Summary Equations for Solid Mechanics 1

Equations we need to know for solid mechanics:

Newton’s second law:
F = ma

Friction:
Limiting friction = fs
fs∝N
Dynamic friction = fd
fd∝N
Dynamic friction < static friction:
f s=μ s N
f d=μ d N
F ≤ μN

Standard acceleration for constant acceleration:
2 2
v2 = u2 + 2as ω 1 =ω0 +2 ω̇ θ
v = u + at ω 1=ω 0+ ω̇ t
1 2
s = ut + ½ at2 θ=ω0 t+ ω̇ t
2

Acceleration under variable force:
Object has thrust T and drag BV2
COME BACK TO THIS IT IS SO LONG HOLY SHIT AND SURELY THERE MUST BE AN EASIER WAY TO DO
ALL THIS STUFF

Power = force x velocity

Moment of a force:
Moment = fd (d = perpendicular distance)

If we know about some other point on line of action of force:




Moment = Fa sinα=( Fsinα ) a

Two equal and opposite forces (not in same line) form a couple

, Moment about any point is Fd

Momentum – useful when force varies with time:
For linear motion:
F = ma
t2 t2 t2 v2
dv
∫ F dt=∫ ma dt=m∫ dt dt=∫ 1 dv
t1 t1 t 1 v 1

If F = constant
F = (t1 – t2) = m(v1 – v2)

Ft = m(v-u)

For rotational motion
Momentum = Iω

Kinetic Energy:

Initial KE = ½ (m1u12 + m2u22) Final KE = ½ (m1v12 + m2v22)

1 m1 m2
Change in KE = (v 1−v 2)2
2 m1 +m2

Statically determinate stuffs:
Frame with
N nodes (joints)
M members
R reaction components
Number of unknowns = m + r
Number of equations = 2n (resolving twice at each node)
Frame is statically determinate if
2n = m + r

Statically determinate  2n = m + r
Statically indeterminate  2n < m + r
Kinematic  2n > m + r

Except in special case  kinematic!!