1. electrical energy: electrical energy that is caused by moving electrons
2. coolant: a mixture of antifreeze and water that removes excess heat from an internal engine
3. electric compressor: a device that <span>acts as a pump, circulating refrigerant throughout the refrigerator
4. the inside of the fridge and the food becomes colder
5. the coolants becomes a hot, high-pressure gas
6. as coolant transfers thermal energy to the air outside, it turns back into a liquid
</span>
Answer:
a)
, b) ![R = 0.312\,m](https://tex.z-dn.net/?f=R%20%3D%200.312%5C%2Cm)
Explanation:
a) The minimum coeffcient of friction is computed by the following expression derived from the Principle of Energy Conservation:
![\frac{1}{2}\cdot k \cdot x^{2} = \mu_{k}\cdot m\cdot g \cdot \Delta s](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20k%20%5Ccdot%20x%5E%7B2%7D%20%3D%20%5Cmu_%7Bk%7D%5Ccdot%20m%5Ccdot%20g%20%5Ccdot%20%5CDelta%20s)
![\mu_{k} = \frac{k\cdot x^{2}}{2\cdot m\cdot g \cdot \Delta s}](https://tex.z-dn.net/?f=%5Cmu_%7Bk%7D%20%3D%20%5Cfrac%7Bk%5Ccdot%20x%5E%7B2%7D%7D%7B2%5Ccdot%20m%5Ccdot%20g%20%5Ccdot%20%5CDelta%20s%7D)
![\mu_{k} = \frac{\left(8050\,\frac{N}{m} \right)\cdot (0.06\,m)^{2}}{2\cdot (0.3\,kg)\cdot (9.807\,\frac{m}{s^{2}} )\cdot (7\,m)}](https://tex.z-dn.net/?f=%5Cmu_%7Bk%7D%20%3D%20%5Cfrac%7B%5Cleft%288050%5C%2C%5Cfrac%7BN%7D%7Bm%7D%20%5Cright%29%5Ccdot%20%280.06%5C%2Cm%29%5E%7B2%7D%7D%7B2%5Ccdot%20%280.3%5C%2Ckg%29%5Ccdot%20%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%29%5Ccdot%20%287%5C%2Cm%29%7D)
![\mu_{k} = 0.704](https://tex.z-dn.net/?f=%5Cmu_%7Bk%7D%20%3D%200.704)
b) The speed of the block is determined by using the Principle of Energy Conservation:
![\frac{1}{2}\cdot k \cdot x^{2} = \frac{1}{2}\cdot m \cdot v^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20k%20%5Ccdot%20x%5E%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20m%20%5Ccdot%20v%5E%7B2%7D)
![v = x\cdot \sqrt{\frac{k}{m} }](https://tex.z-dn.net/?f=v%20%3D%20x%5Ccdot%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D)
![v = (0.06\,m)\cdot \sqrt{\frac{8050\,\frac{N}{m} }{0.3\,kg} }](https://tex.z-dn.net/?f=v%20%3D%20%280.06%5C%2Cm%29%5Ccdot%20%5Csqrt%7B%5Cfrac%7B8050%5C%2C%5Cfrac%7BN%7D%7Bm%7D%20%7D%7B0.3%5C%2Ckg%7D%20%7D)
![v \approx 9.829\,\frac{m}{s}](https://tex.z-dn.net/?f=v%20%5Capprox%209.829%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
The radius of the circular loop is:
![\Sigma F_{r} = -90\,N -(0.3\,kg)\cdot (9.807\,\frac{m}{s^{2}} ) = -(0.3\,kg)\cdot \frac{v^{2}}{R}](https://tex.z-dn.net/?f=%5CSigma%20F_%7Br%7D%20%3D%20-90%5C%2CN%20-%280.3%5C%2Ckg%29%5Ccdot%20%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%29%20%3D%20-%280.3%5C%2Ckg%29%5Ccdot%20%5Cfrac%7Bv%5E%7B2%7D%7D%7BR%7D)
![\frac{\left(9.829\,\frac{m}{s}\right)^{2}}{R} = 309.807\,\frac{m}{s^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%289.829%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%5Cright%29%5E%7B2%7D%7D%7BR%7D%20%3D%20309.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
