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distance, velocity, acceleration. time
x = x0 + v0t + (1/2)at2
velocity, acceleration and distance
v2 = v02 + 2ax
velocity, acceleration and time
v = v0 + at
how does a projectile stay in motion? what keeps it in motion?
peak height of a projectile
v0 = sin(0) - sq.rt.(2gh)
horizontal distance traveled of a projectile
x = vt . cos(0)
no velocity, but acceleration = 10
PE and KE of projectile object at its peak
- PE is maximized
- KE is minimized
(energy must be conserved)
projectile path is independent of....
two objects launched with the same velocity will...
hit the ground at the same moment
what determines the time of flight?
range of projectile is maximized at what angle from the horizontal?
symmetry of projectile says what? (speed wise)
upward mirrors downward -
initial speed = final speed
air resistance is greater on (surface area, shape, and speed)
- larger surface area
- irregularly shaped
- greater speed
does mass affect force or path of air resistance
force = no
path = yes
how does greater mass affect air resistance
force is the same, so it decreases acceleration
centripetal force (equation)
F = m . v2/r
tendency of an object to stay in present state of motion
(keeps projectile in motion)
law of universal gravitation
F = G(m1m2)/r2
friction points in what direction?
always parallel to surface
equation for torque
t = F r sin0
if the board has mass, what do you do with torque?
F=mg at center of board
equation for work (not for gases)
W = Fd cos0
what direction is friction (relative to work)?
friction does negative work!
work done lifting an object
W = Fd = mg x h
what is gravitational potential energy?
work done by gravity:
change PE = -W
energy and power
energy = work + heat
so, P = (w + q)/s
1 revolution is equal to
2 pi r
equation for angular momentum
L = l x m x v
l = lever arm, mv = linear momentum
mechanical energy is conserved
mechanical energy is lost to internal energy (heat)
perfect inelastic collision
2 objects stick together
reverse inelasitc collisions (object dissipates into 2 sep. objects). In what direction do they travel
opposite to each other
ex: man standing on a board and jumps off
what do you need to consider when determining their final positions?
move in opposite directions
consider their centers of gravity
what is impulse?
change in momentum
Machine: inclined plane (how is work minimized?)
straight up: W = ugh
ramp: W = mg x sin x h
What is theta equal to in the ramp
height of ramp / distance of the ramp
the greater the distance (d) the smaller the angle, the less work needed
Machine: lever (torque)
what does F need to equal to lift mass?
F = mg in opposite direction
How do you decrease the force required to life the object?
increasing the lever arm
(doubling lever arm, reduces force by a factor of 2)
In a pulley, what is the tension in the rope?
Tension = Force
In a double pulley system, what is the force required to lift mass m?
F = T
T = 2mg
F = (mg)/2
2 protons, 2 neutrons
traveling of alpha particle
stopped by skin, paper
expulsion of an e-
B+ is emitted (-1 atomic #)
gain e- (-1 atomic number
frequency of a gamma particle
high frequency particle
fussion combining 2 (?) from (?)
combining 2 nuclei
from a heavier nucleus
splitting a single nucleus into 2 lighter nuclei
where does energy for fusion and fission come from?
density = m/v
density constant for gases and liquids?
constant for liquids and solids
change for gases, because they are compressible
What is specific gravity?
density of a substance compared to density of water
so specific gravity of water is
formula for fluid pressure
P = F/A
Do fluids at rest have uniform density in a sealed container?
What is the pressure experience by fluids at rest with uniform density?
P = density x g x y
y = depth of fluid
Where is pressure greatest for a fluid at rest?
greatest depth (P=pgy)
What if you have many fluids layered in a sealed container?
P = (pgy)1 + (pgy)2 + (pgy)3...........
What is the pressure of a fluid at rest with uniform density in an open container
add atmospheric pressure to density x g x y
hydraulic lift (equation)
pressure is transferred completely:
F1/A1 = F2/A2
What is the velocity of a fluid flowing (if you don't know rate or area)?
v = sq.rt (2gh)
upward force acting on a submerged object
what is buoyant force equal to? (not equation)
weight of fluid displaced by submerged object
equation for buoyant force
FB = (density of fluid) x (volume) x (g)
floating object -
submerged portion of object =
density of object/density of fluid
How much of an object will float in water if its specific gravity is 0.4?
does buoyant force change with depth?
What is the apparent mass on an object (when it is submerged)?
mass of the fluid displaced
thats why we weigh so little in water
equation for fluid flow
Q = (area)(volume)
does fluid flow faster in a wider pipe, or a more narrow pipe?
ideal fluid flows at a constant rate
K = Pressure + (density)(g)(h) + (1.2)(p)(v2)
K is constant, specific to fluid in a flow
surface tension and temperature
increase temperature = weaker surface tension
formula for stress
formula for strain
change in dimension/original dimension
what are stress and strain
stress is done on an object
strain is how the object responds
modulus of elasticity
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