI_1%5Comega_1%5E2)
![k_i=\dfrac{1}{2}\times 900\times (0.95)^2](https://tex.z-dn.net/?f=k_i%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20900%5Ctimes%20%280.95%29%5E2)
![k_i=406.12\ rad/s](https://tex.z-dn.net/?f=k_i%3D406.12%5C%20rad%2Fs)
The final rotational kinetic energy is given by :
![k_f=\dfrac{1}{2}(I_1+mr^2)\omega_1^2](https://tex.z-dn.net/?f=k_f%3D%5Cdfrac%7B1%7D%7B2%7D%28I_1%2Bmr%5E2%29%5Comega_1%5E2)
![k_f=\dfrac{1}{2}\times (900+70\times (2.9)^2)(0.574)^2](https://tex.z-dn.net/?f=k_f%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%28900%2B70%5Ctimes%20%282.9%29%5E2%29%280.574%29%5E2)
![k_f=245.24\ rad/s](https://tex.z-dn.net/?f=k_f%3D245.24%5C%20rad%2Fs)
Hence, this is the required solution.
Answer:
Explanation:
Electric field between plates of a parallel plate capacitor is uniform .
In a uniform electric field , relation between electric field and potential gradient is as follows
electric field = potential gradient [ E = - dV / dl ]
in the given case ,
dV = 51 V ,
dl = 4 cm
= 4 x 10⁻² m
E = 51 / 4 x 10⁻²
= 12.75 x 10² V / m
= 1275 V / m