Electric Force - Uses the symbol “q” and the unit for charge is coulomb, “C” - Coulomb’s Law: two charged objects attract each other with a force that is proportional to the charge on the objects and inversely proportional to the square of the distance between them - Fis proportional ¿ q 1 q 2 d 2 - This answer comes out in Newtons - Magnitude of Coulomb’s Law: - Electric force = (electrostatic constant*charge #1*charge #2)/(distance squared) - F = kq 1 q 2 d 2 - This answer comes out in Coulombs - Electrostatic constant: 9.0 * 10^9 N*m^2/C^2 Electric Fields - Area of influence around a charged object - E = F q o - Unit is newtons per coulomb (N/C) - Represented as vectors - For point charges (spherical charge distribution), magnitude is written as: - E = kq d 2 - Static occurs when two non conductors rub against each other - Dynamic occurs when the electricity is flows through a conductor - Credits to Faraday for coming up with static and dynamic electricity A particle carrying a charge of 4.0 × 10 − 9 C experiences an electric field of 1.2 × 10 6 N/C. What is the electric force acting on the particle? E = F q o E = 4.8 × 10 − 3 N An electron beam in a TV tube is steered across the screen by the field between two charged plates. If the electron experiences a force of 3.0 × 10 − 6 N, how large is the field between the deflection plates? Charge of an Electron: − 1.6 × 10 − 19 C E = F q o

E = 1.9 × 10 13 N / C A sphere acquires a charge of − 8.0 × 10 − 9 C . What is the magnitude and direction of the electric field at a point 0.40 m from the center of the charged sphere? E = kq d 2 E = 450 N / C (forwards) Two spheres are hung side by side so that their centers are 0.40 m apart. The left sphere acquires a charge of 6.0 × 10 − 6 C and the right sphere acquires a charge of 4.0 × 10 − 6 C . What is the electric field at a point 0.15 m to the right of the sphere on the left? E = kq d 2 E L = 2,400,000 N / C E R = 576,000 N / C E f = E L − E R E f = 18 × 10 5 to the right How many electrons would there be in a Leyden Jar which holds 3 Coulombs of Charge? 6.24*10^18 electrons in one Coulomb 1.87 * 10^19 electrons If a proton is placed in an electric field with a magnitude of 200 N/C, what is the resulting electric force? E = F q o F = 3.2 × 10 − 17 N Voltage/Electrical Potential Difference - Electrical Potential Difference - The work done to move a positive test charge from one location to the other - The unit for potential difference is volt (V) which equals a joule per Coulomb (J/C) - V = W q o - The field that exists between two charged parallel plates is uniform except near the plate edges, and depends on the potential difference between the plates and the plate separation.

Pressure - The amount of force per unit of area - P = F A - Hydrostatic Pressure - The pressure exerted on an object by a column of fluid - The farther an object is located below the surface of the fluid, the greater the pressure acting on it - P h = P a + Dgh - Hydrostatic pressure = atmospheric pressure + (density*acceleration due to gravity*height) - Normal atmospheric pressure = 1.01 *10^5 Pa - The unit is a Pascal (Pa) which is equal to a newton per square meter (N/m^2) - Pascal’s Principle - The change in pressure on one part of the confined fluid is equal to the change in pressure on any other part of the confined fluid - Δ P = F 1 A 1 = F 2 A 2 - Can the calculation for pressure be simplified to P=Dgh What is the difference in pressure between a place and two meters above it for a liquid that has a density of 1.05 * 10^3 kg/m^3? Δ P = ρg Δ h 20580 Pascals How much pressure is needed to move water 410 meters above the ground? P h = P a + ρgh 4.2 ∗ 10 6 Pascals What the longest you could draw up milk whose density is 1030 kg/m^3, considering the difference in pressure between the atmosphere and human lungs is 1.05 *10^5 Pa? h = Δ P ρg 10.4 meters Someone changes the pressure from atmosphere to 9.98 * 10^4 Pascals and raises a liquid 0.09 meters. What is the density of the liquid?

Δ P gh = 1.01 ∗ 10 5 Pa − 9.98 ∗ 10 4 Pa 9.8 m s 2 ∗ 0.09 m 1330 kg/m^3 a)Does a 1.7 kg book lying flat or a 1.7 kg book standing on end exert a greater force? b) Which applies a greater pressure? c) If each book measures 0.26 m * 0.210 m * 0.04 m, calculate the pressure in each of those two scenarios. a)they exert the same amount of force b)the one standing on end exerts a greater pressure c) P = F A F = 17 N A1 = 0.054 m^2 A2 = 0.0084 m^2 P1 = 314.8 Pa P2 = 2023.8 Pa Calculate the amount of pressure of two objects on the ground where both have a mass of 60 kg, but one has an area of 0.4 cm^2 and the other has an area of 6 cm^2. P= F A F = 600 N P1 = 1500 N/cm^2 P2 = 100 N/cm^2 How much area does something weighing 85 kilograms and applying a pressure of 9530 N/m^2 on a surface have? A = F P 0.09 m^2 A circle applies 630 N/m^2 of force and weighs 0.5 kg. a) what is its area? b) what is the radius of the circle? a)A= F P F=5N P=630N/m^2 A=0.0079m^2 b) r = √ ❑

Denser on the bottom: Oil Water Glycerin Buoyancy - Archimedes’ Principle - An object completely or partially immersed in a fluid is pushed up by a force that is equal to the weight of the displaced fluid - F b = DgV - If the object is partially submerged, the volume used in the calculation is that of the submerged portion - In a floating object, buoyant force = weight of object/force of gravity A 5450 m^3 blimp is suspended in the 1.21 kg/m^3 atmosphere. The density of the helium in the balloon is 0.178 kg/m^3. a) What is the buoyant force that suspends the blimp in the air? b) How does the buoyant force compare to the blimp’s weight? a) F b = Dgv F b = 65,945 N b) Equal because the net force is 0 A bar of soap that measures 9.00 cm by 6.00 cm by 3.00 cm and has a density of 994 kg / m 3 is suspended below the surface of the water. What is the buoyant force acting on the soap? F b = Dgv 1.61 N If a person is floating on top of water and they have a density of 980 kg / m 3 and a volume of 0.060 m 3 , what is the buoyant force that supports them in sea with a density of 1025 kg / m 3 ? What buoyant force is exerted on a 0.9000 m 3 inner tube as it pushed so it completely submerged under water? When let go, it pops to the surface with a force of 8990 N. What is its weight? F b = Dgv F b = 9000 N Weight = 10 N Mixing Experiment Final Temperature of a Mixture of Uneven Amounts of Liquids of Different Temperatures: T f = m 1 T 1 + m 2 T 2 ( m 1 + m 2 )

Horn’s Lecture Notes