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urp:physgen [2021-10-18] nerf_herder |
urp:physgen [2021-10-19] 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) | ||
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* 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) | ||
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- | **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 | ||
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- | ===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 | ||
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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: | ||
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parallel force = force parallel to the inclined plane | parallel force = force parallel to the inclined plane | ||
f = m*g*sin(θ) | f = m*g*sin(θ) | ||
- | When it is unbalanced objects will move down the plane, sometimes called net force | + | When parallel force > friction, it is unbalanced and objects will move down the plane |
+ | Applied force - friction = net force | ||
static friction - | static friction - | ||
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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: 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=== | + | ====Projectile fired at an angle==== |
Vx = Vo*cos(θ) | Vx = Vo*cos(θ) | ||
Vy = Vo*sin(θ) - gt | Vy = Vo*sin(θ) - gt | ||
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y = Ax² + Bx | y = Ax² + Bx | ||
y = -gx²/(2(VoCos(θ))²) + xtan(θ) | y = -gx²/(2(VoCos(θ))²) + xtan(θ) | ||
- | time of flight: | + | time of flight: t = 2Vosin(θ)/g |
- | t = 2Vosin(θ)/g | + | max height: H = (Vosin(θ))²/2g |
- | max height: | + | distance: x = sin(2*θ)*Vo² / g |
- | H = (Vosin(θ))²/2g | + | |
- | distance: | + | |
- | x = sin(2*θ)*Vo² / g | + | |
Vo = initial velocity | Vo = initial velocity | ||
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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 | ||
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=> 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 | ||
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- | ===Kinematics=== | + | ====Kinematics==== |
no use of forces in the equations | no use of forces in the equations | ||
typical equations: | typical equations: | ||
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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 |