Answer:
false
Explanation:
discovered colours of the rainbow
Answer:
Failure rate = 20%
MTBF = 880 hours
Explanation:
given data
batteries = 10
tested = 200 hours
one failed = 20 hours
another fail at = 140 hours
solution
we know that Mean Time between Failures is express as = (Total up time) ÷ (number of breakdowns) ....................1
so here Total up time will be
Total up time = 200 × 10
Total up time = 2000
and here
Number of breakdown = 1 at 20 hour and another at 140 hour = 2
so it will be = (Total up time) ÷ (number of breakdowns) .......2
=
= 1000
so here gap between occurrences is
gap between occurrences= 140 - 20
gap between occurrences = 120 hour
and
MTBF will be
MTBF = 1000 - 120
MTBF = 880 hours
and
Failure rate (FR) will be
Failure rate (FR) = 1 ÷ MTBF ................3
Failure rate (FR) = R÷T ......................4
as here R is the number of failures and T is total time
so Failure rate (FR) = 20%
Answer:
8.829 m/s²
Explanation:
M = Mass of Earth
m = Mass of Exoplanet
= Acceleration due to gravity on Earth = 9.81 m/s²
g = Acceleration due to gravity on Exoplanet
![m=M-0.1M\\\Rightarrow m=0.9M](https://tex.z-dn.net/?f=m%3DM-0.1M%5C%5C%5CRightarrow%20m%3D0.9M)
![g_e=G\frac{M}{r^2}](https://tex.z-dn.net/?f=g_e%3DG%5Cfrac%7BM%7D%7Br%5E2%7D)
![g=G\frac{0.9M}{r^2}](https://tex.z-dn.net/?f=g%3DG%5Cfrac%7B0.9M%7D%7Br%5E2%7D)
Dividing the equations we get
![\frac{g}{g_e}=\frac{G\frac{0.9M}{r^2}}{G\frac{M}{r^2}}\\\Rightarrow \frac{g}{g_e}=0.9\\\Rightarrow g=0.9g_e\\\Rightarrow g=0.9\times 9.81\\\Rightarrow g=8.829\ m/s^2](https://tex.z-dn.net/?f=%5Cfrac%7Bg%7D%7Bg_e%7D%3D%5Cfrac%7BG%5Cfrac%7B0.9M%7D%7Br%5E2%7D%7D%7BG%5Cfrac%7BM%7D%7Br%5E2%7D%7D%5C%5C%5CRightarrow%20%5Cfrac%7Bg%7D%7Bg_e%7D%3D0.9%5C%5C%5CRightarrow%20g%3D0.9g_e%5C%5C%5CRightarrow%20g%3D0.9%5Ctimes%209.81%5C%5C%5CRightarrow%20g%3D8.829%5C%20m%2Fs%5E2)
Acceleration due to gravity on the surface of the Exoplanet is 8.829 m/s²
Answer:
The spring constant = 104.82 N/m
The angular velocity of the bar when θ = 32° is 1.70 rad/s
Explanation:
From the diagram attached below; we use the conservation of energy to determine the spring constant by using to formula:
![T_1+V_1=T_2+V_2](https://tex.z-dn.net/?f=T_1%2BV_1%3DT_2%2BV_2)
![0+0 = \frac{1}{2} k \delta^2 - \frac{mg (a+b) sin \ \theta }{2} \\ \\ k \delta^2 = mg (a+b) sin \ \theta \\ \\ k = \frac{mg(a+b) sin \ \theta }{\delta^2}](https://tex.z-dn.net/?f=0%2B0%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20k%20%5Cdelta%5E2%20-%20%5Cfrac%7Bmg%20%28a%2Bb%29%20sin%20%5C%20%5Ctheta%20%7D%7B2%7D%20%20%5C%5C%20%5C%5C%20k%20%5Cdelta%5E2%20%3D%20mg%20%28a%2Bb%29%20sin%20%5C%20%5Ctheta%20%5C%5C%20%5C%5C%20k%20%3D%20%5Cfrac%7Bmg%28a%2Bb%29%20sin%20%5C%20%5Ctheta%20%7D%7B%5Cdelta%5E2%7D)
Also;
![\delta = \sqrt{h^2 +a^2 +2ah sin \ \theta} - \sqrt{h^2 +a^2}](https://tex.z-dn.net/?f=%5Cdelta%20%3D%20%5Csqrt%7Bh%5E2%20%2Ba%5E2%20%2B2ah%20sin%20%5C%20%5Ctheta%7D%20-%20%5Csqrt%7Bh%5E2%20%2Ba%5E2%7D)
Thus;
