Newton's First Law (Inertia)

An object in motion at constant velocity or at rest will stay that way, unless acted upon by an external force.

Newton's Second Law

F(net) = ma

Newton's Third Law

F(AB) = -F(BA)

Force on X

Product of (mass of X) and (acceleration of X) F=ma

If you have a POSITIVE net acceleration, he normal force must be ( > or < ) m*g

Greater than (>)

*Fill in the blank with: ( > ) or ( < )*

If you have a NEGATIVE net acceleration, the normal force must be _______ m*g

Less than (<)

F(net) =

F(net) = F(N) - mg = m a(net)

Air resistance

Function of v^2 and k, where "k" is proportional to the density of air and the surface area of the mass.

Kinetic friction

f(k) =u(k)F(n)

Static Force: F(s)

F(s) = F(applied)

Fs(max)

minimum force required to get object to move = u(s)F(n)

Static and kinetic co-efficient relationship

µ_{s} is ALWAYS > µ_{k}

What forces are acting on a box at rest on an inclined plane

f(s) = f(applied) = mgsin(theta)

fs(max)=

u(s)mgcos(theta)

As the angle of an inclined plane (θ ) increases, what happens to the

a) applied force,

b) static force f_{s}

c) MAXIMUM static friction (f_{s,max})?

As θ increases,

a) f_{applied} increases,

b) the static force increases

c) f_{s,max} DECREASES

Gravitational Force

F= (Gm_{1}m_{2})/r^{2 }

*Two masses will exert an attractive force on one another inversely proportional to the square of the distance between them.*

Uniform Circular Motion

The net force on an object moving at a constant speed on a circular path points toward the center of the circle.

F(centripetal)

F(c)=(mv^2)/r

Centripetal Acceleration

a(c) = v^2/2

Circumference of a circle

C = 2(pi)r Conversion: 2(pi)rad = 360 degrees

Theta of a circle (relation to arc length (s) and radius (r) )

theta= s/r

Angular speed (w)

2(pi)f = v/r

Torque

rotational analog of force is a vector Units: Newton meter (N*m) NOTE: Joules are (N*m) but scalar Torque= F*l l=(r)(sin(theta))

Torque rotational convention

Torque > 0: Counterclockwise Torque < 0: Clockwise

Rotational equilibrium

An object is in rotational equilibrium when the sum of the torques acting on it is zero.

Work

Work=Fd cos (theta) SCALAR unit: joules "transfer of energy" N*m = Joules

"Positive Work"

Work done on a system = transfer of energy INTO system. KE goes up

Energy

JOULES Kinetic Energy = (1/2)mv^2

Average Power (Watt)

Watt = Joules/second P=change in energy/change in time P= F*v

Work Energy Theorum

Work(net) = change in KE +work: gain KE -work: lose KE

How much work is done by F(Grav) in a satellite moving in a circular orbit?

Work in a circle: speed isn't changing W(net) = change in KE = zero [although velocity IS changing bc the direction is changing, the SPEED is not. Speed is scalar)

Gravitational Potential Energy

U = mgh = F*d

Types of PE

**1.Gravitational Potential Energy**

2.Elastic Potential Energy

3.Chemical Potential Energy

**4.Electrical Potential Energy**

**5.Nuclear Potential Energy**

Conservation of Mechanical Energy

When conservative forces act on an object, its total mechanical energy is conserved. Work(cons force) = [(delta) KE - [(delta) PE)]

Conservative Forces: i) Is Mechanical energy conserved? ii) Is it path independent? iii) Examples

i) Yes, Mech Energy is conserved ii) Yes, it is path independent iii) Ex: Gravity, Electrostatic, Elastic

Non-Conservative Forces: i) Is Mechanical energy conserved? ii) Is it path independent? iii) Examples

i) No, mech energy is NOT conserved ii) NO, it is NOT path independent iii) Ex: friction, drag, pushing+pulling (pressure) (don't forget energy lost to heat)

If you push a rock up a mountain, you raise its gravitational PE, but not its KE. Why does this not violate the Work-Energy Theorum?

Work(net) = Work(person put in) + Work(gravity) But W(person) is a non-conservative source added to the system. W(gravity) is a conservative source. Conservative forces only TRANSFER "funds". They never make you richer/poorer. (ie: Checking=KE; Savings=PE) W(net) - W(cons) = W(noncons) (delta)KE - (-(delta)PE) = (delta)KE + (delta)PE = W(noncons)

Conservation of Linear Momentum

The total momentum of a system of objects is conserved as long as no external forces act on that system. Momentum = p= vector.

Inlastic Collision

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- When a collision results in production of heat, light, sound, or deformation

**As long as no external forces are present:
Conservation of Momentum:**

m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1} +m_{2}v_{2}

**No Conservation of Kinetic Energy**

KE_{i} > KE_{f }

*because:* KE_{i} = KE_{f + }*Energy lost to heat or light*

(1/2)m_{1}v_{1i}^{2 }+ (1/2)m_{2}v_{2i}^{2} > (1/2)m_{1}v_{1f}^{2} + (1/2)m_{2}v_{2}^{2}

Completely Elastic Collision

__Conservation of Momentum:__

m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1} +m_{2}v_{2}

**Conservation of Kinetic Energy**

KE_{i} = KE_{f}

(1/2)m_{1}v_{1i}^{2 }+ (1/2)m_{2}v_{2i}^{2} = (1/2)m_{1}v_{1f}^{2} + (1/2)m_{2}v_{2}^{2}

Inelastic Collision

Conservation of Momentum:

m1v1 + m2v2 = m1va +m2v2

No Conservation of Energy:

KE(initial) = KE(final) + heat and deformation energy

Totally inelastic collisions

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- objects collide and stick together rather than bouncing off of each other and moving apart

__Conservation of Momentum__

m_{1}v_{1i} + m_{2}v_{2i} = (m_{1}+m_{2})v_{f}

*Energy not Conserved: *

*KE(initial) = KE(final) + heat and deformation energy*

Two objects with equal masses are moving toward each other with the same speed. How do they move after the collision if the collision is (i) elastic? (ii) totally inelastic?

i) Velocities maintain same speed but switch directions ii) they stop: m1v1 + m2v2 = (m1 + m2)vf vf = zero. (so they stop)

Impulse

A force applied to an object over time causes a change in the object's momentum called an impulse. I = (delta)p = F(avg)*(delta)t

Power

Work Energy Theorum

a direct relationship between the work done by all the forces acting on an object and the change in kinetic energy of that object. The net work done on or by an object will result in an equal change in the object's kinetic energy

Efficiency

Mechanical Advantage

Hanging block by two strings

Two pulley system

Six pulley system

Center of Mass diagram

Center of Mass

Work, Energy Momentum

Essential Equations