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Chapter 2 Kinematics 1. Acceleration - a =
v
t 2. Uniformly Accelerated Motion and The Big Five 1 a. s = (v0 + v)t 2 b. v = v0 + at c. s = v0 t + d. v
2
=
2 0 +
v
1
at 2
2 2a s
3. Kinematics With Graphs a. s-t graph Differe Differentia ntiatio tion n v-t graph
a-t graph
b. Slope of s-t graph: Velocity c. Slope of v-t graph: Acceleration d. Area under v-t graph: Displacement 4. Projectile Motion a. Constant horizontal velocity b. Varying vertical velocity c. Vertical velocity is zero at the highest d. Horizontal velocity is only used for calculating horizontal displacement (Horizontal velocity x time) 5. Some Tips for Projectile Motion Question a. Draw v-t graph for vertical velocity (No complex equation using!) b. Slope of v-t graph is acceleration; therefore, a=g=10m/s2 c. If time value or velocity value is given, it can possibly calculate velocity and time (v/t=10) d. Area under the graph/2 indicates the highest point of the motion
Chapter 3 Newton’s Laws 1. Newton’s Laws of Motion a. The First Law says that an object will continue in its state of motion unless compelled to change by a force impressed upon it. b. The Second Law - F net = ma c. The Third Law is commonly remembered as, to every action, there is an equal but opposite reaction.
2. Weight is the gravitational force exerted on it by Earth - F w = mg 3. Object pulled upward using string or two objects connected by string or pulleys
Ex) A can of paint with a mass of 6kgs hangs from a rope. If the can is to be pulled up to a rooftop with an acceleration of 1m/s 2, what must be the tension in the rope?
F net = F tension F weight F net = ma
F tension F weight = ma F tension = ma + F weight = 6x1 + 6x10 = 66 N Ex) Objects with mass of 4kgs and 6kgs are connected by a rope and pulled by 10N. What is acceleration of each object?
F net = ma = ( M + m)a F net = 10 N F net = (4 + 6)a 10 = (4 + 6)a a = 1m / s 2 4. The Normal Force is the component of the contact force that is perpendicular to the surface. Opposite force of weight force. 5. Friction arises from electrical interactions between atoms that make up the object and those that make up the surface. a. Static Friction occurs when there is no relative motion between the object and the surface (No sliding)
F static friction = s F N b. Kinetic Friction occurs when there is relative motion (Yes sliding)
F kinetic friction = k F N Static friction can take on all values, up to a certain maximum, and you must overcome the maximum static friction force to get the object to slide. 6. Inclined Planes (p70 ~ p71)
7. Uniform Circular Motion It changes only the direction of the velocity to keep the object on its circular path. Also, to produce an acceleration, there must be a force Acceleration - a =
v2 r
mv 2 Centripetal Force - F = r
Chapter 4 Work, Energy, and Power 1. Work - W = Fd Work is a scalar quantity Directions of F and d need to be parallel 2. Force Applied in Certain Angle Question Work done by horizontal force - W = ( F cos )d Work done by vertical force - W = ( F sin )d 3. Relationship Between Force and Energy
Force = Energy Ex) Force exerted by a spring
F = kx ,
kxdx = k 1
4. Kinetic Energy - K =
2
x dx =
1 2
kx2 = E
mv2
5. Work-Energy Theorem - W total = K = Fd 6. Potential Energy - U = mgh 7. Conservation of Energy - K i + U i = K f + U f 8. Power - P =
W Fd t
=
t
=
Fv
Chapter 5 Linear Momentum 1. Linear Momentum - p = mv
K =
1 2
mv
2
=
(mv)2 2m
=
p2 2m
2. Impulse - I = p = F t
Impulse is change in momentum 3. Conservation of Linear Momentum Elastic Collision (e=1): Both kinetic energy and momentum are conserved Inelastic Collision (0
e=
v2
v1
u2 u 1
* In all cases, momentum is always conserved when objects collide 4. Center of Mass Set a point for the calculation (usually origin)
xcm =
m1 x1 + m2 x2 + ... + mn xn m1 + m2 + ... + mn
m1 y1 + m2 y2 + ... + mn yn m1 + m2 + ... + mn m1 = mass of object 1 x1 = Distance between the set point and the center of object 1 ycm =
Chapter 7 Laws of Gravitation 1. Kepler’s Third Law - T2 µ R3 2. Newton’s Law of Gravitation - F =
Gm1m 2 r 2
G = Universal Gravitational Constant r = Distance between centers of two objects 3. Velocity of Satellite Orbiting Question -
mv 2 R
=
GMm R 2
-> v =
GM R
Centripetal Force Experienced by a Satellite = Gravitational Force v = Velocity of Satellite R = Radius of earth M = Mass of earth m = Mass of a satellite 4. Period of Satellite Orbiting Question - v =
2 R T
=
GM R
T = Period of a Satellite 5. Gravitational Potential Energy - U =
GMm
r r = Distance between an object and center of earth
6. Escape Speed - K = U At Escape Speed, Kinetic Energy = Magnitude of Gravitational Potential Energy.