Mechanics - Equations Flashcards
(23 cards)
What is the equation for impulse
Ft = mv - mu
F - Force
t = Time through which the force acts
m - mass of object
v - final velocity
u - initial velocity
What is the equation for impulse of a varying force
I = ∫F dt .
What is the equation for the coefficient of restitution
e = v₁ - v₂ / u₂ - u₁
What does it mean if the coefficient of restitution in 0
Perfectly inelastic collision
What does it mean if the coefficient of restitution in 1
Perfectly elastic collision
What is the equation for the work done by a force in the horizontal direction
Includes Trigonometry
W = Fd cos x
What is the equation for kinetic energy
K.E = 0.5 mvv
What is the equation for GPE
GPE = mgh
What is the equation for Hookes Law in base form
T= kx
T -Tension
k - spring constant
x - extension
What is the equation for spring constant
K = λ/L
K - Spring constant
λ - Modulus of elasticity
L - Natural Length
What is the equation for hooke’s law without the spring constant
F = λx/L
What is the equation for the work done by a variable force
W = ∫Fdx
What is the equation for elastic potential energy in base form
EPE = 0.5 kxx
What is the equation for elastic potential energy without the spring constant
EPE = 0.5 λxx/L
How do you find the work done in compressing a spring from x1 to x2
W = ∫Fdx
W = ∫λx/Ldx between bounds x1 and x2
W = λ/2L (x^2 -x^2)
Why do you use the Integrated version of EPE rather than the given equation in most scenarios
The integrated scenario can be used in all scenarios where a string has been extended from one non zero extension to another whereas the geenral equation can only be used from 0 extension to another
What is the work energy principle including strings
Work done by Propulsive forces - Work done by Resistive forces = Gain in KE
So for an object suspended by a string moving down a sloped plane
Work done by Gravity - Work done by tension - Work done by friction = Gain in KE
What is the equation for power
P = Fv
What is the equation for linear speed
v = s/t
What is the equation for angular speed
ω = x/t
x - angle traversed
t - time taken
ω - angular velocity
What is the equation linking linear and angular speed
v = rω
r - The radius of the circle
What are the two equation for centripetal acceleration
a = v²/r
a = ω²r
