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urp:physgen
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urp:physgen [2021-10-18] nerf_herder |
urp:physgen [2021-11-05] nerf_herder |
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| * [[#Miscellaneous]] | * [[#Miscellaneous]] | ||
| - | ===Newton's 3 laws=== | + | ====Newton's 3 laws==== |
| 1) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia") | 1) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia") | ||
| 2) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration) | 2) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration) | ||
| Line 24: | Line 24: | ||
| * J = F*d = applying 1 newton for 1 meter (units of kg * m²/s²) | * J = F*d = applying 1 newton for 1 meter (units of kg * m²/s²) | ||
| * F = J/d | * F = J/d | ||
| + | * power = work/time (joules/sec or watts) | ||
| Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration) | Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration) | ||
| Line 34: | Line 35: | ||
| - | **dimensional homogeneity** - units must be correct, parts added together, left side matches right side, etc. | + | **dimensional homogeneity** - units must be correct for parts added together, left side matches right side, etc. |
| - | ===Distance, time, velocity, acceleration=== | + | ====Distance, time, velocity, acceleration==== |
| Displacement is change in position. | Displacement is change in position. | ||
| s(t) = s0 + t*(v0+vt)/2 | s(t) = s0 + t*(v0+vt)/2 | ||
| Line 48: | Line 49: | ||
| - | ===Collisions=== | + | ====Collisions==== |
| * **elastic**: Two objects bounce off each other. Kinetic energy, momentum conserved, no other energy created | * **elastic**: Two objects bounce off each other. Kinetic energy, momentum conserved, no other energy created | ||
| * **inelastic** Two objects stick to each other. Momentum conserved, kinetic energy is not conserved (some energy converted to heat, sound, etc.) | * **inelastic** Two objects stick to each other. Momentum conserved, kinetic energy is not conserved (some energy converted to heat, sound, etc.) | ||
| - | conservation of momentum: p1i + p2i = p1f + p2f | + | **coefficient of restitution** = ratio of energy conserved after collision |
| + | e = (vel. after collision) / (vel. before collision) | ||
| + | (for collision with immovable object) | ||
| + | e = (Vfa * Vfb) / (Via * Vib) | ||
| + | (for collision between objects a and b. f = final, i = initial velocity) | ||
| + | e = 1 for perfectly elastic, 0 for perfectly inelastic | ||
| + | |||
| + | **conservation of momentum**: p1i + p2i = p1f + p2f | ||
| for m1 having velocity u1 to the right, m2 initially at rest, ends with velocity v2. | for m1 having velocity u1 to the right, m2 initially at rest, ends with velocity v2. | ||
| x dimension: m1u1 = m1u2cosθ1 + m2v2cosθ2 | x dimension: m1u1 = m1u2cosθ1 + m2v2cosθ2 | ||
| Line 60: | Line 68: | ||
| Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees. | Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees. | ||
| - | ===Inclined plane=== | + | ====Inclined plane==== |
| normal force = force perpendicular to the plane | normal force = force perpendicular to the plane | ||
| normal force on a block resting on a slope, θ = degrees from horizontal: | normal force on a block resting on a slope, θ = degrees from horizontal: | ||
| Line 77: | Line 85: | ||
| only one type of friction applies at a time | only one type of friction applies at a time | ||
| - | ===Spring and Lever=== | + | ====Spring and Lever==== |
| - | Hooke's law for springs: F=-kx, k=spring constant, x = displacement | + | **Hooke's law** for springs: F=-kx, k=spring constant, x = displacement |
| - | Fulcrum: t = r * f (torque = radius * force) | + | **Fulcrum**: t = r * f (torque = radius * force) |
| just add the torques for multiple objects on one side of a fulcrum | just add the torques for multiple objects on one side of a fulcrum | ||
| - | ===Projectile fired at an angle=== | + | ====SHM - Simple Harmonic Motion==== |
| + | ma = -kx | ||
| + | |||
| + | angular frequency ω = √(k/m) | ||
| + | |||
| + | period of oscillation T = 2π √(m/k) (horizontal or vertical springs) | ||
| + | |||
| + | In a vertical spring, the weight Mg of the body produces an initial elongation to equilibrium, such that Mg − kyₒ = 0. | ||
| + | |||
| + | If y is the displacement from this equilibrium position the total restoring force will be Mg − k(yₒ + y) = −ky | ||
| + | |||
| + | |||
| + | ====Projectile fired at an angle==== | ||
| Vx = Vo*cos(θ) | Vx = Vo*cos(θ) | ||
| Vy = Vo*sin(θ) - gt | Vy = Vo*sin(θ) - gt | ||
| Line 102: | Line 122: | ||
| Vf² = Vi² + 2ad ? | Vf² = Vi² + 2ad ? | ||
| - | ===Buoyant force=== | + | ====Buoyant force==== |
| pressure P = F/A (force/area) | pressure P = F/A (force/area) | ||
| + | |||
| hydrostatic gauge pressure: P = pgh, p = density of fluid, g=gravity, h=height (depth) | hydrostatic gauge pressure: P = pgh, p = density of fluid, g=gravity, h=height (depth) | ||
| + | |||
| buoyant force Fb = Fup - Fdown | buoyant force Fb = Fup - Fdown | ||
| Fb = pgVf, where Vf = volume of displaced fluid, and density * volume = mass, so | Fb = pgVf, where Vf = volume of displaced fluid, and density * volume = mass, so | ||
| Line 110: | Line 132: | ||
| => buoyant force depends on mass of displaced fluid, not the mass of the object | => buoyant force depends on mass of displaced fluid, not the mass of the object | ||
| - | ===Gravity=== | + | ====Gravity==== |
| gravitational constant between two bodies | gravitational constant between two bodies | ||
| F = G * m1 * m2 / r² | F = G * m1 * m2 / r² | ||
| Line 117: | Line 139: | ||
| - | ===Kinematics=== | + | ====Kinematics==== |
| no use of forces in the equations | no use of forces in the equations | ||
| typical equations: | typical equations: | ||
| Line 125: | Line 147: | ||
| vf = v0 + at | vf = v0 + at | ||
| - | coefficient of restitution = ratio of energy conserved after collision | + | ====Miscellaneous==== |
| - | e = (vel. after collision) / (vel. before collision) | + | |
| - | (for collision with immovable object) | + | |
| - | e = (Vfa * Vfb) / (Via * Vib) | + | |
| - | (for collision between objects a and b. f = final, i = initial velocity) | + | |
| - | e = 1 for perfectly elastic, 0 for perfectly inelastic | + | |
| - | + | ||
| - | ===Miscellaneous=== | + | |
| IV = independent variable - the variable you control, typically x axis | IV = independent variable - the variable you control, typically x axis | ||
urp/physgen.txt · Last modified: 2022-02-01 by nerf_herder
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