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translational motion:
distance, velocity, acceleration. time
x = x0 + v0t + (1/2)at2
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translational motion:
velocity, acceleration and distance
v2 = v02 + 2ax
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translational motion:
velocity, acceleration and time
v = v0 + at
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how does a projectile stay in motion? what keeps it in motion?
inertia
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peak height of a projectile
v0 = sin(0) - sq.rt.(2gh)
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horizontal distance traveled of a projectile
x = vt . cos(0)
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peak velocity
no velocity, but acceleration = 10
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PE and KE of projectile object at its peak
- PE is maximized
- KE is minimized
(energy must be conserved)
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projectile path is independent of....
mass
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two objects launched with the same velocity will...
hit the ground at the same moment
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what determines the time of flight?
vertical velocity
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range of projectile is maximized at what angle from the horizontal?
450
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symmetry of projectile says what? (speed wise)
upward mirrors downward -
initial speed = final speed
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air resistance is greater on (surface area, shape, and speed)
- larger surface area
- irregularly shaped
- greater speed
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does mass affect force or path of air resistance
force = no
path = yes
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how does greater mass affect air resistance
force is the same, so it decreases acceleration
(F=ma)
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centripetal force (equation)
F = m . v2/r
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inertia
tendency of an object to stay in present state of motion
(keeps projectile in motion)
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law of universal gravitation
F = G(m1m2)/r2
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friction points in what direction?
always parallel to surface
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equation for torque
t = F r sin0
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if the board has mass, what do you do with torque?
F=mg at center of board
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equation for work (not for gases)
W = Fd cos0
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what direction is friction (relative to work)?
friction does negative work!
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work done lifting an object
W = Fd = mg x h
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what is gravitational potential energy?
work done by gravity:
change PE = -W
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energy and power
energy = work + heat
so, P = (w + q)/s
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1 revolution is equal to
2 pi r
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equation for angular momentum
L = l x m x v
l = lever arm, mv = linear momentum
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elastic collision
mechanical energy is conserved
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inelastic collision
mechanical energy is lost to internal energy (heat)
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perfect inelastic collision
2 objects stick together
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reverse inelasitc collisions (object dissipates into 2 sep. objects). In what direction do they travel
opposite to each other
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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
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what is impulse?
change in momentum
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Machine: inclined plane (how is work minimized?)
straight up: W = ugh
ramp: W = mg x sin x h
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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
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Machine: lever (torque)
what does F need to equal to lift mass?
F = mg in opposite direction
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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)
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In a pulley, what is the tension in the rope?
constant
Tension = Force
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In a double pulley system, what is the force required to lift mass m?
F = T
T = 2mg
F = (mg)/2
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alpha decay
2 protons, 2 neutrons
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traveling of alpha particle
not far
stopped by skin, paper
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beta decay
expulsion of an e-
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positron
B+ is emitted (-1 atomic #)
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electron capture
gain e- (-1 atomic number
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frequency of a gamma particle
high frequency particle
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fussion combining 2 (?) from (?)
combining 2 nuclei
from a heavier nucleus
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fission
splitting a single nucleus into 2 lighter nuclei
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where does energy for fusion and fission come from?
mass defect
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density formula
density = m/v
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density constant for gases and liquids?
constant for liquids and solids
change for gases, because they are compressible
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What is specific gravity?
density of a substance compared to density of water
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so specific gravity of water is
1
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formula for fluid pressure
P = F/A
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Do fluids at rest have uniform density in a sealed container?
yes
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What is the pressure experience by fluids at rest with uniform density?
P = density x g x y
y = depth of fluid
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Where is pressure greatest for a fluid at rest?
greatest depth (P=pgy)
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What if you have many fluids layered in a sealed container?
P = (pgy)1 + (pgy)2 + (pgy)3...........
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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
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hydraulic lift (equation)
pressure is transferred completely:
F1/A1 = F2/A2
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What is the velocity of a fluid flowing (if you don't know rate or area)?
v = sq.rt (2gh)
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buoyant force
upward force acting on a submerged object
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what is buoyant force equal to? (not equation)
weight of fluid displaced by submerged object
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equation for buoyant force
FB = (density of fluid) x (volume) x (g)
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floating object -
submerged portion of object =
density of object/density of fluid
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How much of an object will float in water if its specific gravity is 0.4?
60%
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does buoyant force change with depth?
No
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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
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equation for fluid flow
Q = (area)(volume)
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does fluid flow faster in a wider pipe, or a more narrow pipe?
narrow
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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
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surface tension and temperature
increase temperature = weaker surface tension
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formula for stress
force/area
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formula for strain
change in dimension/original dimension
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what are stress and strain
stress is done on an object
strain is how the object responds
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modulus of elasticity
stress/strain
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