Answer:
Mass = 2154 grams
Explanation:
Given the following data;
Acceleration = 520m/s²
Force = 11.2N
To find the mass;
Force = mass * acceleration
Mass = force/acceleration
Substituting into the equation, we have;
Mass = 11.2/520
Mass = 2.154 kg
Therefore, the value of mass in grams;
1000 grams = 1 kilograms
x grams = 2.154 kilograms
Cross-multiplying, we have;
2.154 * 1000 = 2154 grams.
Mass = 2154 grams.
Therefore, the mass of the model rocket is equal to 2154 grams.
Answer:
Dispersion
Explanation:
<u>Dispersion is the phenomenon of the splitting of the light into its constituent colors when it passes through the prism.</u> White light is composed of seven colors which are Violet, Indigo, Blue, Green, Yellow, Orange, Red, written in the form of increasing wavelength. When the light passes through the prism it splits into these seven colors.
<u>Explanation</u>:
Consider the given function ![K(t)=\frac{1}{2} m(t) \cdot v(t)^{2}](https://tex.z-dn.net/?f=K%28t%29%3D%5Cfrac%7B1%7D%7B2%7D%20m%28t%29%20%5Ccdot%20v%28t%29%5E%7B2%7D)
Given that the velocity of rocket is increases at the rate of ![15 m / \sec ^{2} \text { Hence } \frac{d v}{d t}=15](https://tex.z-dn.net/?f=15%20m%20%2F%20%5Csec%20%5E%7B2%7D%20%5Ctext%20%7B%20Hence%20%7D%20%5Cfrac%7Bd%20v%7D%7Bd%20t%7D%3D15)
The mass of rocket is decreasing at rate of
.
Hence ![\frac{d m(t)}{d t}=-10](https://tex.z-dn.net/?f=%5Cfrac%7Bd%20m%28t%29%7D%7Bd%20t%7D%3D-10)
Now find the rate of change of kinetic energy when
and ![v(t)=5000 m / \mathrm{sec}^{2}=5 \times 10^{3} \mathrm{m} / \mathrm{sec}^{2}](https://tex.z-dn.net/?f=v%28t%29%3D5000%20m%20%2F%20%5Cmathrm%7Bsec%7D%5E%7B2%7D%3D5%20%5Ctimes%2010%5E%7B3%7D%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bsec%7D%5E%7B2%7D)
Now consider the given equation,
![\begin{aligned}&K(t)=\frac{1}{2} m(t) \cdot v(t)^{2}\\&\frac{d K}{d t}=\frac{1}{2}\left[m(t) \times 2 v(t) \times \frac{d v(t)}{d t}+v(t)^{2} \frac{d m}{d t}\right]\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26K%28t%29%3D%5Cfrac%7B1%7D%7B2%7D%20m%28t%29%20%5Ccdot%20v%28t%29%5E%7B2%7D%5C%5C%26%5Cfrac%7Bd%20K%7D%7Bd%20t%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bm%28t%29%20%5Ctimes%202%20v%28t%29%20%5Ctimes%20%5Cfrac%7Bd%20v%28t%29%7D%7Bd%20t%7D%2Bv%28t%29%5E%7B2%7D%20%5Cfrac%7Bd%20m%7D%7Bd%20t%7D%5Cright%5D%5Cend%7Baligned%7D)
Now substituting the values
and ![v(t)=5000 m / \mathrm{sec}^{2}=5 \times 10^{3} \mathrm{m} / \mathrm{sec}^{2}](https://tex.z-dn.net/?f=v%28t%29%3D5000%20m%20%2F%20%5Cmathrm%7Bsec%7D%5E%7B2%7D%3D5%20%5Ctimes%2010%5E%7B3%7D%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bsec%7D%5E%7B2%7D)
![\begin{aligned}\frac{d K}{d t} &=\frac{1}{2}\left[2 \times 10^{3} \times 2 \times 5 \times 10^{3} \times 15+\left(5 \times 10^{3}\right)^{2}(-10)\right] \\&=\frac{1}{2}\left[300 \times 10^{6}+(-250) \times 10^{6}\right] \\&=\frac{1}{2}\left[(50) \times 10^{6}\right] \\&=25 M J\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cfrac%7Bd%20K%7D%7Bd%20t%7D%20%26%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B2%20%5Ctimes%2010%5E%7B3%7D%20%5Ctimes%202%20%5Ctimes%205%20%5Ctimes%2010%5E%7B3%7D%20%5Ctimes%2015%2B%5Cleft%285%20%5Ctimes%2010%5E%7B3%7D%5Cright%29%5E%7B2%7D%28-10%29%5Cright%5D%20%5C%5C%26%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B300%20%5Ctimes%2010%5E%7B6%7D%2B%28-250%29%20%5Ctimes%2010%5E%7B6%7D%5Cright%5D%20%5C%5C%26%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B%2850%29%20%5Ctimes%2010%5E%7B6%7D%5Cright%5D%20%5C%5C%26%3D25%20M%20J%5Cend%7Baligned%7D)
The rate at which kinetic energy changing is 25MJ
Answer:
Explanation:
Properties of Projectile Motion. Objects experiencing projectile motion have a constant velocity in the horizontal direction, and a constantly changing velocity in the vertical direction. The trajectory resulting from this combination always has the shape of a parabola.
Answer:
Fn = 246.2 N
Explanation:
I assume you meant meters per second squared for acceleration of the elevator. All you have to after your picture/free-body diagram is made is add the forces together. You could do this by finding them separately like I did or use Fn = m(Fg + Fe). I just calculated magnitude and didn't worry about signs.