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F
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Eq
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max
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Fnetx=
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Momentum
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P=mv
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Work-Energy Theorem
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W=ΔKE
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Ohm's Law
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V=IR
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Young's Modulus (Y=)
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(F/A)/(Δl/lo)
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Potential Difference
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V=W/Qwork/unit charge
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Sin(theta_critical) =
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n2 / n1
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elastic collision
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KE is conserved
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What is average acceleration?
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Picture.
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Young`s Modulus
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modulus for tesnsile stress
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Radiation
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Heat transfer by electromagnetic waves, which can travel through a vacuum.
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Newton seconds, Ns
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Units of impulse?
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SI unit for length
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Meter (m)
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What is the unit circle?
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Charges repel each other
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Positive FE means?
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Adhesion
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Type of attractive force that molecules of a liquid feel toward molecules of another substance, such as in the adhesion of water droplets to a glass surface.
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base x height
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Area of a triangle
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Capacitance
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Capacitance= charge/voltage ; C = Q/V
[C] = farad (F) ; 1F = 1C/V
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centripetal acceleration
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radial component of acceleration
a = v2/r
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joules/Coulumb which is Volt(V)
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Units for Potential is?
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RMS Voltage
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V(max)/(√2); average voltage in an AC circuit, where voltage alternates in a sinusoidal pattern.
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________ is a numerical description of how far apart objects are at any given moment in time.
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distance
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Power SI symbol and units
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Watt(W) 1W=1 J/s
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force of Sliding Friction
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f sliding = μkN
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What are the units of gravitational potential energy?
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joules
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gamma decay
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high energy photons; release doesn't change A or Z
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What are the image characteristics of an object located in front of C in a concave mirror?
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conservative force
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a force that doesn`t change mechanical energy when worked
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On an incline, what is the equation for the F of weight in the parallel direction?
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Fwsin(x)
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Electric Dipole
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Result of having two charges of opposite sign and equal magnitude separated by a short distance d.
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Spherical Mirror
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Curved mirror that is essentially a small, cut-out portion of a sphere mirror, having a center of curvature C and a radius of curvature r.
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Elastic Collision Equations
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Momentum and Kinetic energy are conserved:
v(1)=[u(1)x[m(1)-m(2)] + 2m(2)u(2)]/ [m(1)+m(2)]
v(2) can be derived from v(1) as approach velocity and separation velocity must have the same absolute value.
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Gauge pressure
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Gauge Pressure = total pressure- atm pressure
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From slow medium to fast medium, the incident of light goes __ from the normal.
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away
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constructive interference
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two waves in phase interact and amplitudes add
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What are inelastic collisions?
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◦Conservation of momentum only. ◦Kinetic energy is lost during an inelastic collision due to heat or other non-conservative force. ◦Collisions in everyday life are inelastic to varying extents. ◦When things stick together after a collision, it is said to be a Perfectly inelastic collision. But many inelastic collisions just involve objects who have the same equal and opposite or the same velocities (from momentum), but lower speeds (from kinetic energy). The equation for inelastic collisions is: m1v1 + m2v2 = (m1+m2)*vfinal. The final velocity of the stuck together masses (m1 and m2) is vfinal. v1 and v2 are the initial velocities of the masses. With ELASTIC collisions, note this question: With one mass AT REST, as the mass of the incoming mass increases, how do the final velocities of each mass relate to the initial velocity of the incoming mass? Answer : As the incoming mass gets bigger .. it's velocity stays the same as the initial velocity that it had, and the other mass's velocity will start to approach twice the initial velocity of the incoming mass! Also, say you have an object m2 with a mass three times greater than m1, and m2 is at rest and m1 strikes m2, what is the velocity of m2 in an elastic collision? Well, first know that m1 has a smaller mass than m2, so it will bounce in the opposite direction. Because of this, it's final momentum is going to be negative. The m2 will have a positive momentum. So when figuring out the velocity of m2, know that whatever the velocity is, it has to create a momentum that is greater than the initial momentum of m1, because the final momentum of m2 and final momentum of m1 (which is negative) have to equal the initial momentum of m1. Once again, it's not the individual momentums that are conserved (and KE for elastic collisions), but the sum of the momentums and KEs.
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What are inelastic collisions?
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For inelastic collisions, initial momentum is equal to final momentum.
The initial momentum of an isolated system equals the final momenturn of an isolated system. However, because momentum is a vector, we must pay close attention to its direction. In a 2 dimensional system, if we have momentum in both the x and y
directions, one equation is required for each direction.
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Work
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• transfer of energy via a force
W = F•d•cosθ --> for all forces except friction
Frictional Forces are the exception to the equation because they ∆ internal energy as well as mechanical energy.
OR
W = F•d
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Current
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Flow of charge as it moves across a potential difference (voltage), denoted as I and measured by the amount of charge passing through a conductor over a unit of time: Δq/Δt
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A ________ is the path a moving object follows through space.
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Trajectory
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(m1x1 + m2x2 + m3x3...)/(m1 + m2 + m3)
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xcenterofmass
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converging lens = convex lens
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diverging lens = concave lens
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sound level
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β = 10 log I/I0
I0 = 10-12 (hearing threshold)
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How do you determine the direction of a vector from Cartesian coordinates?
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This formula
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What is the conductivity theory?
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◦Conductivity is affected by electrolyte concentration: No electrolyte, no ionization, no conductivity. Optimal concentration of electrolyte, greatest conductivity due to greatest mobility of ions. Too much electrolyte, ions are too crowded, less ion mobility, less conductivity. Conductivity is affected by temperature: In metals, conductivity decreases as temperature increases. In semiconductors, conductivity increases as temperature increases. At extremely low temperatures (below a certain critical temperature typically a few degrees above absolute zero), some materials have superconductivity - virtually no resistance to current flow, a current will loop almost forever under such conditions. When superconductive, a material has an electrical resistance of exactly zero. ◦Conductivity (σ) is the inverse of resistivity (ρ). Place a capacitor inside a solution, the solution will conduct a current between the plates of the capacitor, thus you can measure the conductivity of a solution using a capacitor.
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The force inbetween two molecules
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FE of Electrical Force(sbscrpt E) is?
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electric field between the plates of a parallel plate capacitor
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E = V/d
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Impulse (J)
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Impulse = force x time
J = FΔt ; Impulse is a vector quantity
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What does resistance depend on?
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length (R increases as L increases)
cross sectional area (R decreases as A increases)
temperature (R increases with temperature)
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What is dispersion?
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The speed of light is slower in various materials than it is in a vacuum or outer space. When the light passes into a material at an angle, the light beam is bent or refracted according to Snell's Law and the index of refraction of the material. But also, the speed of light through a material varies slightly with the wavelength or frequency of the light. Thus, each wavelength is refracted at a slightly different angle when passing through a material at an angle. This spreading out of the beam of light is called dispersion or chromatic dispersion. This can be seen when sunlight passes through a glass prism. Dispersion: change of index of refraction with wavelength. Blue light refracts more than red light in a prism. White light passes through a prism and gets split into colors of the rainbow due to dispersion. Generally the index of refraction decreases as wavelength increases, and blue light travels more slowly in the transparent material than red light. Longer wavelengths (lower frequencies like red light) move faster through a medium than shorter wavelengths (higher frequencies like blue/violet light) and so the longer wavelengths bend less dramatically at the media interface because they move quicker through it.
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Systems not in Equilibrium
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• the center of mass is accelerating or its parts are accelerating rotationally.
∑F = ma
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Newton's Third Law
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If a body exerts a force (F) on another body, there will be an equal and opposite reaction (-F).
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KE(Initial) + PEi = KE(final) + PEf
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Conservation of Total Mechanical Energy Equation
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Addition in parallel
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1/Rp = 1/R1 + 1/R2 .... 1/Rn
Cp = C1 + C2 ... Cn
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What is power?
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◦Power is the rate of work, or work over time: P = W/t
◦The unit for power is the Watt, or W (don't confuse this W with the shorthand of work).
◦Watt = Joule / second
Power is also: P = Fv. Power is equal to Force multiplied by velocity. Why you ask? Because work is equal to Fd, and since power equals W/t = (Fd)/t, power is equal to Fv.
The rate of doing work is equal to the rate of using energy since the a force transfers one unit of energy when it does one unit of work.This calculation is only for cases where the force is in the direction of the velocity, and there are many cases where that is not so. Then for instantaneous power, you just multiply the product of force and velocity by the cosine of the angle between them to get the power P = Fcos*theta *v. In the more general cases where everything varies, one often calculates the work first and then divides by the time to get the average power. A constant force that moves something at a constant velocity could be a frictional force.
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Is a Convex lens converging or diverging?
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Converging (bc the surface is convex)
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force of Static Friction
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f static, max = μsN
There is only a formula for the maximum force of static friction
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How do you find a projectiles total time in flight?
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y = voyt + 1/2at2
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What is Bernoulli’s equation?
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P + ½ρv^2 + ρgh = constant. This is constant throughout.
The Bernoulli equation is for an IDEAL fluid and it states that where points 1 and 2 lie on a streamline: 1)the fluid has constant density 2)the flow is steady, and 3) there is no friction. The Bernoulli Equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids. The qualitative behavior that is usually labeled with the term "Bernoulli effect" is the lowering of fluid pressure in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy. In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
P = static pressure - it's the energy stored in the work of compressing - it's the energy the fluid can expend in performing work as it decompresses from one area to another- it's like the potential energy of the fluid after it has been compressed. ½ρv^2 is the velocity pressure or speed of the fluid, (associated with the kinetic energy) and ρgh is the fluid's potential energy. P + ½ρv^2 is the total pressure of the system. The h in the second term is similar to gravitational potential energy and is measured from the bottom to the top (opposite from the direction of measurement of y in P = ρgy. The zero value for h can be chosen arbitrarily. If a spigot is attached to a tank of fluid is opened, and we choose h = 0 to be the point of the spigot, the velocity of the fluid coming from the spigot can be derived from Bernoulli's equation as v = sqrt(2gh) because all of the potential energy in the container (ρgh) is converted into kinetic energy.
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What is Bernoulli’s equation?
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The constant is specific to a fluid in a given situation of flow, and P, h, and v refer to the pressure, height, and velocity of the fluid at any given point. WARNING: h in Bernoulli's equation is NOT the same as y in P = ρgy. h is the distance ABOVE some arbitrary point; y is the distance beneath the surface. If we multiply any of the terms in Bernoulli's equation by volume, we get units of energy. The second term ρgh gives the gravitational potential energy per unit volume (mgh/V). The third term gives the kinetic energy from the uniform translational motion of the molecules per unit volume (1/2mv^2/V). The first term, pressure, is the energy per volume from the random motion of the molecules. Because energy is conserved in ideal fluid flow, the total energy must remain constant, thus the sum of the 3 terms is constant throughout the fluid. P = ρgh in the second term of Bernoulli's equation is NOT the pressure, it is the potential energy of the fluid. P = Pa + ρgy is the absolute pressure.
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Length of lines is magnitude; Lines are how positive charges would act so arrows point toward negative charge and away from positive
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For an electric field the convention of the vector lines is?
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m₁v₁ + m₂v₂ = m₁v'₁ + m₂v'₂
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Pi = Pf can be written as
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What is the Reflection from plane surface for geometric optics?
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Angle of incidence equals angle of reflection. Mirrors completely reflect light. Going from one medium to another results in partial reflection of light. The reflection at any plane surface is found to obey the laws of reflection. The laws of reflection are: 1) The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane. 2) The angle of incidence is equal to the angle of reflection. The angle of reflection is separate from the angle of refraction.
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Object's total mechanical energy will remain throughout the motion
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If the forces acting on an object are only conservative then?
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Describe the force experienced by a charge in an electric field
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F = qE
positive - force is in direction of the field
negative - force is opposite direction of the field
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What is friction (static and kinetic)?
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Friction is a force that is always in the direction to impede motion. μ is the coefficient of friction and N is the normal force. •Like any other force, friction is a vector. However, its direction is easy because it's always opposite to motion. •The coefficient of friction is intrinsic to the material properties of the surface and the object, and is determined empirically. •The normal force at a horizontal surface is equal to the weight •The normal force at an inclined plane is equal to the weight times the cosine of the incline angle. If there is a block on a board and the board from a horizontal position and raise one end of it, the block will slide. The only way to measure the static friction is to find out the normal force, which is only calculated by finding the angle of the board. A board tilted at an angle with respect to the horizontal causes a component of the gravitational force on the block to point down the length of the board. The coefficient of static friction is the ratio of the force along the board to the normal force (which also changes because of the angle). The mass of the block cancels in the ratio. Only the angle of the tilt determines the static friction result. Not the time for the block to slide down the board, not the distance the block slid down the board before coming to rest, and not the mass of the board. •We can walk and cars can run because of friction.
•Lubricants reduce friction because they change surface properties and reduce the coefficient of friction.•Every time there is friction, heat is produced as a by-product. The FORCE OF FRICTION (Static and kinetic) is EQUAL AND OPPOSITE TO THE APPLIED FORCE!!! So, if you have a weight at rest, there is no force of friction. It's chillin. If you have something pushing that object, but the object doesn't bulge, then the force of friction is equal the the amount of force used to push that object. That force of friction = μN. N could be the weight of the object, which could be a larger force than the applied force. The coefficient of static friction is what divides the N and make it equal to the force of friction (for instance, the weight could be 50 N and the applied force could be 10 N, so the coefficient of friction is 1/5 where Force of friction = μ*50N = 10N, and μ = 1/5. When I figure out frictional forces, realize that the MAXIMUM static frictional force is F = μFn, where Fn is the normal. But the ACTUAL static frictional force could be less and is the applied force. So applied forces can be different values that are less that what the maximum force is. Once the applied force is beyond the maximum static frictional force, the object moves.
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No, only forces exerted on the object of mass m is apart of Fnet
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Is the force exerted by the object included in the Fnet?
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What is the Conservation of energy ?
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◦The total amount of energy before = the total amount of energy after.
◦Gravitational potential energy is converted to kinetic energy as an object falls, but the total amount of energy stays the same.
◦Kinetic energy is converted to heat and sound energy as a crate slides to a stop on a rough surface.
Kinetic energy at the highest point of a projectile is not zero - only the vertical velocity (and acceleration and force) is zero. Even though kinetic energy is = 1/2 mv^2, the v that we use to find kinetic energy is the horizontal velocity - it stays the same throughout the whole trip of a projectile.
Always try to solve a mechanics question first by using conservation of energy.
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What is the Conservation of energy ?
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A system is any defined area that we choose to consider separately from the rest of the universe. The rest of the universe is called the surroundings. Together, mass and energy define the three basic systems in physics: the open system, where
energy and mass are exchanged with the surroundings; the closed system, where energy is exchanged with the surroundings but mass is not: the isolated system, where neither energy nor mass is exchanged with the surroundings. By definition, although the form of energy in an isolated system may change, the energy of an isolated system is conserved. Thus the Law of Conservation of Energy states that, since the universe is an isolated system, the energy of the universe remains constant. Conservation of energy does NOT say that a certain type of energy (i.e.kinetic energy or potential) must be conserved, just that the SUM of all energy types must remain constant in an ISOLATED system. In a closed system, the change in the sum of all energy types must equal the energy leaving or entering the system. Energy can enter or leave a closed system only as work or heat.
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The i means electrical point vector is moving in the positive x direction from q, so -i means it's moving in the negative x direction away from q
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What does the i stand for in E= (3600N/C)i?
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What is the speed of a standing wave?
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A vibration in a string is a wave. Vibrations are standing waves in a string. Tense, light strings can produce faster standing waves.
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What is the formula for kinetic energy?
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KE = (mv squared)/2 ***mv is mass times velocity
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