![\textbf{2500 }\dfrac{\textbf{kg}}{\textbf{s}^{\textbf{2}}}](https://tex.z-dn.net/?f=%5Ctextbf%7B2500%20%7D%5Cdfrac%7B%5Ctextbf%7Bkg%7D%7D%7B%5Ctextbf%7Bs%7D%5E%7B%5Ctextbf%7B2%7D%7D%7D)
Explanation:
Natural length of a spring is
. The spring is streched by
. The resultant energy of the spring is
.
The potential energy of an ideal spring with spring constant
and elongation
is given by
.
So, in the current problem, the natural length of the spring is not required to find the spring constant
.
![\text{Potential Energy in the spring = }\dfrac{1}{2}kx^{2}\\0.5\text{ }J\text{ }=\text{ }\dfrac{1}{2}k(0.02\text{ }m)^{2}\\k\times0.0004\text{ }m^{2}\text{ }=\text{ }1\text{ }J\text{ }=\text{ }1\text{ }kg\frac{m^{2}}{s^{2}}\\k\text{ }=\text{ }\dfrac{1\text{ }kg\dfrac{m^{2}}{s^{2}}}{0.0004\text{ }m^{2}}\text{ }=\text{ }2500\text{ }\frac{kg}{s^{2}}](https://tex.z-dn.net/?f=%5Ctext%7BPotential%20Energy%20in%20the%20spring%20%3D%20%7D%5Cdfrac%7B1%7D%7B2%7Dkx%5E%7B2%7D%5C%5C0.5%5Ctext%7B%20%7DJ%5Ctext%7B%20%7D%3D%5Ctext%7B%20%7D%5Cdfrac%7B1%7D%7B2%7Dk%280.02%5Ctext%7B%20%7Dm%29%5E%7B2%7D%5C%5Ck%5Ctimes0.0004%5Ctext%7B%20%7Dm%5E%7B2%7D%5Ctext%7B%20%7D%3D%5Ctext%7B%20%7D1%5Ctext%7B%20%7DJ%5Ctext%7B%20%7D%3D%5Ctext%7B%20%7D1%5Ctext%7B%20%7Dkg%5Cfrac%7Bm%5E%7B2%7D%7D%7Bs%5E%7B2%7D%7D%5C%5Ck%5Ctext%7B%20%7D%3D%5Ctext%7B%20%7D%5Cdfrac%7B1%5Ctext%7B%20%7Dkg%5Cdfrac%7Bm%5E%7B2%7D%7D%7Bs%5E%7B2%7D%7D%7D%7B0.0004%5Ctext%7B%20%7Dm%5E%7B2%7D%7D%5Ctext%7B%20%7D%3D%5Ctext%7B%20%7D2500%5Ctext%7B%20%7D%5Cfrac%7Bkg%7D%7Bs%5E%7B2%7D%7D)
∴ The spring constant of the spring = ![2500\text{ }\frac{kg}{s^{2}}](https://tex.z-dn.net/?f=2500%5Ctext%7B%20%7D%5Cfrac%7Bkg%7D%7Bs%5E%7B2%7D%7D)
It means the speed is constant with a value of 4 units.
Answer:
<u>20 Minutes</u>
<u></u>
Explanation:
Well we know Mph (Miles per hour) is distance over time : ![\frac{distance}{time} \\](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%7D%7Btime%7D%20%5C%5C)
R (rate) = 60
d (distance) = 20
t (time) = Unknown
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
R =
↓
60 =
↓
t = ![\frac{20}{60}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B60%7D%20)
↓
t =
or 0.3333
<em>So basically it would take one third of an hour. Lets change these units to minutes.</em>
60 * 0.333333 = 20
<em>So it would take you </em><u><em>20 minutes</em></u><em> to drive 20 miles on a bus that drives 60 mph</em>
<em />
Hope that helps
<em>~Siascon~</em>
Answer:
Velocidad en m / s = 72,25 m / s
Explanation:
Dado
Distancia a recorrer por el coche de carreras = 87 Km
1 km = 1000 m
Por lo tanto, 87 km = 87000 m
Tiempo necesario para viajar 87 km / 87000 metros = 20 minutos o 20 * 60 = 1200 segundos
Velocidad en m / s = 87000/1200
Velocidad en m / s = 72,25 m / s
<span>step 1: energy required to heat coffee
E = m Cp dT
E = energy to heat coffee
m = mass coffee = 225 mL x (0.997 g / mL) = 224g
Cp = heat capacity of coffee = 4.184 J / gK
dT = change in temp of coffee = 62.0 - 25.0 C = 37.0 C
E = (224 g) x (4.184 J / gK) x (37.0 C) = 3.46x10^4 J
step2: find energy of a single photon of the radiation
E = hc / λ
E = energy of the photon
h = planck's constant = 6.626x10^-34 J s
c = speed of light = 3.00x10^8 m/s
λ = wavelength = 11.2 cm = 11.2 cm x (1m / 100 cm) = 0.112 m
E = (6.626x10^-34 J s) x (3.00x10^8 m/s) / (0.112 m) = 1.77x10^-16 J
step3: Number of photons
3.46x10^4 J x ( 1 photon / 1.77x10^-16 J) = 1.95x10^20 photons</span>