Understanding Buoyancy

Buoyancy

• Buoyancy arises from an object's ability to float in a fluid, whether gas or liquid.
• A buoyant force is an upward force that acts on an object that is partially or fully submerged and it opposes the gravitational force.
• Fluid displacement and loss of mass methods to determine buoyant force

Fluid Displacement Method

• An object is fully submerged in a fluid, displacing some of the fluid.
• The volume of fluid displaced equals the volume of the submerged object: Vdisplaced = Vblock.
• Determine buoyant force experienced by the block: B₁ = ρmedium ⋅ g ⋅ Vdisplaced, where ρmedium is the fluid density and 'g' is the 9.80 m/s² gravitational acceleration.

Loss of Mass Method

• Weigh an object in the air, then weigh it while fully submerged in a fluid to determine loss of mass due to buoyant force
• An object submerged in fluid weighs less than in air due to buoyant force.
• Calculate buoyant force via loss of mass method B₂ = W₁ − W₂, where W₁ is the object's weight in air and W₂ is its weight in fluid.

Percent Difference

• To ascertain the percent difference between buoyant forces found via fluid displacement (B₁) and loss of mass (B₂), the following formula is employed: % difference = |B₂ - B₁| / [½(B₂ + B₁)] x 100.

Coefficient of Linear Expansion

• Measuring the thermal expansion of metal alloys will assist with the determination of linear expansion coefficients
• Materials expand or contract with temperature change and linear thermal expansion is defined as ∆L.
• The linear expansion is directly proportional to the object's length.
• Coefficient of proportionality alpha is related to the expansion of the material.
• Metals have a typical coefficient of linear expansion α ≈ 10⁻⁵/°C.

Equation for determining Coefficient of Linear Expansion

• Use the equation below to determine coefficient of linear expansion: α = ∆L / (Lo ∆T)
• α represents the coefficient of linear expansion (units of /°C).
• '∆L' signifies the change in length.
• Lo is the original length.
• '∆T' refers to the change in temperature, calculated as Tf − Ti, with Tf being the final temperature and Ti the initial.

Percent Error

• To find the theoretical coefficient of linear expansion with the experimental: % error = |αtheo − αexp| / αtheo x 100.
• The theoretical coefficient of linear expansion for steel (αsteel) 1.2x10⁻⁵/C°.
• The theoretical coefficient of linear expansion for brass (αbrass) 2.0x10⁻⁵/C°.

Van de Graaff Generator

• A Van de Graaff generator is a hollow metal sphere, that generates static electricity using a moving belt to accumulate charges on the surface.
• It creates a very high electric potential resulting in a large electric field.
• The Van de Graaff generator was invented by American physicist Robet J. Van de Graaff.

Simple Circuits

• Simple circuits can be built and correpsonding circuit diagrams can be drawn
• Different materials and electrical components can be tested for their conductivity

Concepts

• Current: The rate at which electric charge moves, or the movement of electrons, through an amount of area over time.
• Conductors: Materials that allow electrons to flow through easily.
• Insulators: Materials that do not permit the easy flow of electrons.
• Resistance: Anything impeding the flow of electrons is defined as resistance.
• Potential Difference: Potential difference measures electrical potential energy change per charge unit between two positions.
• Chemical potential energy converts to electrical energy in a battery.
• Electrical potential energy transforms into thermal, light, or mechanical as electricity travels through different materials.
• Electrical Circuit: A set of connected electrical components provide paths for charge movement.
• Schematic Diagrams: Graphical circuit representations

Schematic Symbols for Components in a Circuit

• Standard schematic symbols represent components: wire, bulb/lamp, battery, resistor, open switch, and closed switch

Capacitors

• The time constant in an RC circuit is defined as the time it takes to charge a capacitor to approximately 63% of the maximum voltage; calculated via 𝜏 = RC
  • '𝜏' represents the time constant in seconds (s).
  • R stands for resistance, measured in ohms (Ω).
  • C represents capacitance, measured in farads (F).
• A capacitor requires approximately five time constants (5τ) to reach a full charge or steady state.

Charging and Discharging Capacitors

• Electrons flow onto one plate to charge a capacitor.
• Electrons flow off the other plate until the potential difference equals the battery's voltage.
• Net voltage to charge the capacitor equals the difference between capacitor voltage Vc and source V.
• The capacitor's EMF rises, which consequently slows charging rate.
• The charging current is significantly reduced when Vc approximates V.
• Formula for Voltage across a capacitor during charging: Vc = V(1-e^(-t/τ)). -'𝑉c' represents the voltage across the capacitor.
  • 'V' the supplied voltage.
  • 'τ' the time constant.
  • 't' time.
• When a charged capacitor disconnects from voltage source 'V' and switch turns on it discharges.
• Plates voltage drops gradually until Vc = 0.
• Formula for Voltage across a capacitor during discharge: Vc = Vi * e^(-t/τ)
  • 'Vc' stands for voltage across the capacitor throughout discharging (V).
  • 'Vi' signifies initial voltage across that capacitor (V).
  • 't' means any given moment (s).
  • 'τ' represents what is known time constant (s).

Ohm's Law

• Ohm's Law relates voltage across with the current through a resistor: V = IR.
• 'V' is voltage (in volts).
• 'I' is current (in amperes).
• 'R' is resistance (in ohms).
• Resistors in appliances turn electrical to thermal energy.
• Ohm's Law: potential difference across a resistors is proportional to the current.

Percent Error for Resistance

• The percent error to compare experimental resistance: % error = |Rtheo - Rexp| / Rtheo * 100.
• The theoretical resistance Rtheo = 47Ω

Resistance of a Wire

• Electrical resistance indicates how strongly a material opposes electrons flow.
• The electrical resistance of a material depends on the resistivity coefficient, length, and cross sectional area of component.
• The resistivity coefficient is basically dependent on the material, with some materials able to conduct material more easily than others.
• Electrons in metals are not fixed to one atom but instead shared around all the pieces of metal making it low resistance to current