![R = 0.312\,m](https://tex.z-dn.net/?f=R%20%3D%200.312%5C%2Cm)
Answer:
d) The screen is in a short distance from the hole
Answer:
![0.00027646\ T](https://tex.z-dn.net/?f=0.00027646%5C%20T)
![2.33\times 10^{-5}\ H](https://tex.z-dn.net/?f=2.33%5Ctimes%2010%5E%7B-5%7D%5C%20H)
-0.04194 V
Explanation:
= Number of turns in outer solenoid = 330
= Number of turns in inner solenoid = 22
= Current in inner solenoid = 0.14 A
= Rate of change of current = 1800 A/s
= Vacuum permeability = ![4\pi \times 10^{-7}\ H/m](https://tex.z-dn.net/?f=4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5C%20H%2Fm)
r = Radius = 0.0115 m
Magnetic field is given by
![B=\mu_0\dfrac{N_2}{l}I\\\Rightarrow B=4\pi \times 10^{-7}\times \dfrac{330}{0.21}\times 0.14\\\Rightarrow B=0.00027646\ T](https://tex.z-dn.net/?f=B%3D%5Cmu_0%5Cdfrac%7BN_2%7D%7Bl%7DI%5C%5C%5CRightarrow%20B%3D4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5Ctimes%20%5Cdfrac%7B330%7D%7B0.21%7D%5Ctimes%200.14%5C%5C%5CRightarrow%20B%3D0.00027646%5C%20T)
The average magnetic flux through each turn of the inner solenoid is ![0.00027646\ T](https://tex.z-dn.net/?f=0.00027646%5C%20T)
Magnetic flux is given by
![\phi=BA\\\Rightarrow \phi=0.00027646\times \pi 0.0115^2\\\Rightarrow \phi=1.14862\times 10^{-7}\ wb](https://tex.z-dn.net/?f=%5Cphi%3DBA%5C%5C%5CRightarrow%20%5Cphi%3D0.00027646%5Ctimes%20%5Cpi%200.0115%5E2%5C%5C%5CRightarrow%20%5Cphi%3D1.14862%5Ctimes%2010%5E%7B-7%7D%5C%20wb)
Mutual inductance is given by
![M=\dfrac{N_1\phi}{I}\\\Rightarrow M=\dfrac{22\times 1.14862\times 10^{-7}}{0.14}\\\Rightarrow M=2.33\times 10^{-5}\ H](https://tex.z-dn.net/?f=M%3D%5Cdfrac%7BN_1%5Cphi%7D%7BI%7D%5C%5C%5CRightarrow%20M%3D%5Cdfrac%7B22%5Ctimes%201.14862%5Ctimes%2010%5E%7B-7%7D%7D%7B0.14%7D%5C%5C%5CRightarrow%20M%3D2.33%5Ctimes%2010%5E%7B-5%7D%5C%20H)
The mutual inductance of the two solenoids is ![2.33\times 10^{-5}\ H](https://tex.z-dn.net/?f=2.33%5Ctimes%2010%5E%7B-5%7D%5C%20H)
Induced emf is given by
![\epsilon=-M\dfrac{dI_2}{dt}\\\Rightarrow \epsilon=-2.33\times 10^{-5}\times 1800\\\Rightarrow \epsilon=-0.04194\ V](https://tex.z-dn.net/?f=%5Cepsilon%3D-M%5Cdfrac%7BdI_2%7D%7Bdt%7D%5C%5C%5CRightarrow%20%5Cepsilon%3D-2.33%5Ctimes%2010%5E%7B-5%7D%5Ctimes%201800%5C%5C%5CRightarrow%20%5Cepsilon%3D-0.04194%5C%20V)
The emf induced in the outer solenoid by the changing current inthe inner solenoid is -0.04194 V
Answer:
t = 134834.31 years
Explanation:
First we find the speed of the ship:
v = 0.890 c
where,
v = speed of the ship = ?
c = speed of light = 3 x 10⁸ m/s
Therefore, using the values, we get:
v = (0.89)(3 x 10⁸ m/s)
v = 2.67 x 10⁸ m/s
Now, we find the distance in meters:
Distance = s = (1.2 x 10⁵ light years)(9.461 x 10¹⁵/1 light year)
s = 11.35 x 10²⁰ m
Now, for the time we use the following equation:
s = vt
t = s/v
t = (11.35 x 10²⁰ m)/(2.67 x 10⁸ m/s)
t = (4.25 x 10¹² s)(1 h/3600 s)(1 day/24 h)(1 year/365 days)
<u>t = 134834.31 years</u>