Lect. 1: Translational Motion, Lect 2. Force, Lect. 3-Torque, Equilibrium, & Lect. 4-Momentum, Machines, Radioactive Decay Flashcards
Equation: Speed
speed = distance / time
Eequation: Velocity
velocity = displacement / time
Equation: Acceleration
acceleration = change in v / time
Equation: Side opposite angle in triangle
O = H * sin(ø)
Equation: Side adjacent to angle in triangle
A = H * sin(ø)
Equation: Displacement in linear motion
x = x(initial) + v(initial) * t + (1/2) * a * t^2
Equation: Linear motion, Final Velocity w/ a & t
V(final) = V(initial) + a * t
Equation: Linear motion, final V w/ a & x
V(final)^2 = V(initial)^2 + 2 * a * x
Equation: Average V w/ uniform Accel
V(avg) = 1/2 (V final + V initial)
Slope on Displacement vs Time Graph
instantaneous velocity, + or – indicated direction from starting point
Area under curve in Displacement vs Time graph
N/A
Slope in Velocity vs. Time graph
Instantaneous Acceleration; + or – indicates direction from starting point
Area under curve in Velocity vs Time graph
Distance or Displacement
Equation: Displacement w/ constant acceleration
X = V(avg) * time
Equation: Time in V vs. time graph
t = change in V / Acceleration (constant)
Equation: Peak height of a projectile
V(initial) * sin(ø) = √(2gh)
Equation: Initial vertical velocity (in projectile motion)
V(intial) * sin(ø)
Horizontal Acceleration during projectile motion?
Always = 0
Path of a projectile is INDEPENDENT of the object’s _______.
mass
What dictates the time in flight of an object in projectile motion?
Vertical velocity (Acceleration is constant at -10 m/s^2)
_________ is constant through the course of an object’s flight in projectile motion
Acceleration; = g = 10 m/s^2
In the absence of ________ , mass does not affect projectile motion.
Air Resistance
3 factors that change air resistance
speed
surface area
shape
Lg surface area __________ air resistance
increases; allows more collisions w/ air molecules
The higher the velocity, the ______ the air resistance.
greater.
Mass doesn’t change the ____ of air resistance. It does change the ______ of the object experiencing the air resistance.
Force; Path
Mass and acceleration are _____ related in air resistance.
Inversely; Acceleration must decrease as mass increases; (*Doesn’t apply to gravitational constant. Only to deceleration due to air resistance)
Larger masses experience _____ deceleration due to air resistance bc they are _____ affected by the same force
Less; Less; Air resistance has less effect on a more massive object!
3 Forces on the MCAT
Gravitational: m*g
Electromagnetic: charged object
Contact: acts parallel or perpendicular to object
Equation: Newton’s second law of motion
F = ma (Force applied to center of mass)
Equation: Law of Gravitation
F = G * (m1 * m2)/r^2 (G = universal constant)
The Force of Gravity is ______ to the mass of each body and __________ to the square of the distance between their centers of gravity.
Proportional
Inversely proportional
Equation: Sum of Normal Force and Gravitational Force
F = m * g * sin(ø)
*Acts directly along the inclined plane
Equation: Normal Force on an object on an inclined plane
F(normal) = m * g * cos(ø)
sin(90) = ?
1
sin(0) = ?
0
In CIRCULAR motion, _____ is constant but ____ is not. Why?
Speed = constant
Acceleration = changing
Because the direction is always changing in circular motion
Equation: Centrepital acceleration
a (c) = v^2 / r
Note: An object moving in a circle at CONSTANT SPEED experiences a centripetal accel that is proprotional to the square of its speed and INVERSELY proportional to the radius of the circle; Always points to CENTER of circle
Equation: Centripetal Force
F(c) = m * (v^2 / r)
Note: Some force F(c) must be applied to an object in order to give that object a(c); Always points toward center of circle
**Equate w/ the Force causing centripetal motion (i.e. Gravity)
____ is a contact force that always acts parallel to the surface; Contiguous surfaces may exert equal and opposite forces against each other parallel to their surfaces.
