Answer:
Quick question do you mean what are some safety rules
Explanation:
Crosswalk, Stop sign,
BaCI2 stands for Barium Chloride.
To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.
![I = MR^2](https://tex.z-dn.net/?f=I%20%3D%20MR%5E2)
Here,
M = Mass
R = Radius of the hoop
The precession frequency is given as
![\Omega = \frac{Mgd}{I\omega}](https://tex.z-dn.net/?f=%5COmega%20%3D%20%5Cfrac%7BMgd%7D%7BI%5Comega%7D)
Here,
M = Mass
g= Acceleration due to gravity
d = Distance of center of mass from pivot
I = Moment of inertia
= Angular velocity
Replacing the value for moment of inertia
![\Omega= \frac{MgR}{MR^2 \omega}](https://tex.z-dn.net/?f=%5COmega%3D%20%5Cfrac%7BMgR%7D%7BMR%5E2%20%5Comega%7D)
![\Omega = \frac{g}{R\omega}](https://tex.z-dn.net/?f=%5COmega%20%3D%20%5Cfrac%7Bg%7D%7BR%5Comega%7D)
The value for our angular velocity is not in SI, then
![\omega = 1000rpm (\frac{2\pi rad}{1 rev})(\frac{1min}{60s})](https://tex.z-dn.net/?f=%5Comega%20%3D%201000rpm%20%28%5Cfrac%7B2%5Cpi%20rad%7D%7B1%20rev%7D%29%28%5Cfrac%7B1min%7D%7B60s%7D%29)
![\omega = 104.7rad/s](https://tex.z-dn.net/?f=%5Comega%20%3D%20104.7rad%2Fs)
Replacing our values we have that
![\Omega = \frac{9.8m/s^2}{(8*10^{-2}m)(104.7rad)}](https://tex.z-dn.net/?f=%5COmega%20%3D%20%5Cfrac%7B9.8m%2Fs%5E2%7D%7B%288%2A10%5E%7B-2%7Dm%29%28104.7rad%29%7D)
![\Omega = 1.17rad/s](https://tex.z-dn.net/?f=%5COmega%20%3D%201.17rad%2Fs)
The precession frequency is
![\Omega = \frac{2\pi rad}{T}](https://tex.z-dn.net/?f=%5COmega%20%3D%20%5Cfrac%7B2%5Cpi%20rad%7D%7BT%7D)
![T = \frac{2\pi rad}{\Omega}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%20rad%7D%7B%5COmega%7D)
![T = \frac{2\pi}{1.17}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B1.17%7D)
![T = 5.4 s](https://tex.z-dn.net/?f=T%20%3D%205.4%20s)
Therefore the precession period is 5.4s
Answer:
T = 0.017s
Explanation:
period is the time it takes a particle to make one oscillation
An electric current is periodic in nature
The current reaches 3.8A ten times.
So there must have been 10 cycles (10 periods) in 0.17s. let 'T' be the period:
![T=\frac{t}{n}](https://tex.z-dn.net/?f=T%3D%5Cfrac%7Bt%7D%7Bn%7D)
t is the total time interval
n is the number of oscillations
![T=\frac{0.17}{10}](https://tex.z-dn.net/?f=T%3D%5Cfrac%7B0.17%7D%7B10%7D)
10T = 0.17
T = 0.17/10 = 0.017s
(a) Let's convert the final speed of the car in m/s:
![v_f = 61 km/h = 16.9 m/s](https://tex.z-dn.net/?f=v_f%20%3D%2061%20km%2Fh%20%3D%2016.9%20m%2Fs)
The kinetic energy of the car at t=19 s is
![K= \frac{1}{2}mv_f^2= \frac{1}{2}(1400 kg)(16.9 m/s)^2=2.00 \cdot 10^5 J](https://tex.z-dn.net/?f=K%3D%20%5Cfrac%7B1%7D%7B2%7Dmv_f%5E2%3D%20%5Cfrac%7B1%7D%7B2%7D%281400%20kg%29%2816.9%20m%2Fs%29%5E2%3D2.00%20%5Ccdot%2010%5E5%20J%20%20)
(b) The average power delivered by the engine of the car during the 19 s is equal to the work done by the engine divided by the time interval:
![P= \frac{W}{\Delta t}](https://tex.z-dn.net/?f=P%3D%20%5Cfrac%7BW%7D%7B%5CDelta%20t%7D%20)
But the work done is equal to the increase in kinetic energy of the car, and since its initial kinetic energy is zero (because the car starts from rest), this translates into
![P= \frac{K}{\Delta t}= \frac{2.00 \cdot 10^5 J}{19 s}=1.05 \cdot 10^4 W](https://tex.z-dn.net/?f=P%3D%20%5Cfrac%7BK%7D%7B%5CDelta%20t%7D%3D%20%5Cfrac%7B2.00%20%5Ccdot%2010%5E5%20J%7D%7B19%20s%7D%3D1.05%20%5Ccdot%2010%5E4%20W%20%20)
(c) The instantaneous power is given by
![P_i = Fv_f](https://tex.z-dn.net/?f=P_i%20%3D%20Fv_f)
where F is the force exerted by the engine, equal to F=ma.
So we need to find the acceleration first:
![a= \frac{v_f-v_i}{\Delta t}= \frac{16.9 m/s}{19 s}=0.89 m/s^2](https://tex.z-dn.net/?f=a%3D%20%5Cfrac%7Bv_f-v_i%7D%7B%5CDelta%20t%7D%3D%20%20%5Cfrac%7B16.9%20m%2Fs%7D%7B19%20s%7D%3D0.89%20m%2Fs%5E2%20)
And the problem says this acceleration is constant during the motion, so now we can calculate the instantaneous power at t=19 s: