UWorld Mechanics and Energy

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157 Terms

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Potential Energy

A form of stored energy that depends on the spatial position or configuration of objects. The capacity of an object to do work in the future based on work completed in the past. ______ accumulates in mechanical system because of the work performed by a force applied over some distance.

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Gravitational potential energy accumulates when:

The height of an object increases because a force must act against gravity to raise the object.

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Stretching or compressing a spring away from its equilibrium point:

Increases its elastic potential energy. The potential energy in stretched or compressed springs explains why harmonic oscillations

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Elastic Potential Energy Equation

U(el) = ½ kx² (k = spring constant, x = spring displacement)

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Elastic Potential Energy

Refers to the potential energy of springs and other elastic objects.

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Elastic Potential Energy Increases:

Following the application of a stretching or compressing force that displaces a spring from its equilibrium position.

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Power Equation

Power = Work/Time (Watt = Joules/Second)

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Power (Translational Motion) and Power (Mechanical Work)

Power = (Force x Distance) / Time = Force x Velocity

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Mechanical Work Equation

W = F x d x cos Theta

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Cardiac Output Equation

CO = A x v (A = cross sectional area of aorta) (v = velocity of the blood)

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for cm³ / L there is:

1000 cm³ / L

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Kinetic Energy Equation

KE = 1/2mv² (Joules kg(m²/s²)

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Exercise (Blood Flow)

During exercise, blood flow to the skin increases to maintain normal body temperature. Excess body heat generated during exercise can be transferred to the surface to the surface through convection and dissipated into the environment through radiation.

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The molar volume for all gases at standard temperature and pressure

22 L / mol

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Displacement (Delta X)

Delta X = Xf - Xi = (v)(t). The area under the curve of a. velocity (y axis) vs time (x axis) graph is equal to displacement.

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Displacement (graph equation)

Displacement = Rectangle Area + Triangle Area

Displacement = R base length x hR eight length + ½ T base length x T height length

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Conservation of Energy

E = KE + PE = constant

Potential Energy Equation: PE = mgh

Kinetic Energy Equation: KE = 1/2 mv²

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Torque

The tendency of an applied force to cause the rotation of an object around a pivot point located at some radial distance from where the force is applied.

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Torque Equation

r(f)(sin)(theta)

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Rotational Equilibrium

When the sum of all torques acting on an object is equal to zero.

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Left Torque = Right Torque

F r sin theta (right side values) = F r si5n theta (left side values)

F = mass x gravity

Add torques if there are multiple torques on one side

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Frictional Forces

Attractive intermolecular forces between the atoms of two surfaces contribute frictional forces that oppose motion along the interface between two objects that are in direct contact with another.

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Static Equilibrium

Motionless, a frictional force that resists the initiation of motion is called static friction.

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Static Friction Equation

F(s) = (Normal Force)(Static Coefficient)

If the force applied to an object does not exceed Fs, the object will not move. If Fs is exceeded, the object will accelerate and static friction becomes kinetic friction.

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Tension

T = Weight = mg

Horizontal Component of Tension (Tx = T cos Theta)

Vertical Component of Tension (Ty = T sin Theta)

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Tension and Force for a block in static equilibrium

F(s) must be equal to T(x) and F(n) + T(y) = weight of other block.

So coeffecient (static friction)(vertical block - T(y) = T(x) or F(s) (same thing)

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Gravitational Potential Energy

Measures the potential of gravity to do work on a mass. Conventionally, gravitational potential energy is expressed using negative numbers and is inversely proportional to the radial distance between masses. U = - (G)(M)(m)/r)

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Periodic Motion

Occurs when an object moves in a cyclical fashion, returning to the same location after a certain period of time. Is modeled in the terms of wave motion where the cycle of motion is defined as a period (T).

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Frequency (f) Equation

f = 1/T

(cycle/time in Hz)

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Work-Energy Principle

The total work (W) done by a force is equal to the charge in kinetic energy (Delta KE) of the object. W = Delta KE

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Conservation of Energy in Mechanical Systems

Delta KE = - Delta PE

Delta KE + Delta PE = 0

KEf - KEi + PEf - PEi = 0

KEi + PEi = KEf + PEf

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The kinetic energy of an object launched upward in gravity is converted:

into gravitational potential energy

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When R and f is perpendicular Theta is equal to:

90 degrees and the torque is maximal

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When R and f is parallel Theta is equal to:

0 degrees and the torque is zero.

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Clockwise or Counterclockwise Direction (Torque)

The direction the force is applied

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Electromagnetic Waves (EM)

EM waves are arranged by frequency or wavelength in the EM spectrum, ranges from very low frequency/long wavelength to high frequency/small wavelength.

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EM Spectrum ,

Big Wavelength/Low Energy to Small Wavelength/High Energy

  1. Radio

  2. Microwaves

  3. Infrared

  4. Ultraviolet

  5. X Rays

  6. Gamma

Raging Martians Invaded Venus Using X-ray Guns

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Photon Energy

When EM waves are emitted or absorbed they behave as photons.

Photon Energy = (h)(f)

h = Planck’s constant

f = frequency

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Radiation Energy (Temperature)

Radiation is related to the temperature of the object that emits radiation. Hotter objects radiate waves at the higher frequency region in the spectrum and colder objects radiate waves at the lower frequency region.

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Power Equation

Power = Energy / Time

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average veloctiy

v(x)f -v(x)i / t

v(y)f -v(y)i / t

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Hooke’s Law

Elastic Force = -kx

k = spring constant

x = displacement from equilibrium point

Models the elastic forces generated by sprnigs

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Newton’s Second Law of Motion

An object will accelerate if the net force acting along each axis of a given coordinate system is a nonzero quantity

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Dynamic Equilibrium

Describes an object moving at velocity without acceleration. Free body diagrams can be used to assess the forces.

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Parallel Angle of Incline is:

Sine

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Perpendicular Angle of Incline is:

Cos

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Static Equilibrium of Torque on Fulcrum Equation

Torque = CCW (T) - CW(T) = 0

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Pressure Equation

Pressure = Force / Area

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If the torque on one side of the fulcrum decreases:

The torque on the other side of the fulcrum must also decrease for the system to remain equilibrium.

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Mechanical Work Equation

Work = (Force)(Distance) = - (Pressure)(Volume)

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In a graph of force on object vs distance on object

The work performed on the object is equal to the area under the curve.

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Hooke’s Law (Derived)

F = k/x

k = F/x = slope = (F2 - F1) / (x2 - x1)

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Power Equation

Power = Work/Time or Power = Energy/Time (Watts J/s)

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Elastic Potential Energy (Spring)

Elastic Potential Energy = ½ kx²

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Work Energy Theorem

Work = Delta PE = mg (delta)h

P = W / t = mg (delta)h / t

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Work (from area under the curve)

Work = triangle area + rectangle area

triangle area = ½ (triangle height)(triangle base)

rectangle area = (rectangle height)(rectangle base)

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Mechanical Advantage

The force amplification that occurs through the use of a device/mechanical system. The mechanical advantage is related to the number of load sharing pulleys but not fixed pulleys.

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Heat of Fusion

The amount of heat energy required to transform a substance between its liquid phase and solid phase. The material remains at its freezing temperature during this phase change until it is in its solid form.

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Snell’s Law

The refraction of light is given by snell’s law. n1 sin theta1 = n2 sin theta2

(n1 = refractive index of air, theta1 = incident angle of light, n2 = refractive index of glass, theta2 = incident angle of air)

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Refractive Indexes

Light travels between materials and undergoes refraction, it bends as it passes to a new material. The refractive index depends on the speed of light with agreater refractive index indicating a slower speed of light.

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Work Equation (Pull object with constant force along horizontal surface)

Work = (Force)(Distance)

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Newton’s First Law of Motion

Net force of an object is zero when it is in constant motion

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Reflection of light from mirror equation

Angle of incident light = Angle of reflected light

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Block Sliding on an Incline (Steps)

F parallel = 0 = F(w)sin theta - Fk (Fk = F(n) and k constant)

F perpendicular = 0 = F(N) - F(w) cos theta

get k constant alone so k constant = F(N) / F(w)

plug in Fw sin theta / Fw cos theta and cross out and solve

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Doppler Effect

Occurs when a periodic signal (sound or light) is perceived by an observer to have a different wavelength due to the relative motion between the source and the observer. The magnitude of the change in wavelength is proportional to the relative speed between source and observer.

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If the sound/light source is moving toward the observer:

the perceived wavelength of the signal decreases.

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If the sound/light source is moving away from the observer:

the perceived wavelength of the signal increases.

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Y Forces and X Forces (Static Equilibrium)

Y forces = (+ y forces) + (- y forces) = 0 (- y force = gravity)

X forces = (+ x forces) + (- x forces) = 0

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Displacement Equation

Delta x = x(f) - x(i) = v(x) multiplied by t

Delta y = y(f) - y(i) = v(y) multiplied by t

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Velocity

A vector quantity characterized by magnitude and direction

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Conservation of Energy Equation

1/2mv² + mgh = 1/2mv^2 + mgh

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Law of Conservation of Energy

Energy cannot be created or destroyed, only transformed from one form to another.

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Electric Force F(E)

F(E) on a charged object equals the product of the object’s charge (q) and electric field (E)

F(E) = (q)(E)

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Electric Field

The electric field exists when there is a difference in the electric potential (Voltage) between two locations. The component of the electric field in the y direction is:

E(y) = Delta V / Delta y

change in voltage over change in distance

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Newton’s Second Law

F = ma

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Period Equation

Period = Distance / Speed

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Distance needed to complete one cycle in a circle

Is equal to the circumference so d = 2 pi r

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The area under the curve in a graph of force versus distance equa;s:

the work done on an object

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Power Equation

Power = Energy / Delta Time

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Distance and Kinetic Energy

Distance is proportional to Kinetic Energy

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Instantaneous Velocity (Graph)

The line with the steepest and most positive slope has the greatest instantaneous velocity.

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Scalar Quantities

Physical properties with only size or magnitude. (time and mass)

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Vector Quantities

properties with only direction and magnitude. (velocity)

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Vector Addition

Displacement is a vector and can be added.

d = d(1) + d(2) or d = (x1 + x2) , (y1 + y2)

The magnitude of any vector is equal to the vector squared so:

d = sqrt( x2 + y2 )

d total = d (of one given) + d (of second given)

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Determining Velocity from plot of position and time

The slope of the position vs time is equal to the velocity. The velocity of the subject is greatest where the slope of the plot is greatest.

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Work Equation

W = Fd = mgd

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When walking towards laser Doppler sensor:

Higher frequency and shorter wavelength

f = (c + v) F(t) / c

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When walking away from laser Doppler:

Lower frequency and higher wavelength

f = (c - v) F(t) / c

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Law of Conservation Energy

E = PE + KE = constant

E = PE initial + KE initial = PE final + KE final

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Cardiac Output Equation

Cardiac Output = Heart Volume + Stroke Volume

Stroke Volume = End Diastolic Volume - End Systolic Volume

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Static Equilibrium and Pivot Point

For an object in static equilibrium, the sum of all torques exerted on the object equals zero. The torque on an object is equal to the product of the distance from the pivot point that the force is applied, magnitude, and sine angle.

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Translational Motion Equation (Displacement/Delta X)

v = v(0) + at

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Translational Motion Equation (Velocity)

v² = v(0)² + 2a (delta x)

For a projectile traveling straight upward: delta x = height and a = gravity, and v@ = 0 so the new equation is: 0 = v(0)²

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Power Equation

Power = (Force)(Velocity)

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Magnification of Two Lens System (Equation)

M = (M1)(M2)

M = Magnification

M1 = Lens 1 of Magnification

M2 = Lens 2 of Magnification

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Magnification Equation

M = i / o

i = image, o = object

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Distance Ratio

The positions of two objects circling a central point can be represented by two vectors. The objects are nearest to each other when the position vectors align in the same direction and farthest away from each other when position vectors in opposite direction.

Distance Ratio = Distance Short : Distance Far

Distance Ratio = Distance 1 - Distance 2 : Distance 1 + DIstance 2

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Vector Components

V(x) = v cos theta

V(y) = v sin theta

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Work and Tension Equations

Work = (F)(d)(cos theta) or (T)(d)(cos theta)

Tension can be swapped with force

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Torque Equation

Torque = r f

Torque 1 = Torque 2 + Torque 3 (r = distance/cm and F = newtons/force)

r1 F1 = r2 F2 + r3 F3 (force could be mg)