September 25, 2002

Perry R. Cook,

Princeton University

### Position as function of time:

- Velocity as function of time is rate of change of Position with respect to time.

- Acceleration as function of time is rate of change of Velocity with respect to time.

Units: m (meters) and s (seconds)

- Position: m

Velocity: m/s

Acceleration: m/s/s = m/s^2

- Force: F = ma (Newton's 2nd Law (with m = constant))

- Acceleration due to gravity, at sea level, on earth, is:

- Force due to gravity (sea level, earth) is: mg Newtons

- Frictional Forces:
- When stationary, the coefficient of static friction is:

- When moving, the coefficient of kinetic friction is:

- Force due to friction acts opposite other forces,
and is equal to

Example:

- When stationary, the coefficient of static friction is:

- Energy: W = F x (force through a distance, if F is constant)

- Power: = Energy flow, or the time rate of work = dW(t)/dt

- Potential Energy: Potential to do work because of
**position**in a**field**

- In a
**conservative field**, potential (and work) only depends on

initial and final positions, not on path or time taken to traverse it.Example: Gravitational Potential Energy =

- Kinetic Energy: Ability to do work because of
**mass**in**motion**

Note that Kinetic Energy being related to the square of the velocity means that stopping a car takes four times the distance (constant frictional forces) if the car is going twice as fast.

**Energy is Conserved**, A Very Important Physical Concept!!!Example: Potential and Kinetic energy, dropping a ball

Initial Potential + Initial Kinetic = Final Potential + Final Kinetic

Mass cancels!! (Galileo and later some moon-walkers proved this experimentally)

**Mass is Conserved**, Another Very Important Physical Concept!!!Example: If I pound water into a hose, it either comes out the other

end or the hose eventually blows up. Mass is conserved.

- All of the above still works, just adjusted slightly

Example: A fulcrum with a pivot at 1/3 its length will balance with

twice as much mass on the short end as on the long end.Assume it's balanced and at rest (acceleration = 0)

- Rotational Energy:

A spring with constant k (Force = -k y)

A mass with mass m

Some oil with damping R (Force = -R v)

y is the signed displacement from equilibrium (at rest with y = 0).

Minus sign on spring term means force acts to restore mass to rest position.

Minus sign on damping term means force acts against motion,

proportional to velocity.

Solutions:

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