Answer:
v (speed) = S / t = 4 * 400 m / (6 * 60 sec) = 4.4 m/s
The average velocity is zero because there is no net vector displacement.
Answer:9.34 A/s
Explanation:
Given
radius of solenoid ![R=1.06 m](https://tex.z-dn.net/?f=R%3D1.06%20m)
Emf induced ![E=8.50\times 10^{-6} V/m](https://tex.z-dn.net/?f=E%3D8.50%5Ctimes%2010%5E%7B-6%7D%20V%2Fm)
no of turns per meter n=450
we know Induced EMF is given by
![\int Edl=-\frac{\mathrm{d} \phi}{\mathrm{d} t}=-\frac{\mathrm{d} B}{\mathrm{d} t}A](https://tex.z-dn.net/?f=%5Cint%20Edl%3D-%5Cfrac%7B%5Cmathrm%7Bd%7D%20%5Cphi%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D-%5Cfrac%7B%5Cmathrm%7Bd%7D%20B%7D%7B%5Cmathrm%7Bd%7D%20t%7DA)
Magnetic Field is given by
![B=\mu _0ni](https://tex.z-dn.net/?f=B%3D%5Cmu%20_0ni)
thus ![\frac{\mathrm{d} B}{\mathrm{d} t}=-\mu _0n\frac{\mathrm{d} i}{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20B%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D-%5Cmu%20_0n%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
Area of cross-section
where
solving integration we get
![E.\cdot 2\pi r=\mu _0n\frac{\mathrm{d} i}{\mathrm{d} t}\pi R^2](https://tex.z-dn.net/?f=E.%5Ccdot%202%5Cpi%20r%3D%5Cmu%20_0n%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%5Cpi%20R%5E2)
where r=distance from axis
R=radius of Solenoid
![\frac{\mathrm{d} i}{\mathrm{d} t}=\frac{Er}{\mu _0nR^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7BEr%7D%7B%5Cmu%20_0nR%5E2%7D)
![\frac{\mathrm{d} i}{\mathrm{d} t}=\frac{8.50\times 10^{-6}\times 3.49\times 10^{-2}}{4\pi \times 10^{-7}\times 450\times 1.06^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7B8.50%5Ctimes%2010%5E%7B-6%7D%5Ctimes%203.49%5Ctimes%2010%5E%7B-2%7D%7D%7B4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5Ctimes%20450%5Ctimes%201.06%5E2%7D)
![\frac{\mathrm{d} i}{\mathrm{d} t}=9.34 A/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20i%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D9.34%20A%2Fs)
The total mechanical energy of the block-spring system is given by the sum of the potential energy and the kinetic energy of the block:
![E=U+K= \frac{1}{2}kx^2 + \frac{1}{2}mv^2](https://tex.z-dn.net/?f=E%3DU%2BK%3D%20%5Cfrac%7B1%7D%7B2%7Dkx%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20)
where
k is the spring constant
x is the elongation/compression of the spring
m is the mass of the block
v is the speed of the block
At the point of maximum displacement of the spring, the velocity of the block is zero: v=0, so the kinetic energy is zero and the mechanical energy is just potential energy of the spring:
![E= \frac{1}{2}kA^2](https://tex.z-dn.net/?f=E%3D%20%5Cfrac%7B1%7D%7B2%7DkA%5E2%20)
(1)
where we used x=A, the amplitude (which is the maximum displacement of the spring).
Since we know
A = 11.0 cm= 0.11 m
E = 1.10 J
We can re-arrange (1) to find the spring constant:
Answer:
The total amount of CO₂ produced will be = 20680 kg/year
The reduction in the amount of CO₂ emissions by that household per year = 3102 kg/year
Explanation:
Given:
Power used by household = 14000 kWh
Fuel oil used = 3400 L
CO₂ produced of fuel oil = 3.2 kg/L
CO₂ produced of electricity = 0.70 kg/kWh
Now, the total amount of CO₂ produced will be = (14000 kWh × 0.70 kg/kWh) + (3400 L × 3.2 kg/L)
⇒ The total amount of CO₂ produced will be = 9800 + 10880 = 20680 kg/year
Now,
if the usage of electricity and fuel oil is reduced by 15%, the reduction in the amount of the CO₂ emission will be = 0.15 × 20680 kg/year = 3102 kg/year
Mmm tricky.
Since the velocity is constant, I'm going to assume there is no acceleration in any direction. This means there is no net force in the I or J forection!
Since there are 2 forces, both must be equal and opposite in direction to perfectly cancel each other out.
So the opposite of F1 is (-2N)I + (6N)J!