Motion----------------------------
Distance
distance = rate x time
This goes way back to your math classes using this formula. In our case, we use different names:
s = vt
where s is displacement (distance from your start) measured in meters, v is velocity (speed and direction) in meters/second and t is still time, usually measured in seconds.
We also use one version of this formula in calculating range: R = Vxt, where R is range in meters, Vx is velocity in the x direction, and t is time in seconds.
Acceleration:
When velocity changes (e.g. speeding up or slowing down) we describe this as acceleration. We use the letter a for this, and the units are meters/second squared or m/ss. Make sure you include these units whenever you answer a question.
You can see that if you multiply acceleration x time, the units would be velocity, so:
v = at
where v is velocity in m/s, a is acceleration in m/ss and t is time in seconds.
total displacement when something is acceleration can be found this way:
s = 1/2at^2
In a special case where something is falling, the a is the acceleration of gravity, or 9.8 m/ss.
There is another version of this formula that has no time:
Vf^2 = Vo^2 + 2as
where Vf^2 is final velocity, Vo^2 is the initial velocity, a is acceleration and s is displacement.
If the situation has no time measured or required, this is a handy relationship to use.
Energy----------------------
3 forms of energy were covered in our group:
PE is potential energy, the potential to fall to a lower height. The lowest height is called 0 PE
PE = mgh
where m is mass in kg, g is usually 9.8 (on earth) and h is height in meters
All forms of energy are measured in Joules, a handy measure of energy.
KE is energy of motion:
KE = 1/2 mv^2
where m is mass in kg, v is velocity in m/s and KE is measured in Joules (again). Note that there is no g in this equation, so it involves only mass and velocity.
SE is spring energy, or the energy stored in a spring.
Springs require force to be stretched. This force can be represented by this formula:
F = -kx
This means that if a spring is stretched, it will take a certain force (F) to stretch it a distance (x)
I know we used s for displacement and now we are using h for height and x for stretch, we are a whimsical science, what can I say?
Work or energy is Force • distance, so Energy = Force • distance would mean the energy stored in a spring would be these squared, but the spring has more force at the end, so we instead use this average:
SE = 1/2kx^2
where k is the stiffness of the spring in N/m (N is Newtons, a measure of force), and x is the amount the spring is stretched.
A good strategy in every problem is to ask yourself:
Mass and spring:
In a mass/spring system, there is usually a mass, a spring and an equilibrium position. When the mass is pulled from this equilibrium position, and the spring exerts a force to restore it to this position, the amount of time it takes to get there and back to the same spot in the same direction is the period.
In short, this means if something is bouncing, the period is the amount of time it takes for the mass to return to the same place, moving in the same direction:
There are several other systems that "oscillate" in this fashion, you might see in the next few years.
Waves and Sound-----------------------
Waves can be described as transverse, meaning the wave displacement is 90° to the direction of travel (like sideways pulses on a spring), or longitudinal, meaning the displacement is along the direction of travel (like sound waves).
In both cases, the relationship between velocity, frequency and wavelength is:
V = f • wavelength
We use the character lambda for wavelength:
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