Dynamics (Review) Flashcards
What is a force?
Anything that changes or tends (you may apply force to an object, but fail to change its state of rest/motion) to change an object’s state of motion/rest (in other words, forces cause acceleration [can also change the shape and direction of an object]). Force is a vector because it has acceleration (also, scalar x vector = vector). All forces can be grouped into two: contact forces and field forces.
Equation: F = ma
*Only works when there’s only one force present (as opposed to Fnet)
Unit: Newton or Kgm/s^2
What are contact forces? What are field forces?
Contact forces result from physical contact between two objects (FUNT - normal reaction force, friction, tension, upthrust [air resistance is debatable]). Field forces do not involve physical contact and can act from a distance (GEMA - gravitational force, electrostatic force, magnetic force, and air resistance [we’ll list air resistance here]).
Adding forces
Opposite forces have opposite signs, and the sum of all forces acting on an object is known as net or resultant force (forces in different directions can’t be added).
Depicting forces in free-body diagrams…
As a vector, force can be represented by arrows (the length tells us the magnitude of the force and the direction is shown by where it points to).
What are unbalanced forces?
Unbalanced forces are two unequal, opposite forces.
Types of forces
GENMUFTA
Gravitational force (force due to gravity)
Electrostatic force (forces between charges)
Normal reaction force (force between two objects in contact)
Magnetic force (between magnets)
Friction (opposes motion)
Tension (involved during pull or push [rope, spring, elastic, etc.])
Upthrust (upward force exerted by a liquid)
Air resistance (opposes motion in air)
What are balanced forces?
Forces on an object are said to be balanced if the net (resultant) force is zero
For the net force to be zero:
- Vertical forces must be equal
- Horizontal forces must be equal
Forces you need to remember (as illustrated in free-body diagrams)
Friction (F [can be lowercase]) always opposes motion and is at point of contact (center or not).
Upthrust (U) is the force that keeps objects floating in the water, so arrows are drawn from the surface of the water upwards (towards [and past?] the object)
Air resistance (R [same as normal, but that doesn’t really matter]) - for simplicity (or aesethetics), we normally connect it and gravity’s arrows.
Free-body diagrams
Free-body diagrams show us the key/all forces acting on AN object.
NOTE:
We’ll get a sentence/scenario: if it says at rest, we know our arrows must be the same length (you must indicate this)
For an object resting on a ramp, gravity should be longest (we can guess as to the length)
They will tell you if say air resistance should be considered
Ropes and such are not considered separate objects? Also, tension would be longer for objects attached to the ceiling BECAUSE the object is attached to the ceiling
The vertical forces must balance out for an object to be moving in a horizontal direction
If it’s a car, each wheel has normal reaction force, and we can say W = 2R
Terminal velocity is when velocity is constant
Newton’s First Law
States that an object at rest tends to stay at rest, and an object in motion tends to stay in motion, unless acted on by an external unbalanced force (in other words, for an object to accelerate, there must be an unbalanced force applied to it); also called the Law of Inertia.
What is inertia?
The tendency of an object to preserve its state of motion. Three types: inertia of rest (tendency to resist change in state of rest), inertia of motion (tendency to resist change in state of uniform motion), and inertia of direction (tendency to resist change in direction of motion).
What is equilibrium?
An object is said to be equilibrium if it is at rest or moving with constant velocity (acceleration is zero, so net force is zero): in other words, the object doesn’t accelerate and its net force is zero.
Necessary conditions:
Object’s speed may be constant (zero acceleration).
Object may be at rest.
Object’s net force must be zero.
Newton’s Second Law
States that the acceleration of an object is directly proportional to the net force applied to it and (two parts) inversely proportional to the mass of the object.
a = Fnet/m
a is directly proportional to Fnet (both in numerator)
a is inversely proportional to m (m is in denominator)
NOTE:
*In those three-part formula pyramids, Fnet would be at the top (m and a would be in the bottom)
If the problem gives you a value in grams, you have to convert it to kg
Newton’s Third Law
States that for every action, there’s an equal and opposite reaction: when two objects interact, they exert some force on each other (these forces are equal and opposite in magnitude, and are called action-reaction pairs: action-reaction pairs always act on different objects [so normal reaction force and weight are not an action-reaction pair]).
Action-reaction pair ex.
With a moving car colliding with a wall, the action would be the force exerted by the car on the wall and the reaction would be the force exerted by the wall on the car.
What is mass?
Mass is the amount of matter in an object and it is measured using a digital beam balance or lever: it is an intrinsic value, it never changes, and can never be zero.
Unit: kg
Remember: def, measurement, intrinsic/extrinsic, changeability, ability to be zero.
What is weight?
