Answer:
576 joules
Explanation:
From the question we are given the following:
weight = 810 N
radius (r) = 1.6 m
horizontal force (F) = 55 N
time (t) = 4 s
acceleration due to gravity (g) = 9.8 m/s^{2}
K.E = 0.5 x MI x ω^{2}
where MI is the moment of inertia and ω is the angular velocity
MI = 0.5 x m x r^2
mass = weight ÷ g = 810 ÷ 9.8 = 82.65 kg
MI = 0.5 x 82.65 x 1.6^{2}
MI = 105.8 kg.m^{2}
angular velocity (ω) = a x t
angular acceleration (a) = torque ÷ MI
where torque = F x r = 55 x 1.6 = 88 N.m
a= 88 ÷ 105.8 = 0.83 rad /s^{2}
therefore
angular velocity (ω) = a x t = 0.83 x 4 = 3.33 rad/s
K.E = 0.5 x MI x ω^{2}
K.E = 0.5 x 105.8 x 3.33^{2} = 576 joules
1 Amp = 1 Coulomb/sec
1 Coulomb/sec = 6.25*10^18 electrons/sec
Therefore,
5.0 A = 5 C/s = 5*6.25*10^18 = 3.125*10^19 e/s
In 10 second, number of electrons are calculated as;
Number of electrons through the device = 3.125*10^19*10 = 3.125*10^20 electrons
Answer:
![v=0.9833\ c](https://tex.z-dn.net/?f=v%3D0.9833%5C%20c)
Explanation:
The density changes means that the length in the direction of the motion is changed.
Therefore,
![$\text{Density} = \frac{m}{lwh}$](https://tex.z-dn.net/?f=%24%5Ctext%7BDensity%7D%20%3D%20%5Cfrac%7Bm%7D%7Blwh%7D%24)
Given :
Side, b = h = 0.13 m
Mass, m = 3.3 kg
Density = 8100 ![kg/m^3](https://tex.z-dn.net/?f=kg%2Fm%5E3)
So,
![$8100=\frac{3.3}{l \times 0.13 \times 0.13}$](https://tex.z-dn.net/?f=%248100%3D%5Cfrac%7B3.3%7D%7Bl%20%5Ctimes%200.13%20%5Ctimes%200.13%7D%24)
![$l=\frac{3.3}{8100 \times 0.13 \times 0.13}$](https://tex.z-dn.net/?f=%24l%3D%5Cfrac%7B3.3%7D%7B8100%20%5Ctimes%200.13%20%5Ctimes%200.13%7D%24)
l = 0.024 m
Then for relativistic length contraction,
![$l= l' \sqrt{1-\frac{v^2}{c^2}}$](https://tex.z-dn.net/?f=%24l%3D%20l%27%20%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%24)
![$0.024= 0.13 \sqrt{1-\frac{v^2}{c^2}}$](https://tex.z-dn.net/?f=%240.024%3D%200.13%20%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%24)
![$0.184= \sqrt{1-\frac{v^2}{c^2}}$](https://tex.z-dn.net/?f=%240.184%3D%20%20%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%24)
![$0.033= 1-\frac{v^2}{c^2}}$](https://tex.z-dn.net/?f=%240.033%3D%20%201-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%24)
![$\frac{v^2}{c^2}= 0.967$](https://tex.z-dn.net/?f=%24%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%3D%200.967%24)
![$\frac{v}{c}=0.9833$](https://tex.z-dn.net/?f=%24%5Cfrac%7Bv%7D%7Bc%7D%3D0.9833%24)
![v=0.9833\ c](https://tex.z-dn.net/?f=v%3D0.9833%5C%20c)
Therefore, the speed of the observer relative to the cube is 0.9833 c (in the units of c).
60 days, tell me if I'm correct please.