PHYS 231: Exam 3
over its base of support
An object will be stable if its center of gravity lies where?
not change, decrease
An old-fashioned tire swing exerts a force on the branch and a torque about the point where the branch meets the trunk. If you hang the swing closer to the trunk, this will ____ the force and ____ the torque.
will read low
A car speedometer that is supposed to read the linear speed of the car uses a device that actually measures the angular speed of the tires. If larger-diameter tires are mounted on the car instead, how will that affect the speedometer reading?
F=k∆l
Hooke's law equation
true
True or false: A fluid exerts pressure in every direction.
true
True or false: Total mechanical energy of a simple harmonic oscillator is proportional to the square of the amplitude.
true
True or false: angle of reflection = angle of incidence
density of water, volume of object in water
When using mg to calculate buoyancy force, what are p and V when calculating m?
Y=stress/strain
Young's modulus formula in relation to stress and strain
P=PG+P₀
absolute pressure (P) equation using atmospheric pressure (P₀) and gauge pressure (PG)
rigid
an object is more ____ if it has a higher Young's modulus
α=∆ω/t
angular acceleration formula
L=Iω
angular momentum formula
ω=θ/t
angular velocity formula
ω=2πf=2π/T
angular velocity formulas (2)
F=pgA∆h=mg
buoyant force formulas (2)
p=m/V
density formula
kg/m³
density units
displacement
distance (x) of the mass from the equilibrium point at any moment
wavelength
distance between two successive crests
PE=1/2kx²
elastic potential energy formula
intensity
energy per unit time carried across unit area
F=ηA(v/l)
equation for the force required to move something through a viscous fluid using the coefficient of viscosity (η), area, velocity, and distance
p₁A₁v₁=p₂A₂v₂
equation of continuity
P(out)=P(in)
equation representing Pascal's principle
restoring force
force that a spring exerts on a mass that actins in the direction of returning the mass to the equilibrium position
F=kx
formula for force needed to stretch a spring a certain distance
T=2π√m/k
formula for period of oscillation for a mass on the end of a spring
f=1/T
frequency formula
f=ω/2π
frequency formula
viscosity
friction within a fluid
Iα1/r²
intensity formula
v=rω
linear velocity formula
∆m/∆t
mass flow rate formula
amplitude
maximum displacement; greatest distance from the equilibrium point
amplitude
maximum height of a crest, or depth of a trough, relative to the normal equilibrium level
1/100 m
meters equivalent to 1 cm
1/10,000 m²
meters equivalent to 1 cm²
1/1,000,000 m³
meters equivalent to 1 cm³
torque
moment of the force about the axis; a twisting force that causes rotation
frequency
number of cycles per second
frequency
number of full wavelengths (crests) that pass a given point per unit time
frequency
number of revolutions per second
T=1/f
period formula
T=2π√l/g
period of a simple pendulum of length l
P=P₀+pg∆h
pressure equation being measured by a manometer
P=F/A=pgh
pressure formulas (2)
Pa
pressure units
Pascal's principle
principle stating that if an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount
Archimedes' principle
principle stating that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by that object
Bernoulli's principle
principle stating that where the velocity of a fluid is high, the pressure is low, and where the velocity is low, the pressure is high
F(out)/F(in)
quantity representing mechanical advantage
a=v²/r=ω²r
radial acceleration formulas (2)
2π
radians in a 360° circle
longitudinal
refers to a wave in which the oscillations are along the line of travel
transverse
refers to a wave in which the oscillations are perpendicular to the direction in which the wave travels
simple harmonic motion
refers to motion in any oscillating system for which the net restoring force is directly proportional to the negative of the displacement
damped
refers to motion that has friction present; maximum displacement decreases in time, and the mechanical energy is eventually all transformed to thermal energy
sinusoidal
refers to simple harmonic motion having a displacement that is a function of time that follows a sine curve
resonance
refers to the amplitude of oscillation being very large if the frequency of the applied force is near the natural frequency of the oscillator
mr²
represents moment of inertia
F=-kx
restoring force formula
1/2Iω²
rotational kinetic energy formula
∆l/l₀
strain formula
F/A
stress formula
T=Fr(sinθ)
torque formula
E=1/2mv²+1/2kx²
total mechanical energy formula in simple harmonic motion
net force is zero, net torque is zero
two conditions for static equilibrium
v=λf
wave speed formula
A
Bars A and B are attached to a wall on the left and pulled with equal forces to the right. Bar B, with twice the radius, is stretched half as far as Bar A, Which bar has the larger value of Young's modulus?
P₁+1/2pv²₁+pgh₁=P₂+1/2pv²₂+pgh₂
Bernoulli's equation
period
time required for one complete revolution
cycle
1 of these refers to the complete to-and-fro motion from some initial point back to that same point
period
time required to complete one cycle
Q=πR⁴(P₁-P₂)/8ηl
Poiseulle's equation for volume rate of flow (Q) using the radius of the inside of the tube (R), coefficient of viscosity (η), pressure, and length of the tube
law of conservation of angular momentum
Principle: The total angular momentum of a rotating object remains constant if the net torque acting on it is zero.
100 rad
Starting from rest, a wheel with constant angular acceleration turns through an angle of 25 radians in a time t. Through what angle will it have turned after time 2t?
a=rω/t=rα
tangential acceleration formulas (2)
equilibrium position
the position of the mass at a point where the spring exerts no force on the mass