AP Physics C/Printable version

AP Physics C

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Motion in One Dimension

Scalars vs. Vectors

Scalars

measurements that have no direction to them

Examples: Distance, speed

Vectors

measurements that have a direction to them

Examples: displacement, velocity

Displacement vs. Distance

Displacement - the most direct route from one point to another. (The net distance traveled)

Distance- the length traveled

Example Problem:

If a car travels 3m directly east then 5m directly west, what is the displacement and what is the distance traveled?

Displacement: if a car goes 3m east, and then it goes 5m opposite of east, the car will travel enough to cancel out the 3m east traveled, and go an extra 2m after that. This is best represented in an equation:

If east is positive:

=3m (east) + 5m (opp. east)

=3m (east) + (-5)m east

= -2m east

= 2m west

Displacement is often represented by the variable s, or x.

Velocity vs. Speed

Speed- change in distance over change in time

Velocity- the change in displacement divided by the change in time. It is also defined as the derivative of the displacement equation. Velocity is a vector.

Vectors and Motion in Two Dimensions

Vectors in 2D

Vectors in 2 dimensions have both an x and a y component. We can find the components if given an angle, θ, in the following manner:

$v_{0x}=v_{0}\cos {\theta }$

$v_{0y}=v_{0}\sin {\theta }$

Projectile motion

Projectile motion is one of the most common applications of 2D vectors. Lets start with an example, lets say we throw a ball 30 m/s at a 60° angle. We can figure out how far it will land and how long it will take. The acceleration in the y of a projectile motion question is always $a_{y}=-g=-9.8m/s$. Since velocity is the integral of acceleration, $v_{y}=\int a_{y}dt=a_{y}t+C$, and C will always be equal to initial velocity, $v_{y}=v_{0y}+a_{y}t\implies v_{y}=v_{0}\sin {\theta }+a_{y}t$ .

IMPORTANT: Any projectile with an initial height or y of 0 will reach the apex of its height at $t_{0.5}$ (where t is the total time of travel). This is because at the apex, the slope of the tangent line to the y position is equal to zero.

So lets solve for time. $v_{y}=v_{0}\sin {\theta }+a_{y}t\implies 0=30\sin {60}-9.8t\implies -30\sin {60}/-9.8=t\implies t=2.65s$

From here we can solve for the range of the object.

$a_{x}=0$

$v_{x}=v\cos {\theta }$

$x=\int v_{x}\implies \int v\cos {\theta }$

$x=v\cos {\theta }*t$

$x=30\cos {60}*2.65\implies x=39.8m$

Fundamentals of Electric Charge

• Intrinsic to fundamental particles
• 2 types: positive (+), negative (-)

Positive - Lack of electrons Negative - More electrons No charge = Neutral

Same charges repel: + and + or - and - Opposite charges attract: + and -

• Coulomb: Measurement of the amount of electric charge (similar to moles in chemistry)

Atomic Particle	Mass	Charge
Neutron	1.675 * 10−27 kg	0 C
Proton	1.673 * 10−27 kg	1.602 * 10−19 C
Electron	9.11 * 10−31 kg	-1.602 * 10−19 C

Atomic Notation

$_{Z}^{A}E$

• A = Atomic mass = # protons + # neutrons
• Z = Atomic Number = # protons
• E = element symbol (like U for Uranium)