AP Tests are coming up soon! Let’s do some physics review.

FLUIDS KEY CONCEPTS AND PRINCIPLES:

1. Density of a fluid is given as its mass over volume; D = m/v
2. Specific gravity of a substance is the density of a substance over the density of water; for example, the density of iron is 7800 kg per cubic meter, while the density of water is 1000 kg per cubic meter; thus, the specific gravity of iron is 7800/1000 = 7.8
3. Pressure is mathematically defined as a scalar quantity given by the force per unit area. Standard pressure is given as P₀ = 1 atm or 1.013 * 10⁵ Pascals
   • Pressure in fluids is dependent on the depth (which can be given by a liquid’s volume divided by the cross sectional area of the container). The gauge pressure is then given as the density of the fluid (rho) multiplied by g, multiplied by the depth (h); P_G = 𝜌gh
   • The absolute pressure is the standard pressure added to the gauge pressure in a fluid (P_G = 𝜌_fluidgh, or the gauge pressure in air subtracted from the standard pressure (P_G = 𝜌_airgh)
4. Pascal’s principle and the Hydraulic Lift:
   • For a hydraulic press in the form of an U-shaped tube with two branches and two different cross sectional areas, the ratio of the applied force to the area of one branch is the same as the ratio of the applied force to another area of the branch: F₁/A₁ = F₂/A₂
5. Archimedes’ Principle:
   • Applicable to static fluids (fluids that do not move)
   • If an object sinks, then it keeps sinking until it reaches the bottom
   • For all submerged objects in a fluid, there is a force exerted on it by the fluid (buoyant force)
     • The buoyant force always points UPWARD
     • The magnitude of the buoyant force is given as 𝜌_fluid*V_displaced*g, or the density of the fluid multiplied by the displaced volume multiplied by the gravity
     • When an object floats, the buoyant force is equal to the force of gravity
     • When an object sinks to the bottom (and touches the bottom) of a container, the force of gravity is greater than the sum of the normal force and the buoyant force
     • When an object is completely submerged in a fluid, but stands still (because it is being suspended by an applied force), then the sum of the applied force and the buoyant force is equivalent to the force of gravity
6. Bernoulli’s Principle:
   • Deals with dynamic (or moving) fluids
   • The conditions for Bernoulli’s Principle entail low or no viscosity and a constant density throughout the fluid
   • Based on the conservation of energy, it is given as: P₁ + 𝜌₁gh + $\frac{1}{2}*\rho_1*v_1^2$ = P₂ + 𝜌₂gh + $\frac{1}{2}*\rho_2*v_2^2$
   • v is the velocity of the fluid, rho is the density of the fluid, h is the elevation, and P is the pressure
   • Spigot Hole:
     • When a fluid is filled to a height of $h_o$ and it comes out of the spigot at height $h_{spigot}$, the velocity at which it comes out is given by $v = \sqrt{(2g(h_o – h_{spigot})}$. See if you can derive this from Bernoulli’s Principle!
7. Continuity Principle:
   • The flow rate in different sections of the pipe remains the same; $V_1=V_2 = v_1A_1 = v_2A_2$, where V is the volumetric flow rate, v is the velocity of the fluid, and A is the cross sectional area

That’s the fluids review for today! Come back soon for another unit, probably physics 2 :).

We’ve covered quantum information, and we’ve covered circuits, so it feels right to combine the two.

Quantum circuits (the topic of my science fair project!) are used to aid in quantum systems designed primarily for computational studies. In a quantum circuit, you will of course find qubits, but you may also encounter gates or measurement sites! A gate helps create entanglement, allowing for more information to be contained in a quantum system. However, entanglement saturates at a value dependent on the number of qubits in the system (around n/2 * ln(2) for a system with n qubits and no measurement).

Measurement acts as a kind of anti-gate – it reduces the entanglement in a system, because whenever we measure the state of a qubit, we collapse its superposition, reverting the qubit into a classical bit. At a measurement site, the probability that a measurement actually occurs can be given as p; as p increases, the total entanglement of the system decreases.

That is all I have to share today about quantum circuits! I forgot to attach the solution to the circuits problem to the last post, so here it is:

Original problem: “We have two resistors in series, with resistance 2 Ohms and 4 Ohms, respectively. These resistors are in parallel with another resistor of 6 Ohms. Calculate the current of the circuit if these resistors are in a closed loop circuit with a battery of voltage 9 V.”

Solution: First, we take the resistors in series and calculate the total resistance of that branch (2+4 = 6 ohms). Next, we take this resistance and calculate the total resistance in the circuit via calculations for parallel resistors; 1/(1/6 + 1/6) = 1/(1/3) = 3 ohms. Lastly, we apply Ohm’s law V = I*R to get I = V/R = 9/3 = 3 Amperes.

Let’s learn a little about circuits!

Electric circuits have many usages in our everyday life – our lights, fridges, phones, computers, cars, and so much more.

Let’s take a simple circuit with two resistors (both 4 Ohms) and a battery with voltage 8 V.

An important relation in circuits is the equation V = IR, where V is the potential difference (in this case, 8 V), R is resistance, in Ohms, and I is current, in Amperes.

To calculate resistance, we first must determine if the resistors are in series or parallel.

If the resistors are in series, then the total resistance is calculated by summing the resistance of each individual resistor. However, if they are in parallel, then we take the reciprocal of the resistance of each resistor and then sum them together. After summing them, we take the reciprocal of our sum to calculate the total resistance of the current.

Thus, if the two resistors are in series, the total resistance is 8 Ohms, and by V = IR, we calculate the current to be 1 Ampere.

If the two resistors are in parallel, then we have the total resistance to be 1/(1/4 + 1/4) = 2 Ohms, and by V = IR, the current is 4 Amperes.

Hooray! Now we have solved a simple circuit problem 🙂

If you want another problem, consider the following:
We have two resistors in series, with resistance 2 Ohms and 4 Ohms, respectively. These resistors are in parallel with another resistor of 6 Ohms. Calculate the current of the circuit if these resistors are in a closed loop circuit with a battery of voltage 9 V.

A solution will be attached to the next post!

• Data scientists have to analyze huge amounts of information!
• There are many means of collecting and transporting information.
• One such way is quantum information.
  • Quantum information is transmitted through bits of information called qubits.
    • Qubits can transmit vast quantities of data.
    • They are generally found in one of two states: 0 and 1.
    • Qubits can be entangled with other qubits; during entanglement, we can determine information about properties of one qubit based off the other qubit it is entangled with! This is because during entanglement, the two qubits influence each other’s states, and thus their properties correlate.
    • Whenever a qubit is measured, the quantumness of the system is destroyed; that is to say that the superposed state a qubit is in becomes a definite classical state (the aforementioned 0 or 1) with predetermined probability. This process is irreversible.

• The job of a data scientist, as one might expect, is to analyze vast quantities of data and determine trends.
  
• Data science is used everywhere in industries:
  • Used to predict the future of the stock market
  • Aids in predicting outbreaks of disease
  • Sports industries commonly use data science to draw trends and make conclusions about YOUR favorite sports teams
    
• What I like about data science:
  • Statistics. I enjoy solving statistics problems and can’t wait to take AP Stats!
  • Drawing conclusions. When given a set of data, I love finding patterns and making charts to display information!
  • Computer science involvement. I like coding a lot, and when analyzing large quantities of data, I have to create programs to help with analysis. It’s very interesting!

I like spending time with my friends.

I like Math and Physics.

I like the stars and solving problems.

I really like eating my Dad’s grilled lamb-chops 😛 😛

Hi, I am Adhrit and this is my blog :-).