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