Know when you are starting and stopping your virtual stopwatch, and assign numbers to variables accordingly.
You can, and probably should, call down positive in some situations, such as a drop or throw-down problem. But whichever direction you call positive:
- Speeding up? v and a have the same sign.
- Slowing down? v and a have opposite signs.
For projectiles problems, the problem ends just before the object hits the ground, so v at the bottom is not zero.
When acceleration changes, a new phase of the problem must commence, indicating a multistep problem.
If you don't know Newton's Laws
by heart, you're just pretending to be a physics student.
At this stage, the only force we are working with that does not require physical contact is the force of gravity. So in drawing force diagrams, look for what is making physical contact with the object, then include gravity.
Surfaces typically exert two forces, the normal force (a push perpendicular to the surface) and friction (parallel to the surface).
Tension forces from ropes, strings, cables and chains always pull away from the object.
The net force and the acceleration will always be in the same direction. ΣF = ma!
In Active Physics, CP Physics, AP Physics 1, and AP Physics 2, pulleys are assumed to be massless and frictionless, and strings are assumed to be massless. Hence: same string, same tension. In AP Physics C, we explore pulleys with mass as part of multi-object systems, and the need for unbalanced torque supplied by differences in string tension.
You feel "weightless" when gravity is the only force on you. (Ironic, or just unfortunate?)
- What we think of as feeling normal is the slight compression that results from gravity pulling down on us, while the normal force pushes on our feet (standing), our butt (sitting), or our back (lying down).
- In Einstein's relativity theory, gravity isn't like other forces. According to Einstein, what feels like a conventional force is actually the result of the curvature of space created by all objects with mass. So it makes sense that what we feel with only gravity acting on us is similar to the feeling of floating freely in space.
Energy and Momentum
The law of conservation of energy and the law of conservation of momentum are the pillars of both classical and modern physics.
Conservation laws relate to quantities which remain the same in closed, isolated systems
. There are very important corresponding theorems that relate to objects:
|Topic||Theorem for Objects||Law for Systems|
|Momentum||Impulse-Momentum Theorem||Conservation of Momentum|
|Energy||Work-Energy Theorem||Conservation of Energy|
These theorems and laws are consistent with Newton's laws of motion.
As is always the case in physics, we model certain real-world systems as being closed and isolated when in fact there are small exchanges and influences from the environment outside.
Where conservation of energy is concerned, we pay attention only to relevant forms of energy. For macroscopic systems, these are kinetic and potential energies which affect the motion of objects in the system. Some forces (such as gravitational forces) merely exchange energy from one form to another while retaining the energy for future use within the system.
In a pendulum with negligible friction, energy is continuously exchanged between kinetic and gravitational potential forms, with no change in the total energy.
Other forces (such as friction) convert energy to a form which prevents it from being reused by the macroscopic system.
Friction converts kinetic energy into thermal energy, which is distributed and no longer available to be converted to other forms of energy.
Conservative forces must satisfy two requirements:
- The total mechanical energy of a system remains constant in any isolated system of objects that interact only through conservative forces.
- Work done by conservative forces is independent of the path taken.
Some forces are legitimately conservative (gravity) while others are modeled that way as an approximation (springs with negligible friction).