Force

Unit 4 Forces

Newton's Three Laws, Momentum, Forces, Motion, and Vectors

My Bio Page	By Mr. Palmer	Email Me Link
Unit 4	Unit 5	Unit 6

Newton's Three Laws:

1^st Law: (A.K.A. Inertia Law)
	A body in Motion stays in Motion.
	A body at Rest stays at Rest.
	Unless an outside force is applied.
		•Basic formula for the inertia law is momentum.
2^nd Law: (A.K.A. Force Law)
	The acceleration of a mass is proportional to the force applied.
	If the mass is increased for the same force applied the acceleration is inversely proportional.
	The force equation: F = m(a)
		•F: stands for force measured in Newton's (N)
		•a: stands for acceleration measured in meters/second/second (m/s/s or m/s²)
		•m: stands for mass measured in kilograms (kg)
3^rd Law: (A.K.A. Action/Reaction Law)
	For every force applied there is an equal and opposite reaction force.
		•A rocket's ability to fly are due to the 3^rd Law.
		•A rowboat's ability to move through water is due to the 3^rd Law.

Momentum:

Momentum is Inertia:
	Conservation of Momentum (Elastic)
		•Elastic means that all of the momentum is transferred to the second object.
		•m₁v₁ = m₂v₂
		•m₁and m₂ are different masses (units = kg)
		•v₁ and v₂ are different velocities (units = m/s)
	Conservation of Momentum (Inelastic)
		•Inelastic means that all of the momentum is transferred to both the first mass and the second mass.
		•m₁v₁ = (m₁+ m₂)v₂
		•m₁and m₂ are different masses (units = kg)
		•v₁ and v₂ are different velocities (units = m/s)
		•v₂ is always less then v₁.
	Impulse Momentum
		•The momentum of an object in motion can be altered by a force applied for a unit of time results in a new momentum vector.
		•m₁v₁ + F(Δt) = m₂v₂
		•F is a force applied (units = N)
		•Δt is a change in time (units = seconds (s))

Forces:

Forces in General:
	Types of Forces (Applied)
		•Push Force or Compression Force
		•Pull Force or Tension Force
		•Centrifugal Force (DOES NOT EXIST)
		•Centripetal or Rotational Force
	Types of Forces (Body)
		•Gravitational Force
		•Charged Forces-
			-opposite charges attract.
			-like charges repel.
		•Magnetic Forces-
			-opposite poles attract.
			-like poles repel.
	Types of Forces (Reactant Forces)
		•Friction Force Sliding-
			-static friction.
			-kinetic friction.
			-frictionless surface.
		•Friction Force Air Resistance
		•Friction Force Heating

Calculating Forces:
	Draw a Picture
	Setting a Frame of Reference (2-D)
		•x-axis (horizontal axis)
		•y-axis (vertical axis)
	List Assumptions
		•Friction vs No Friction-
			-frictionless surface.
			-no air resistance.
			-no heat created by object interactions.
	List Known Values
		•For example: m₁= 30 kg -
			-m tells you it is a mass.
			-1 distinguishes it from another mass.
			-30 is the value.
			-kg tells you the units of measurement.
		•Another example: F_1x= 200 kN -
			-F tells you it is a force.
			-1 distinguishes it from another force.
			-x tells you it is along the x-axis.
			-200 is the value.
			-kN tells you the units of measurement.
	List Unknown Values
		•For example: a₁= ? m/s/s -
			-a tells you it is an acceleration.
			-1 distinguishes it from another acceleration.
	Write Down Equations
		•In order to solve for unknowns you will need to have an equation for each unknown.
		•For example a static problem-
			-sum of the forces in the x-direction: Σ F_x = 0
			-sum of the forces in the y-direction: Σ F_y = 0
			-sum of the moments about a point A: Σ M _A = 0
	Rearrange Equations for Unknowns
	Plug in Known Values and Solve
	Do Dimensional Analysis on Units
	Put Down Final Answer

Example: Moving a Block
	Problem
		•Draw a Picture.
		•Frame of reference x-axis along the surface.
		•No air resistance/No heat energy generated.
		•List Known Values-
			-mass: m₁ = 100 kg
			-force: F₁ = 30 N
			-coefficient of Friction: μ_k = 0.1
		•List Unknown Values-
			-acceleration: a_x = ? m/s/s
			-Friction force: F_f = ? N
		•Write Down Equations-
			-Σ F_x = F₁ - F_f = m₁(a_x)
			-F_f = μ_k m₁(g)
		•Rearange for Unknown Variable-
			-a_x = (F₁ - F_f)/ m₁
			-a_x = (F₁ - μ_k m₁(g))/ m₁
		•Plug in Known Values-
			-a_x = (F₁ - μ_k m₁(g))/ m₁
			-a_x = (100 - 0.1(30)(9.8))/30
			-a_x = 2.35
		•Do Dimensional Anaylsis-
			-a_x = (F₁ - μ_k m₁(g))/ m₁
			-a_x = (N - kg(m/s/s))/kg
			-a_x = (kg(m/s/s) - kg(m/s/s))/kg
			-a_x = m/s/s
		•Final Answer-
			-a_x = 2.35 m/s/s

Motion:

Constant Velocity (no Acceleration)
	Variables:
		•v: stands for velocity (units: m/s)
			-v = d/t
			-v = distance/time
		•d: stands for distance (units: m for meter)
			-d = v(t)
			-d = velocity(time)
		•t: stands for time (units: s for second)
			-t = d/v
			-t = distance/velocity
Constant Acceleration
	Variables:
		•a: stands for acceleration (units: m/s/s)
			-a = v/t
			-a = velocity/time
		•v: stands for velocity (units: m/s)
			-v = a(t)
			-v = acceleration(time)
		•t: stands for time (units: s for second)
			-t = v/a
			-t = velocity/acceleration
General Equations
	Variables:
		•Distance and Acceleration
			-d = a(t²)/2 (no initial velocity)
			-d = v_ot + a(t²)/2 (initial velocity = v_o)

Projectile Motion:

Break Velocity into two Vectors:
	Vertical Component of Velocity
		•v_y = v(sinθ)
		•t_peak = v_y/g
		•h = v_yt_peak - g(t_peak²)/2
	Horizontal Component of Velocity
		•v_y = v(cosθ)
		•T_flight = 2(t_peak )
		•D = v_xT_flight (assuming no wind resistance)

Other Types of Motion :

Two Trains Approaching Each Other:
	To solve this type of problem you can treat one train as having a velocity of zero while the other has the sum of the two velocities of the trains.
		•v_total = v_{train 1} + v_{train 2}
Two Cars Chasing Each Other:
	To solve this type of problem you can treat one car has a velocity of zero the second has the velocity of the difference of the two cars.
		•v_total = v_{car 1} - v_{car 2}

Vectors:

Definition of a Vector
	Vector Direction
		•A vector has two parts the most obvious point of a vector is that it shows direction. Such as-
			-200 m North
			-20 m/s South by South West
	Vector Magnitude
		•The second part of a vector is that it shows a value such as-
			-200 N at angle of 30^o
			-3.50 m/s² along the x-axis

Property of SOESD

November 30, 2008