P+12ρv2+ρgh=Constantcap P plus one-half rho v squared plus rho g h equals Constant
y=xtanθ−gx22u2cos2θy equals x tangent theta minus the fraction with numerator g x squared and denominator 2 u squared cosine squared theta end-fraction Since this equation matches the standard parabolic form ( ), the path of a projectile is a parabola. 2. Time of Flight (
W=(πr2h)⋅ρ⋅gcap W equals open paren pi r squared h close paren center dot rho center dot g
Work done against this restoring force to stretch/compress it by a small distance
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12mve2=GMmRone-half m v sub e squared equals the fraction with numerator cap G cap M m and denominator cap R end-fraction
To prevent vehicles from skidding on curved paths, roads are tilted upward at the outer edge by an angle be the normal reaction, be friction, and be the mass of the vehicle. Resolving vertical forces: Resolving horizontal forces providing centripetal force: Divide the horizontal equation by the vertical equation:
ΔU=Δm⋅g(h2−h1)cap delta cap U equals delta m center dot g of open paren h sub 2 minus h sub 1 close paren The change in kinetic energy ( ) of the fluid mass is:
τ⃗=r⃗×F⃗modified tau with right arrow above equals modified r with right arrow above cross modified cap F with right arrow above Expressing r⃗modified r with right arrow above F⃗modified cap F with right arrow above in their rectangular components: P+12ρv2+ρgh=Constantcap P plus one-half rho v squared plus
This unit connects forces with the resulting motion of bodies. 1. Conservation of Linear Momentum
For the streamline flow of an ideal (non-viscous and incompressible) fluid, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant at every point along the flow.
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Wnet=W1−W2=P1A1v1Δt−P2A2v2Δtcap W sub n e t end-sub equals cap W sub 1 minus cap W sub 2 equals cap P sub 1 cap A sub 1 v sub 1 delta t minus cap P sub 2 cap A sub 2 v sub 2 delta t By the equation of continuity, the mass entering and leaving is the same: To turn this guide into an offline PDF
Here’s the best way to approach what you need:
a=dvdt=dvds⋅dsdta equals d v over d t end-fraction equals d v over d s end-fraction center dot d s over d t end-fraction a=vdvdsa equals v d v over d s end-fraction a⋅ds=v⋅dva center dot d s equals v center dot d v Integrate both sides within the limits of motion (from for displacement, and for velocity):
Parallel Axis Theorem and Perpendicular Axis Theorem. Unit 5: Gravitation
Now, let one mole of the same gas be heated at a constant pressure through the same temperature interval . According to the First Law of Thermodynamics: dQ′=dU+dWd cap Q prime equals d cap U plus d cap W
Ultimate Guide to Class 11 Physics Derivations: Free PDF Download & Key Concepts
T=2πlgcap T equals 2 pi the square root of l over g end-fraction end-root