Chapter 4

NEWTONS LAWS

Newton’s 3 Laws

Force Diagrams

Equilibrium

Unbalanced Forces

Terminal Velocity

Newtons 1st Law: Law of Inertia

A body at rest remains at rest,

A body in motion remains in motion, at a constant velocity, in a straight line

Until an Unbalanced force acts on it.

INERTIA: Tendency to resist changes in motion.

Inertia is a property of matter

Newtons 2nd LawAn unbalanced force causes acceleration

Acceleration is:

• directly related to force.

• inversely related to mass.

𝑎 = 𝐹𝑚

1 kg * 1m/s2 = 1 Newton

Newtons 3rd Law

• When one object exerts a force on a second object, the 2nd object exerts an equal Force in the opposite direction on the first object.

• For every action there is an equal and opposite reaction.

• All Forces come in pairs, equal in magnitude, opposite in direction.

Force Diagrams (Free Body Diagrams)

• Identify the object you will draw a diagram for.

• Identify all the forces acting directly on the object and the object exerting them.

• Draw a dot or line to represent the object of interest.

• Draw a vector from the dot to represent each force. Draw it in the direction the force is being exerted.

• Label it by (a) the type of force, and/or(b) the object exerting the force

Force Diagrams (Free Body Diagrams)Determine the net Force on each object below,

• If the vectors should graphically add up to zero, the object is stationary or is moving at a constant velocity,

• If the object is accelerating, the sum of the vectors should produce a vector in the same direction as the acceleration.

Balanced Forces• Equilibrium :

• Net Force = Zero• Object is at rest or moving at a constant velocity

Tacos(10 kg) PIZZA (5kg)

40o 40o

Find the Tension on each chain

Balanced Forces The ninja has a mass of 50 kg, ϴ =30o

Find the Tension in Each Rope

Unbalanced ForcesWorker pushes a 100 kg box with a Force of 85N. Friction exerts a Force of 65 N. What is the acceleration of the box?1) Draw Force diagram

2) Determine Net Force

3) Solve the Problem

Unbalanced ForcesA Rescue Helicopter lifts 2 people with a total mass of 200kg with an acceleration of 3.0m/s2.

What is the Tension on the Rope holding the people?

1) Draw Force diagram2) Determine Net Force3) Solve the Problem

Riding in an elevator

A 50 kg woman is standing on a scale in an elevator. The scale reads 55kg. What is the acceleration of the elevator?

A 50 kg woman is standing on a scale in an elevator. The scale reads 45kg. What is the acceleration of the elevator?

A 50 kg woman is standing on a scale in an elevator. The scale reads 0 kg. What is happening to the elevator?

1) Draw Force diagram2) Determine Net Force3) Solve the Problem

Unbalanced Forces

Net Force = ?Net Force = ?Net Force = ?

TERMINAL VELOCITY

Drag Force – Force exerted by fluid that resist motion

Depends on many factors, most importantly:Properties of FluidSpeed of object in fluidInteraction between object on fluidArea of object

Can be modeled:

Slow speed: 𝐹 = 𝑘𝑣

High speed: 𝐹 = 𝑘𝑣2

TERMINAL VELOCITY

• Drag Force increases as velocity increases.

• Acceleration Decreases as Velocity increases

• Net Force Decreases as velocity increases

𝐹𝑛𝑒𝑡 = 𝑚𝑔 𝐹𝑛𝑒𝑡 = 𝐹𝑑 −𝑚𝑔 0 = 𝐹𝑑 −𝑚𝑔

𝐹𝑑 = 𝑚𝑔

TERMINAL VELOCITY

• Occurs when the drag force is equal to the weight of falling object

• Occurs when the net force on a moving object is zero

𝐹 = 𝑘𝑣 = 𝑚𝑔 → 𝑣 =𝑚𝑔

𝑘

Or

𝐹 = 𝑘𝑣2 = 𝑚𝑔 → 𝑣 =𝑚𝑔

𝑘

TERMINAL VELOCITY• Slow speed: 𝐹 = 𝑘𝑣

• High speed: 𝐹 = 𝑘𝑣2

• Force depends on Velocity → acceleration depends on force →change in velocity depends on velocity Example:

𝐹𝑛𝑒𝑡 = 𝑚𝑔 − 𝐹𝑑

𝑚𝑎 = 𝑚𝑔 − 𝑘𝑣

𝑚𝑑𝑣

𝑑𝑡= 𝑚𝑔 − 𝑘𝑣

Determine Velocity based on time

• 𝐹𝑛𝑒𝑡 = 𝑚𝑔 − 𝐹𝑑

• 𝑚𝑎 = 𝑚𝑔 − 𝑘𝑣

• 𝑚𝑑𝑣

𝑑𝑡= 𝑚𝑔 − 𝑘𝑣

𝑚𝑑𝑣

𝑑𝑡= 𝑚𝑔 − 𝑘𝑣

න𝑑𝑣

𝑣 − 𝑣𝑡= −

𝑘

𝑚න𝑑𝑡

𝑙𝑛𝑣𝑡 − 𝑣

𝑣𝑡= −

𝑘

𝑚𝑡

1 −𝑣

𝑣𝑡= 𝑒

−

𝑘

𝑚 𝑡

𝑣 = 𝑣𝑡[1 − 𝑒−

𝑘

𝑚 𝑡]

𝑣 = 𝑣𝑡[1 − 𝑒−

𝑘

𝑚 𝑡]

𝑎 = 𝑔𝑒−

𝑘

𝑚 𝑡