friction
This contact force resists motion when an object is not moving
Static Friction: F(s)
This contact force resists motion when objects slide past each other
Kinetic Friction: F(k)
Equation: static friction & F(n)
F(s) ≤ coefficient of F(s) * F(n)
Equation: kinetic friction & F(n)
F(k) = coefficient of F(k) * F(n)
This is a contact force that acts through a massless object (i.e. rope) the force is equal throughout; Requires equal forces on both sides of the object but the Force is = to the force on only ONE side
Tension
Equation: Hooke’s Law
F = -k * ∆x
*Force due to a stretched or compressed object
-k : spring constant (can ignore - for MCAT)
∆x: change in position from rest when stretched / compressed
Equation: Spring Constant (k)
k = (m * g) / ∆x
∆x : change in position from rest when stretched / compressed
Describes a system in which there is no angular or translational acceleration, or if the translational velocity of its center of mass and angular velocities of all its parts are CONSTANT
Equilibrium
System in which all velocities = 0.
Example?
static equilibrium
Ex: F(n) and F (g)
System in which all velocities are nonzero but constant.
Example?
dynamic equilibrium
Ex: F(air resistance) = F (gravity) in a parachute
Equation: System in translational equilibrium
F(up) = F (down)
F (left) = F (right)
*Sum forces on each side and set equal to each other
How do you solve a problem for a system that is not in equilibrium? (Assume system MUST have translational acceleration)
- Write equations as though system is in equilibrium
- Add (m*a) to side with less Force acting on it
- Solve for acceleration
A twisting force; Usually describes as clockwise or counterclockwise; Product of a Force and a position vector; Vector quantity
Torque (T)
Equation: Torque (magnitude)
T = F * r * sin(ø)
ø: angle b/w F and position vectors
r : position vector; distance from point of rotation to point of application of the F
*Pt of rotation is arbitrary point of your choosing
Equation: Torque (used w/ lever arm)
T = F * L L = lever arm; distance between point of rotation and where F acts at 90°
3 steps to solving a Torque equation (Note: ALWAYS a statics problem)
- Set F(up) = F(down)
- Set F(right) = F(left)
- Set T(clockwise) = T(counterclockwise)
* If there are no horizontal forces, throw out second equation)
* Assume this is a statics problem and that you want to prevent the object from turning/twisting
The mechanic Energy of a moving mass?
Equation?
Kinetic Energy
K.E. = 1/2 * m * v^2
Energy of position due to gravity
Equation?
Gravitational potential energy: U(g)
U(g) - m * g * h
Energy of position due to resistive Force by a deformed object
Equation?
Elastic potential energy: U(e)
U(e) = 1/2 * k * ∆x^2
A system in which both energy and mass are exchanged
open system
a system in which energy is exchanged but mass is not
closed system
a system in which neither energy nor mass is exchanged (i.e. Universe)
isolated system
The transfer of energy due to Force; Scalar quantity; Measured in Joules
Work
Equation: Work done by any Force EXCEPT when Friction is present
W = F * d * cos(ø)
ø: angle b/w F and displacement
SI Unit: Joules (J)
Equation: Energy transfer due to Forces and NO HEAT
W = ∆K + ∆U + ∆E
Equation: Energy transfer due to Forces with NO heat or friction
W = ∆K + ∆U
Equation: Conservation of Energy
∆E = W + q
______ and ______ are the only two ways energy leaves a system
work and energy
A Force in which the strength depends only on position (i.e. Potential Energy) No work is done
Conservative Force
Equation: Conservative Force
K1 + U1 = K2 + U2
Equation: Conservative force w/ no hear
∆K + ∆U = 0
A force causes a change in mechanical energy through work, Work equals the change in mechanical energy of this system
Nonconservative Force
Equation: Nonconservative force (except kinetic friction)
W = ∆K + ∆U
Mechanic Energy due to Kinetic Friction:
F(k) * d * cos(ø) = ∆K + ∆U
Work applied at a smaller horizontal angle creates a greater horizontal component and does _______ work.
