Answer:
W = -1844.513 J
Explanation:
GIVEN DATA:
mass of spider man is m 74 kg
vertical displacement if spider is 11 m
final displacement = 11 cos 60.6 = - 6.753 m
change in displacement is = -6.753 - (-11) = 4.25 m
gravity force act on spiderman is f = mg = 74 × 9.8 = 725.2 N
work done by gravity is ![W = F \delta r cos\theta](https://tex.z-dn.net/?f=W%20%3D%20F%20%5Cdelta%20r%20cos%5Ctheta)
![W = 725.2 \times 4.25 \times cos 180](https://tex.z-dn.net/?f=W%20%3D%20725.2%20%5Ctimes%204.25%20%5Ctimes%20cos%20180)
where 180 is the angle between spiderman weight and displacement
W = -1844.513 J
Answer:
![2.27\cdot 10^{49}](https://tex.z-dn.net/?f=2.27%5Ccdot%2010%5E%7B49%7D)
Explanation:
The gravitational force between the proton and the electron is given by
![F_G=G\frac{m_p m_e}{r^2}](https://tex.z-dn.net/?f=F_G%3DG%5Cfrac%7Bm_p%20m_e%7D%7Br%5E2%7D)
where
G is the gravitational constant
is the proton mass
is the electron mass
r = 3 m is the distance between the proton and the electron
Substituting numbers into the equation,
![F_G=(6.67259\cdot 10^{-11} m^3 kg s^{-2})\frac{(1.67262\cdot 10^{-27}kg) (9.10939\cdot 10^{-31}kg)}{(3 m)^2}=1.13\cdot 10^{-68}N](https://tex.z-dn.net/?f=F_G%3D%286.67259%5Ccdot%2010%5E%7B-11%7D%20m%5E3%20kg%20s%5E%7B-2%7D%29%5Cfrac%7B%281.67262%5Ccdot%2010%5E%7B-27%7Dkg%29%20%289.10939%5Ccdot%2010%5E%7B-31%7Dkg%29%7D%7B%283%20m%29%5E2%7D%3D1.13%5Ccdot%2010%5E%7B-68%7DN)
The electrical force between the proton and the electron is given by
![F_E=k\frac{q_p q_e}{r^2}](https://tex.z-dn.net/?f=F_E%3Dk%5Cfrac%7Bq_p%20q_e%7D%7Br%5E2%7D)
where
k is the Coulomb constant
is the elementary charge (charge of the proton and of the electron)
r = 3 m is the distance between the proton and the electron
Substituting numbers into the equation,
![F_E=(8.98755\cdot 10^9 Nm^2 C^{-2})\frac{(1.602\cdot 10^{-19}C)^2}{(3 m)^2}=2.56\cdot 10^{-19}N](https://tex.z-dn.net/?f=F_E%3D%288.98755%5Ccdot%2010%5E9%20Nm%5E2%20C%5E%7B-2%7D%29%5Cfrac%7B%281.602%5Ccdot%2010%5E%7B-19%7DC%29%5E2%7D%7B%283%20m%29%5E2%7D%3D2.56%5Ccdot%2010%5E%7B-19%7DN)
So, the ratio of the electrical force to the gravitational force is
![\frac{F_E}{F_G}=\frac{2.56\cdot 10^{-19} N}{1.13\cdot 10^{-68}N}=2.27\cdot 10^{49}](https://tex.z-dn.net/?f=%5Cfrac%7BF_E%7D%7BF_G%7D%3D%5Cfrac%7B2.56%5Ccdot%2010%5E%7B-19%7D%20N%7D%7B1.13%5Ccdot%2010%5E%7B-68%7DN%7D%3D2.27%5Ccdot%2010%5E%7B49%7D)
So, we see that the electrical force is much larger than the gravitational force.
Jumping on a trampoline is a classic example of conservation of energy, from potential into kinetic. It also shows Hooke's laws and the spring constant. Furthermore, it verifies and illustrates each of Newton's three laws of motion.
<u>Explanation</u>
When we jump on a trampoline, our body has kinetic energy that changes over time. Our kinetic energy is greatest, just before we hit the trampoline on the way down and when you leave the trampoline surface on the way up. Our kinetic energy is 0 when you reach the height of your jump and begin to descend and when are on the trampoline, about to propel upwards.
Potential energy changes along with kinetic energy. At any time, your total energy is equal to your potential energy plus your kinetic energy. As we go up, the kinetic energy converts into potential energy.
Hooke's law is another form of potential energy. Just as the trampoline is about to propel us up, your kinetic energy is 0 but your potential energy is maximized, even though we are at a minimum height. This is because our potential energy is related to the spring constant and Hooke's Law.
Answer:
Capacitance of the second capacitor = 2C
Explanation:
![\texttt{Capacitance, C}=\frac{\varepsilon_0A}{d}](https://tex.z-dn.net/?f=%5Ctexttt%7BCapacitance%2C%20C%7D%3D%5Cfrac%7B%5Cvarepsilon_0A%7D%7Bd%7D)
Where A is the area, d is the gap between plates and ε₀ is the dielectric constant.
Let C₁ be the capacitance of first capacitor with area A₁ and gap between plates d₁.
We have
![\texttt{Capacitance, C}_1=\frac{\varepsilon_0A_1}{d_1}=C](https://tex.z-dn.net/?f=%5Ctexttt%7BCapacitance%2C%20C%7D_1%3D%5Cfrac%7B%5Cvarepsilon_0A_1%7D%7Bd_1%7D%3DC)
Similarly for capacitor 2
![\texttt{Capacitance, C}_2=\frac{\varepsilon_0A_2}{d_2}=\frac{\varepsilon_0A_1}{\frac{d_1}{2}}=2\times \frac{\varepsilon_0A_1}{d_1}=2C](https://tex.z-dn.net/?f=%5Ctexttt%7BCapacitance%2C%20C%7D_2%3D%5Cfrac%7B%5Cvarepsilon_0A_2%7D%7Bd_2%7D%3D%5Cfrac%7B%5Cvarepsilon_0A_1%7D%7B%5Cfrac%7Bd_1%7D%7B2%7D%7D%3D2%5Ctimes%20%5Cfrac%7B%5Cvarepsilon_0A_1%7D%7Bd_1%7D%3D2C)
Capacitance of the second capacitor = 2C