ENSC2004 - Lecture 15

ENSC2004 - Lecture 14
Conservative Forces - Slides

A force is conservative if the work done is independent of the path followed by the force acting on a particle as it moves from A to B
This also means that the work done by the force in a closed path is zero
$\oint F \cdot d r = 0$
The work done by a conservative force depends only on the positions of the particle and is independent of its velocity or acceleration

The “conservative” potential energy of a particle/system is typically written using the potential function $V$

There are two major components to $V$ commonly encountered:
$V_{t o t a l} = V_{g r a v i t y} + V_{s p r in g s}$

When a particle is acted upon by only conservative forces, the sum of kinetic energy and potential energy remains constant
$T_{1} + V_{1} = T_{2} + V_{2} = Constant$

Note: $T_{n} = 0.5 m (v_{n})^{2}$

Impulse and Motion - Slides

Obtained by integrating the equation of motion with respect to time
$\sum \int_{t_{1}}^{t_{2}} F d t = m v_{2} - m v_{1}$
This equation represents the principle of linear impulse and momentum
- Relates particle’s final and initial velocity and the forces acting upon it as a function of time

Linear momentum $-$ $m v$

Linear impulse $-$ $\int F d t$ (denoted by $I$ )

Equation typically written as:
$m v_{1} + \sum \int_{t_{1}}^{t_{2}} F d t = m v_{2}$

Note: for this diagram, weight force is negligible

Quartz 5