More
the rate of energy transfer; SI unit = Watt = J/s; scalar quantity
Power
Equation: Power
P = ∆E / t
Equation: Instant power due to a Force
P = F * v * cos(ø)
an object’s tendency to continue on its path; Always conserved in isolated system; Vector quantity; SI unit = kg*m/sec
Momentum (p)
Equation: Momentum
p = m*v
A collision in which mechanical energy is conserved; only conservative (Ex: atoms)
Elastic collision
Equation: Elastic Collisions
U(o) + K(o) = U(f) + K(f)
mgh(o) + 1/2 * mv^2(o) = mgh(f) + 1/2 * mv^2(f)
collision in which some mechanical energy is lost to internal energy; Uses conservation of Momentum (p); Vector quantity
In some cases, objects may stick together
Inelastic collisions
Equation: Conservation of Momentum (inelastic collision)
p(o) = p(f) p(o)x = p(f)x / p(o)y = p(f)y
T/F: An unbalanced for on an object will always impact the object’s speed.
False. An unbalanced force will always impact an object’s VELOCITY, but it may just change the direction or just the speed of the object without changing the speed.
Ex: satellite orbiting the Earth w/ constant speed but changing direction
T/F: If the net force on a body is zero, the velocity will not change.
True
Moving objects tend to come to rest in “everyday life” because they are being acted on by an ____________.
Unbalanced (net) outside force
a change in momentum
Impulse (J)
Equation: Impulse
J = ∆p = ∆m * v
Equation: Impulse w/ avg force on either colliding body
J = F(avg) * ∆t
Equation: Impulse w/ avg force from ∆ in momentum
∆p = ∆m * v = F(avg) * ∆t
objects that reduce Force required when doing work
Ex: Ramp, lever, pulley
Machine
a machine that is an incline plane; the fraction by which work is reduced = the fraction by when the distance over which the force acts is increased
Ramp
Equation: Work done when using a ramp
W = m * g * h
NOTE: Same as without using a machine
machine based on Torque
Lever
If the length of the lever arm is doubled when using a lever, the force is reduced by a factor of _______
2
*Place the fulcrum 2x as far from the Force as from the mass
a machine that reduces Force to do work by increasing the distance; Constant tension through a massless rope in frictionless, massless machine, Force and distance are inversely proprotional
Pulley
length of time for 1/2 of an amount of substance to decay
half-life
how to solve a 1/2 life equation
Divide in initial amount of substance by 2 until the final amount is reached. The number of times you divide by 2 = the half life
a process in which atoms spontaneously break apart
radioactive decay
Types: Alpha, Beta, Positron emission, Gamma
radioactive decay in which a He nucleus (2 protons and 2 neutrons) are emitted; (an alpha particle is lost)
atomic number: decreased by 2
mass #: decreased by 4
alpha particle decay
radioactive decay w/ the expulsion of an electron; A neutron creates an electron and a proton and that electron is lost
atomic #: increased by 1
mass #: unchanged
beta decay
radioactive decay w/ the emission of an electron with a + charge; a proton is transformed in a neutron; a positron is emitted
Atomic #: decreased by 1
mass #: Unchanged
Positron emission
radioactive decay where an electron is captured and merged w a proton to form a neutron; Proton is destroyed; Neutron is created
Atomic #: decreased by 1
mass #: Unchanged
electron capture
radioactive decay with a high frequency photon; no charge; does not change the ID of the atom; often accompanies other types of decay
Ex: When an electron and a positron collide
Gamme ray
Equation: Rest Mass Energy
*also shows binding energy holding nucleons together
E = m * c^2 m = amount of mass created or destroyed c = speed of light (3*10^8 m/s)
the latent energy w/in the mass of an object; will only appear on MCAT if mass is created or destroyed
rest mass energy
difference in masses when measuring particles separately then measuring them once they are joined (i.e. protons and neutrons in a nucleon)
The joined particles will have less mass than the sum of the masses of the individual parts
mass defect
process by which two nuclei combine to form one heavier nucleus; exothermic process - releases Energy
Fusion
process by which one nucleus splits to form 2 lighter nuclei; exothermic process-releases Energy
*Energy comes from the mass defect; new bonds in the smaller nuclei are stronger and more stable and release more Energy than it took to break the bond
Fission
