Answer:
(a) 3.24 w (b) 44.44 ohm
Explanation:
It is given that car draws 0.27 A current so current I = 0.27 A
The system has a voltage of 12 V
(a) Electrical power = voltage ×current ![=12\times 0.27=3.24W](https://tex.z-dn.net/?f=%3D12%5Ctimes%200.27%3D3.24W)
(b) The resistance is defined as the ratio of voltage and current
So resistance ![R=\frac{V}{I}=\frac{12}{0.27}=44.44 ohm](https://tex.z-dn.net/?f=R%3D%5Cfrac%7BV%7D%7BI%7D%3D%5Cfrac%7B12%7D%7B0.27%7D%3D44.44%20ohm)
The answer is asthenosphere
Answer:
A
B
![h = 1.3061 \ m](https://tex.z-dn.net/?f=h%20%20%3D%20%201.3061%20%5C%20%20m%20%20)
C
![v = 5.06 \ m/s](https://tex.z-dn.net/?f=%20%20v%20%3D%20%205.06%20%5C%20%20m%2Fs%20)
D
![d = 4.0273 \ m](https://tex.z-dn.net/?f=d%20%3D%204.0273%20%5C%20%20m%20%20)
Explanation:
Considering the first question
From the question we are told that
The spring constant is ![k = 32.50 N/m](https://tex.z-dn.net/?f=k%20%20%3D%20%2032.50%20N%2Fm)
The potential energy is ![PE = 0.640 \ J](https://tex.z-dn.net/?f=PE%20%20%3D%20%200.640%20%5C%20J)
Generally the potential energy stored in spring is mathematically represented as ![PE = \frac{1}{2} * k * x^2](https://tex.z-dn.net/?f=PE%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%20k%20%20%2A%20%20x%5E2)
=>
=>
=>
Considering the second question
From the question we are told that
The mass of the dart is m = 0.050 kg
Generally from the law of energy conservation
![PE = mgh](https://tex.z-dn.net/?f=PE%20%3D%20%20mgh)
=> ![0.640 = 0.050 * 9.8 * h](https://tex.z-dn.net/?f=0.640%20%20%20%3D%20%200.050%20%2A%20%209.8%20%20%2A%20%20h)
=> ![h = 1.3061 \ m](https://tex.z-dn.net/?f=h%20%20%3D%20%201.3061%20%5C%20%20m%20%20)
Considering the third question
The height at which the dart was fired horizontally is ![H = 3.90\ m](https://tex.z-dn.net/?f=H%20%20%3D%20%20%203.90%5C%20%20m)
Generally from the law of energy conservation
![PE = KE](https://tex.z-dn.net/?f=PE%20%3D%20KE%20)
Here KE is kinetic energy of the dart which is mathematical represented as
![KE = \frac{1}{2} * mv^2](https://tex.z-dn.net/?f=KE%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%20mv%5E2)
=> ![0.640 = \frac{1}{2} * 0.050 * v^2](https://tex.z-dn.net/?f=0.640%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%200.050%20%2A%20%20v%5E2%20)
=> ![v^2 = 25.6](https://tex.z-dn.net/?f=%20%20v%5E2%20%3D%2025.6%20)
=> ![v = 5.06 \ m/s](https://tex.z-dn.net/?f=%20%20v%20%3D%20%205.06%20%5C%20%20m%2Fs%20)
Considering the fourth question
Generally the total time of flight of the dart is mathematically represented as
![t = \frac{ 2 * H }{g}](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%202%20%2A%20%20H%20%7D%7Bg%7D)
=> ![t = \frac{ 2 * 3.90 }{9.8 }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%202%20%2A%203.90%20%7D%7B9.8%20%7D)
=> ![t = 0.7959 \ s](https://tex.z-dn.net/?f=t%20%20%3D%20%200.7959%20%5C%20s%20)
Generally the horizontal distance from the equilibrium position to the ground is mathematically represented as
![d = v * t](https://tex.z-dn.net/?f=d%20%3D%20%20v%20%20%2A%20%20%20t)
=> ![d = 5.06 * 0.7959](https://tex.z-dn.net/?f=d%20%3D%205.06%20%20%2A%20%20%200.7959)
=> ![d = 4.0273 \ m](https://tex.z-dn.net/?f=d%20%3D%204.0273%20%5C%20%20m%20%20)
Answer:
4515.49484 N
4329.10484 N
Explanation:
r = Radius of balloon = 4.4 m
m = Mass of balloon with instruments = 19 kg
g = Acceleration due to gravity = 9.81 m/s²
Volume of balloon
![v=\frac{4}{3}\pi r^3\\\Rightarrow v=\frac{4}{3}\pi 4.4^3\\\Rightarrow v=356.8179\ m^3](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%5CRightarrow%20v%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%204.4%5E3%5C%5C%5CRightarrow%20v%3D356.8179%5C%20m%5E3)
The Buoyant force = Weight of the air displaced
![F=\rho vg\\\Rightarrow F=1.29\times 356.8179\times 9.81\\\Rightarrow F=4515.49484\ N](https://tex.z-dn.net/?f=F%3D%5Crho%20vg%5C%5C%5CRightarrow%20F%3D1.29%5Ctimes%20356.8179%5Ctimes%209.81%5C%5C%5CRightarrow%20F%3D4515.49484%5C%20N)
The buoyant force acting on the balloon is 4515.49484 N
Net force on the balloon
![F_n=F-W\\\Rightarrow F_n=4515.49484-19\times 9.81\\\Rightarrow F_n=4329.10484\ N](https://tex.z-dn.net/?f=F_n%3DF-W%5C%5C%5CRightarrow%20F_n%3D4515.49484-19%5Ctimes%209.81%5C%5C%5CRightarrow%20F_n%3D4329.10484%5C%20N)
The net force on the balloon is given by 4329.10484 N
As the balloon goes up the pressure outside reduces as the density of air decreases while the air pressure inside the balloon is high hence, the radius of the balloon tend to increase as it rises to higher altitude.
D. Neutrino
Neutrinos are particles that rarely interact with matter.