U3: Energy and momentum

formula for work done by a constant force

units

W = |F||d|cos(ø)

w = J (Nm)

F = N

*make sure to do magnitude of force and displacement

what is the meaning of Fcosø

force in the direction of displacement

positive and negative work

positive and negtive work depend on the angle:

cos(0) = +1

cos(180) = -1

negative

• force is going according to the acceleration (net force results in acceleration not displacement) which is negative

• displacement is positive

• opposite directions means negative work

what are energy flow diagrams

• can you have energy added and taken away in a system

• give an example of adding energy

• example of taking away energy

energy flow diagrams show if energy is added to or taken away from the system. energy can be added and taken away for 1 system

adding energy: Fa → adding energy by adding work to the system 

removing energy: Ff → removing energy by removing work from the system

draw an energy flow diagram with energy going in and out

how do you know if you have external work?

if you have

• an applied force

• friction

• air resistance

this is why you can have multiple Wext in equations of energy conservation. if multiple of these questions are answered, like there is an applied force and friction, youd have Wext1 and Wext2.

draw an energy bar chart for pushing a box at a constant velocity with friction

energy bar charts show the amount of energy and work gained or lost between 2 events. they should be equal.

the chart matches the energy conservation equation:

how do you calculate work when its:

• constant

• non constant

constant: W = |F||d|cosø

non constant: the graph is not a rectange, you can only get work by getting the area under the graph

on an F,d graph, the area under the graph is the work done (sum all the areas, including negatives)

example: write the full equation from 1 to 3

key idea: you need to account for external work 2x because energy is moved out of the system 2x between event 1 and 3

what is hookes law

F_os = kx

• force of object on spring

• K = spring constant (N/m)

• x = how much the spring was stretched

how do you calculate k (spring constant) graphically

the formula F=kx tells you that on a F vs x graph the slope is k

what is the restoring force

F_rest = -F_os

the restoring force is the force the spring exterts on the object (F_so) which tries to restore the object back to equilibrium 

F_so = -kx → the restoring force is negative bc the force is in the opposite direction of x 

what is the formula for elastic energy? how did we derive it?

Ee = 1/2kx²

work = area under an F-d graph, so Ee (work done by spring)= area under a F-x graph

for a non constant force:

how should you label your events in an elastic energy question

• label at top and bottom of ramp

• at the beginning of spring and at the end of spring (for stretch/compression)

what does the word “max compression” tell you?

tells you at the event of max compression, the velocity of object is 0

what is the acceleration of a mass on a spring

the acceleration is measured from an equilibrium point

Fnet= ma = -kx → its the accleration of the object thats being measured, so we need to use the restoring force because thats Fs,o

using: ma = -kx

a = -k/m (x) → this is the acceleration of a mass on a spring

accleration of the mass on a spring is proportional to ?

accleration is in the opposite dirrection of ?

accleration is ____ constant?

accleration of the mass on a spring is proportional to x, the position

accleration is in the opposite dirrection of displacement

accleration is NOT constant because x is always changing 

• cant use the big 5 kinematics equations

acceleration of object is in the direction of ___

net force

describe the acceleration of a mass on a spring

accleration is proportional to displacement and directed toward the equilibrium

graph of a vs x, accleration of object on spring vs position

simple harmonic motion

the repeating motion of an oscillting mass where the restoring force is proportional to the displacement but in the opposite direction

characteristics of SHM (3)

• period (T) and amplitude (A) are constant

• period is independent of amplitude

• position, velocity and acceleration vs time graphs are sinusoidal functions

you can find the period and amplitude from a ____ vs time graph

you can find the period and amplitude from a displacement vs time graph

period

frequency

period: the time it takes to complete 1 cycle (T) (s)

frequency: the number of cycles per second, f = 1/T (Hz)

T= 1/f

C

what is the period of a x-t graph vs a PE-t graph?

x-t graph:

• period is from one position to its return

• like an actual cycle

PE-t graph:

• 1 period = 2 cycles on PE -t graph

• KE: 0 → max → 0 → max→ 0

• PE: max → 0 → max → 0

what is k and its units

k = spring constant, how stiff the spring is (N/m)