Mechanics Flashcards
Define impulse
F x t
Derive the impulse-momentum principle
F = ma a = (v - u)/t F = m(v - u)/t Ft = mv - mu
What is the equation for momentum conservation for two particles colliding?
m1u1 + m2u2 = m1v1 + m2v2
Equation for work done
W = Fs
Equation for potential energy
W = mgh
Equation for friction
Fr = μR
Equation for kinetic energy
Ek = 1/2 mv^2
Define principle of conservation of mechanical energy
When no external forces (other than gravity) do work on a particle during its motion, the sum of the particle’s kinetic and potential energy remains constant
Define work-energy principle
The change in the total energy of a particle is equal to the work done on the particle
How do you work out a particle’s weight components on a slope of angle θ?
Component down slope is mgsin(θ)
Component perpendicular to slope is mgcos(θ)
What is power?
Rate of doing work
Power equation for work
P=E/t
Power equation for moving particle
P=Fv
Tension equation for stretched spring
T = kx
Hooke’s law equation
T = λx/l
Work done stretching a spring equation
W = 1/2 λx^2/l
What is elastic potential energy?
Equal to the work done to stretch the spring
What is Newton’s law of restitution for two particles colliding?
e = speed of separation/speed of approach e = (v2 - v1)/(u1 - u2)
What is Newton’s law of restitution for a particle colliding with a smooth plane?
e = speed of rebound/speed of approach
What is the range of values for coefficient of restitution?
0 =< e =< 1
What does elastic collision mean?
Total kinetic energy is constant
If a collision is inelastic, what is the equation for loss of kinetic energy?
(1/2 m1u1^2 + 1/2m2u2^2) - (1/2 m1v1^2 + 1/2m2v2^2)
When a particle collides obliquely with a surface, in which direction does the impulse act?
Perpendicular to the surface
A particle hits a surface making angle α at speed u, and rebounds at speed v making angle β. What is the equation for the component of velocity parallel to the surface?
v cos(β) = u cos(α)
A particle hits a surface making angle α at speed u, and rebounds at speed v making angle β. What is the equation for the component of velocity perpendicular to the surface?
v sin(β) = eu sin(α)
A particle hits a surface making angle α at speed u, and rebounds at speed v making angle β. What is the angle of deflection?
α + β
When a particle collides obliquely with a surface, and the speed before and after are given as vectors, how can you find the angle of deflection?
cos(θ) = (u.v)/(|u| x |v|)
When two particles collide obliquely, and one is originally stationary, what can be said about the stationary particle afterwards?
It will move parallel to the line of centres
No component of speed perpendicular to the line of centres