Final Revision Powerpoint Flashcards
What is the moment of a force relative to the cross product of components?
M = r x F
What is Newton’s 2nd Law?
F = ma
What are the conditions of equilibrium?
The resultant forces and moments have to equal 0
How do we draw a simple support in a free body force diagram?
A force perpendicular to the surface of contact
How do we draw a pinjoint in a free body force diagram?
Either with two perpendicular forces or a force at an angle
How do we draw a rigid support in a free body force diagram?
Two perpendicular forces and a moment
What are the simplifying assumptions for a plane truss?
- Members are pin jointed at their ends
- Forces are only applied at joints
- Each member is acted upon by only two forces
What are the two methods to solve a truss?
- Method of Joints:
We isolate one joint where no more than two bars meet. Then we replace the bars with forces which diverge from the joint. Then we solve for the joint to be in equilibrium. Once we have done this, we can then find other joints - Method of Sections:
We cut through bars to create a section of the truss. Then we say that alll of the bars we cut through become diverging forces. Using this, we can then analyse the section with those forces and the external reactionary forces, because all of the internal forces will resolve to 0
What is the equation of friction?
Friction = Friction Coefficient * Reactionary Force
What is the path of a particle?
It is the direction that the particle will travel
What is the velocity of a particle relative to the path?
The velocity is the time derivative of the path
What is the acceleration of a particle relative to the velocity?
The acceleration is the time derivative of the velocity
What is rectilinear motion?
Motion when the path is a straight line
How is a = v * dv/dx?
a = dv / dt = dv / dt * dx / dx = dv / dx * dx / dt = v * dv / dx
What is the displacement of a particle under rectilinear motion if a = 0?
x = (v * t) + x0
x0 is the original displacement
What is the displacement of a particle under rectilinear motion if acceleration is constant?
x = (a0 * (t^2 / 2)) + v0 * t + x0
All terms with 0 are their initial values
What is the displacement of a particle under rectilinear motion if acceleration is constant?
x = (a0 * (t^2 / 2)) + v0 * t + x0
All terms with 0 are their initial values
What equation can be used to compare the initial and final velocity of a particle acting under rectilinear motion with a constant acceleration?
v^2 = u^2 + 2as
Where does the velocity act in curvilinear motion relative to the path?
The velocity is always tangential to the path
What is at and what does it represent?
at is the variation of the magnitude of velocity. It is equal to dv / dt and it acts tanential to the path
What is an and what does it represent?
an is the variation of the direction of velocity. It is equal to v^2 / Radius and it acts normally to the path
What is the equation for work?
W = s * F * cos(a)
What is the equation of Kinetic Energy?
E = 1/2 * m * v^2
What is the equation of work relative to kinetic energy?
W = 1/2 * m * (v^2 - u^2)
What is a conservative field of forces?
This is a field where the work done only depends on the final and initial values of the particle, not the path of motion
What is the equation for gravitational potential energy?
m * g * h
What is the equation for elastic energy?
1/2 * k * s^2