Weight is the force of gravity acting on an object (W = mg [Newtons can be converted to grams]): its unit is the Newton, it’s measured using a spring balance/scale, it changes if gravity does (so it changes with location and altitude, and can be zero [if gravity is zero]), and it is a vector and extrinsic (deals with an external factor) value.
W = mg
*W is weight, m is mass, and g is acceleration due to gravity (approximately 9.8 m/s^2)
Friction (solid)
The force exerted by a surface on an object as the object moves across it or makes effort to move across it (as long as you’re applying pressure, there’ll be friction): this is a more complete definition. Two types: static (Fs) and kinetic/dynamic (Fk).
Static friction
The friction experienced by an object as it makes effort to move (always equal to applied force, as long as there’s no movement [equal and opposite]).
Kinetic friction
Friction experienced by an object as it moves (only sets in object when object starts moving). It is less than Fs (max) as soon as object starts to move (at the point when the object begins to move, it starts to build up, so it’s always less than the max): for an object to experience kinetic friction, its static friction would have reached a maximum.
Coefficient of friction
Friction is directly proportional to normal force (when you want to change that to equal, there must always be a coefficient [no unit: N’s cancel]).
F = μR μ = F/R
Coefficient of static friction:
μs = Fs/R
Coefficient of kinetic friction:
μk = Fk/R
NOTE:
W = R (if object is at rest or going horizontally)
Firstly, if object is at rest/moving horizontally, calculate the weight to get R
If it requires say 12N to set it in motion, it’s static, and we’re using/solving for the coefficient of static friction: if a say 50N force keeps it in motion at constant velocity, then the net force is zero, so 50N has to be it, and we can use that as our force in calculating the coefficient of kinetic friction
Momentum
Symbol: p
Product of mass and velocity (p = mv)
*For an object, mass remains constant (so if velocity changes, momentum changes [they’re directly proportional])
∆p = m∆v
∆p = m(vf-vi)
Unit: kgm/s
Vector because velocity is a vector (has same direction as velocity; changes sign once that of velocity changes)
Relationship between momentum and Newton’s second law
Recall, Fnet = ma (Newton’s second law) A = ∆v/t, so Fnet = m∆v/t But ∆p = m∆v So Fnet = ∆p/t (another statement of Newton’s second law)
According to Newton’s second law, Fnet is directly proportional to the rate (per time = rate) of change of momentum
Impulse
Symbol: I
Recall,
Fnet = m∆v/t
Fnet(t) = m∆v (Impulse - Product of net force and time [also defined as change in momentum])
So I = Fnet(t) or I = m∆v
*Depending on the variables given to you, you can use either formula
Unit: Ns or kgm/s
Law of Conservation of Momentum
States that when two or more objects interact, the total momentum of the system (before and afer) stays constant, provided there’s no external force.
Ex.
For objects A and B,
PA + PB (before interaction) = PA + PB (after interaction)
MAVA(i) + MBVB(i) = MAVA(f) + MBVB(f)
Work
The product of force and displacement in the direction of the force. If there’s no displacement, there’s no work done. It is scalar and can be positive or negative. If the applied force leads to displacement in same direction as the force, then work will be positive. If the applied force leads to displacement in opposite direction to applied force, work will be negative.
Symbol: W
W = fd
W = (ma)d
If force is at an angle to the displacement, W = fdcostheta costheta = x/f x = fcostheta Units: Joules / Nm / Kgm^2/s^2
Other work equations:
W = mgh (when something is lifted vertically)
W = (½)kx^2 (compressing or a string)
Energy
Ability to do work (both work and energy are interchanged). It is a scalar quantity.
Symbol: E
Unit: Joules
Forms of Energy: PNCKS Kinetic energy Potential energy Nuclear energy Chemical energy Solar energy etc.
Conservation of Energy
The principle states that energy can neither be created or destroyed, but transformed from one form to another (the total energy in the universe is constant).
Kinetic energy
Energy due to motion of an object.
Symbol: KE
Unit: Joules
KE = (½)mv^2
Potential energy
The energy held by an object because of its position relative to other objects. The more mass an object has, the greater its potential energy. Two types: gravitational (gPE) and elastic (EPE).
PE = mgh
gPE
PE due to the position or height of an object. Directly proportional to height.
Unit: Joules
gPE = mgh
EPE
PE stored in springs. Directly proportional to extension/displacement.
Unit: Joules
EPE = (½)kx^2
k = spring constant
x = extension/displacement
Power
The rate at which work is done (the rate at which energy is being transferred).
Symbol: P
Unit: J/s or Watt
1 J/s = 1 Watt
P = Work/time or ∆Energy/time
Prove,
P = fv
P = Work/time = fd/t = fv