![k = \frac{mg(a+b) sin \ \theta }{( \sqrt{h^2 +a^2 +2ah sin \ \theta} - \sqrt{h^2 +a^2})^2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7Bmg%28a%2Bb%29%20sin%20%5C%20%5Ctheta%20%7D%7B%28%20%5Csqrt%7Bh%5E2%20%2Ba%5E2%20%2B2ah%20sin%20%5C%20%5Ctheta%7D%20-%20%5Csqrt%7Bh%5E2%20%2Ba%5E2%7D%29%5E2%7D)
where;
= deflection in the spring
k = spring constant
b = remaining length in the rod
m = mass of the slender bar
g = acceleration due to gravity
![k = \frac{(1.53*9.8)(0.6+0.2) sin \ 64 }{( \sqrt{0.6^2 +0.6^2 +2*0.6*0.6 sin \ 64} - \sqrt{0.6^2 +0.6^2})^2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B%281.53%2A9.8%29%280.6%2B0.2%29%20sin%20%5C%2064%20%7D%7B%28%20%5Csqrt%7B0.6%5E2%20%2B0.6%5E2%20%2B2%2A0.6%2A0.6%20sin%20%5C%2064%7D%20-%20%5Csqrt%7B0.6%5E2%20%2B0.6%5E2%7D%29%5E2%7D)
![k = 104.82\ \ N/m](https://tex.z-dn.net/?f=k%20%3D%20104.82%5C%20%5C%20%20N%2Fm)
Thus; the spring constant = 104.82 N/m
b
The angular velocity can be calculated by also using the conservation of energy;
![T_1+V_1 = T_3 +V_3 \\ \\ 0+0 = \frac{1}{2}I_o \omega_3^2+\frac{1}{2}k \delta^2 - \frac{mg(a+b)sin \theta }{2} \\ \\ \frac{1}{2} \frac{m(a+b)^2}{3} \omega_3^2 + \frac{1}{2} k \delta^2 - \frac{mg(a+b)sin \ \theta }{2} =0](https://tex.z-dn.net/?f=T_1%2BV_1%20%3D%20T_3%20%2BV_3%20%20%5C%5C%20%5C%5C%200%2B0%20%3D%20%5Cfrac%7B1%7D%7B2%7DI_o%20%5Comega_3%5E2%2B%5Cfrac%7B1%7D%7B2%7Dk%20%5Cdelta%5E2%20-%20%5Cfrac%7Bmg%28a%2Bb%29sin%20%5Ctheta%20%7D%7B2%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7Bm%28a%2Bb%29%5E2%7D%7B3%7D%20%20%5Comega_3%5E2%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20k%20%5Cdelta%5E2%20-%20%5Cfrac%7Bmg%28a%2Bb%29sin%20%5C%20%5Ctheta%20%7D%7B2%7D%20%3D0)
![\frac{m(a+b)^2}{3} \omega_3^2 + k(\sqrt{h^2+a^2+2ah sin \theta } - \sqrt{h^2+a^2})^2 - mg(a+b)sin \theta = 0](https://tex.z-dn.net/?f=%5Cfrac%7Bm%28a%2Bb%29%5E2%7D%7B3%7D%20%5Comega_3%5E2%20%20%2B%20k%28%5Csqrt%7Bh%5E2%2Ba%5E2%2B2ah%20sin%20%5Ctheta%20%7D%20-%20%5Csqrt%7Bh%5E2%2Ba%5E2%7D%29%5E2%20-%20mg%28a%2Bb%29sin%20%5Ctheta%20%3D%200)
![\frac{1.53(0.6+0.6)^2}{3} \omega_3^2 + 104.82(\sqrt{0.6^2+0.6^2+2(0.6*0.6) sin 32 } - \sqrt{0.6^2+0.6^2})^2 - (1.53*9.81)(0.6+0.2)sin \ 32 = 0](https://tex.z-dn.net/?f=%5Cfrac%7B1.53%280.6%2B0.6%29%5E2%7D%7B3%7D%20%5Comega_3%5E2%20%20%2B%20104.82%28%5Csqrt%7B0.6%5E2%2B0.6%5E2%2B2%280.6%2A0.6%29%20sin%2032%20%7D%20-%20%5Csqrt%7B0.6%5E2%2B0.6%5E2%7D%29%5E2%20-%20%281.53%2A9.81%29%280.6%2B0.2%29sin%20%5C%2032%20%3D%200)
![0.7344 \omega_3^2 = 2.128](https://tex.z-dn.net/?f=0.7344%20%5Comega_3%5E2%20%3D%202.128)
![\omega _3 = \sqrt{\frac{2.128}{0.7344} }](https://tex.z-dn.net/?f=%5Comega%20_3%20%3D%20%5Csqrt%7B%5Cfrac%7B2.128%7D%7B0.7344%7D%20%7D)
![\omega _3 =1.70 \ rad/s](https://tex.z-dn.net/?f=%5Comega%20_3%20%3D1.70%20%5C%20rad%2Fs)
Thus, the angular velocity of the bar when θ = 32° is 1.70 rad/s
Solution:
Let the slope of the best fit line be represented by '
'
and the slope of the worst fit line be represented by '
'
Given that:
= 1.35 m/s
= 1.29 m/s
Then the uncertainity in the slope of the line is given by the formula:
(1)
Substituting values in eqn (1), we get
= 0.03 m/s