PHY Exam 2

conversion of cm to m

100 cm = 1 m

area of circle

πr²

static friction exists when

two objects are NOT moving/sliding across each other because the applied force is not strong enough for movement (f_s=applied force)

coefficient of friction is

the amt of friction between 2 surfaces in contact

coefficient of static friction =

tan(theta_c)

the horizontal force matters when determining

an object’s horizontal acceleration

what does the F stand for in deltaL=(1/y)(F/A)L₀

tension force using F=ma

what does the A stand for in deltaL=(1/y)(F/A)L₀

cross sectional area of the rope using πr²

what does the L₀ stand for in deltaL=(1/y)(F/A)L₀

(original) rope length

[circular motion] 1 revolution = ? radians

2π

[circular motion] 1 revolution = ? degrees

360

[circular motion] w =

angular velocity

[circular motion] angular velocity refers to

how fast/rate @ which an object rotates around a center point (how quickly the angle is changing)

in uniform circular motion, speed/velocity can be constant but since the direction is constantly changing the direction of velocity

constantly changes so acceleration exists

centripetal acceleration a_c refers to

the center seeking acceleration that an object experiences while in uniform circular motion/moving in a circular path (ALWAYS POINTS TOWARD CENTER)

what is the force that contributes for a centripetal acceleration for earth orbiting around the sun

F_c = a_c = gravitational forces

what is the force that contributes for a centripetal acceleration for a person swinging an object with a rope above their head

F_c = a_c = tension (from the string)

what is the force that contributes for a centripetal acceleration for a car on a circular race track

F_c = F_s = a_c = STATIC frictional force (between car tires & the road)

why is the F_c / a_c for a car on a circular track STATIC friction and not KINETIC friction

the tires are rolling without slipping because the bottom of the tire is stationary when it touches the ground (think picture of bicycle tire where spokes at top are blurry vs clear at the bottom)

[centripetal force] toward the center of the circle (inward) is considered

positive (+)

• example: at the bottom of a ferris wheel N (normal force) is positive bc it points toward the center

[centripetal force] away from the center of the circle (outward) is considered

negative (-)

• example: at the top of a ferris wheel N (normal force) is considered negative bc it points away from the center

[rollercoaster loop] what happens to the N formal exerted by the seat onto the person

it always points towards the center no matter the point of the loop, so it always contributes to F_c

[rollercoaster] at the bottom of a roller coaster loop the normal force exerted by the seat points

up towards the center, because the seat is below you and pushes up against you

• N = F_c

[rollercoaster] at the right side of a roller coaster loop the normal force exerted by the seat points

to the left (towards center of the loop)

• N = F_c

[rollercoaster] at top of a roller coaster loop the normal force exerted by the seat points

down (towards the center) because the seat is now above you

• F_c = N & F_g/W/mg

[rollercoaster] at left side of a roller coaster loop the normal force exerted by the seat points

to the right (towards the center of the loop)

• F_c = N

[ferris wheel] what can be said about the force exerted by seat on a person at the bottom vs at the top

since gravity points down while the seat is at the bottom (which is opposite of the direction of the F_c), the seat has to do extra work so the force it exerts is greater at the bottom than at the top

when a car goes around a circular curve on a horizontal/UNBANKED road at a constant speed, what force provides the F_c?

the static friction force between the tires and the road so F_c=f_s

on a frictionless BANKED curve, the F_c is

the horizontal component of the normal force (Nsinθ) so F_c= F_x= Nsinθ = mv²/r

on a frictionless BANKED curve, mg =

Ncosθ

[banked curve] what is the ideal banking eqn/formula to find angle (or velocity if given angle and radius)

tanθ = v²/gr

how is the gravitational force formula, F_g=(Gm₁m₂)/r² , for objects/satellites as one mass and Earth as the other mass

F_g=(GM_Em)/r²

what happens to the acceleration due to gravity as you get farther from the Earth’s surface

it decreases

work (W) depends on the component of the force along

the (direction of) displacement

[WORK] when the force is in the SAME direction as motion, the angle (theta) =

• 0˚

• so cos(0˚)=1

• so W=Fd(1)

[WORK] when the force is PERPENDICULAR to motion, the angle (theta) =

• 90˚

• so cos(90˚)=0

• so W=Fd(0)=0

[WORK] when the fore is in the OPPOSITE direction to motion, the angle (theta) =

• 180˚

• so cos(180˚)=-1

• so W=Fd(-1) == W = -Fd

units of Work (W)

• J (joule)

• N • m

W_net = 1/2 (mv_f²) - 1/2(mv₀²) is simply

KE_f - KE₀

• final KE - initial KE

when the net work done on an object is postive,

its kinetic energy (KE) increases

when the net work done on an object is negative,

its kinetic energy (KE) decreases

when there is zero net work,

there is no change in kinetic energy (KE)

another form of PE_g = mgh

PE_g = mg (h₀-h_f)

[WORK] potential energy (PE) refers to

an object’s stored energy due to its vertical position (height)

[WORK] when you lift an object, gravity

does no work so the object has potential (stored energy), but when the object is release gravity does work so the PE becomes KE as the book falls

a higher (vertical) position means

there is more PE_g

PE does NOT depend on

the path that the object takes, it only depends on height

examples of when to use W_net = PE_g //. KE_i + PE_i = KE_f + PE_f

• when KE & PE is involved (movement & gravity)

• when KE becomes PE so no energy is lost

• gymnast jumping on trampoline

• rollercoaster from top of drop to bottom

• a biker leaping from a high cliff to a shorter cliff

• finding max height after kicking a football

[WORK] if an object moves up & returns to its original height, the positive & negative work by gravity

cancels, so W_g,tot = 0

• work only depends on starting & final positions so returning to the initial position would make the starting & final positions identical

[WORK] when objects go up, gravity is

negative so W_up = -mgh

[WORK] when objects go down, gravity

is positive so W_down = mgh

[WORK] examples of conservative energy

• gravitational force

• spring force

[WORK] example of nonconservative force

frictional force, so the path taken matters (distance matters)

formula for work done by kinetic frictional force

• W=Fdcos(0)

• W = f_kdcos(180˚)

• W=f_kd(-1)

• W = -f_kd

basic idea/formula for conservative forces (e.g gravity & spring forces)

E_i = E_f because energy is conserved (not lost) due to energy changing between KE and PE

basic idea/formula for nonconservative forces (e.g. frictional force)

W_nc = E_f - E_i

(W_nc = W_f & W_f = -f_kd)

[POWER] unit of power (P)

watt (W)

[POWER] 1 horsepower (hp) = ? W

745.7 watts (W)

[POWER] what is the formula for P = change in energy/time

P = (KE_f-KE_i)/T

how do you find mass of an object if given its weight

since W = mg, m = W/g

[POWER] frequency is

the number of oscillations per unit time so f =1/T

[MOMENTUM] unit for momentum

kg • m/s

[MOMENTUM] magnitude refers to

the sum vector

[MOMENTUM] units of impulse

• N(s)

• kg(m/s)

for free fall & projectile motion problems when air resistance is neglibible, horizontal acceleration (a_x) is ALWAYS

zero