Newton’s Second and Third Law of Motion

Newton’s Second Law of Motion

• A commonsense law.

• The force on an object is equal to its mass multiplied by its acceleration.

• Mass is the amount of matter an object has.

• Acceleration is the time rate of change of velocity. (Velocity is speed in a given direction.)

F ma

Newton’s Second Law of Motion

• The more massive an object, the more inertia.

• The more inertia an object has, the harder it is to get it moving.

• Double the force - double the acceleration.• Double the mass - halve the acceleration.

Mass

• …is the measure of the inertia of an object.• Inertia is the tendency of an object to continue in its

original motion• …is measured in kilograms.

• … is how much matter is in an object..

Weight

• The weight of an object FW is the response of MASS to the GRAVITATIONAL FORCE.

• FW = m g

• g = 9.81 m/s2

Units

• The units of mass is the kilogram (in MKS system) and the slug (in Imperial system).

• Mass is a SCALAR quantity.• The unit of force in the MKS system is the

Newtons, where a force of 1 N will give a mass of 1 kg an acceleration of 1 m/s2 . In the Imperial system, the unit of force is the pound.

• Force is a VECTOR quantity.

Units of Force

• SI unit of force is a Newton (N)

• US Customary unit of force is a pound (lb)• 1 N = 0.225 lb

2smkg1N1

Gravitational Force

• Mutual force of attraction between any two objects

• Expressed by Newton’s Law of Universal Gravitation:

• G = universal gravitational constant = 6.67x10-11 N-m2/kg2

221

g rmmGF

Example

If two objects (m1 = 100 kg) and (m2 = 1000 kg) are separated by 0.5m, what is the gravitational force between them?

Example: Answer

Fg G m1m2

r2

Fg 6.67x10 11 N m2

kg2

100kg 1000kg

0.5m 2

Fg 2.668x10 5Newtons

Example: Answer

• Notice the very, very small answer. Gravity is the WEAKESS force by far.

• So - why are WE so aware of it?

• Because we are next to an incredibly large & massive object - the Earth.

Newton’s Second Law of Motion

• Examples:1) Throwing a baseball2) Slingshot (David & Goliath)3) Hail4) Moving cars (1)5) Moving cars (2)

Example

If a mass of 1 kg is accelerated 1 m/s2 by a force of 1 N, what would be the acceleration of 2 kg acted on by a force of 2 N?

(a) 0 m/s2

(b) 1 m/s2

(c) 2 m/s2

(d) 3 m/s2

(e) unable to determine

Answer (b)

• If a mass of 1 kg is accelerated 1 m/s2 by a force of 1 N, what would be the acceleration of 2 kg acted on by a force of 2 N?

F ma

a Fm

a 2N2kg 1m

s2

Newton’s Third Law of Motion

• “To every action (force) there is always opposed an equal reaction (force): or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. ”

• The least intuitive law.

• Every object that exerts a force on another object is always acted upon by a reaction force.

Newton’s Third Law of Motion

Examples:1. Recoil of a gun.2. Thrust of a rocket.3. Rebound of a hammer from a struck nail.4. Book sitting on a table.5. Walking. 6. Lumberjack running on a log in a lake.

Example

If a Mack truck and a Volkswagen have a head-on collision, which vehicle will experience the greater impact force?

a) the Mack truckb) the Volkswagenc) both the samed) ... it depends on other factors

Example: Answer (c)

If a Mack truck and a Volkswagen have a head-on collision, which vehicle will experience the greater impact force?

Answer: Newton’s Third Law ~ action and reaction

Example

Consider the apple at rest on the table. If we call the gravitational force exerted on the apple action, what is the reaction force according to Newton's 3rd Law?

Example: Answer

Consider the apple at rest on the table. If we call the gravitational force (by the earth) exerted on the apple action, what is the reaction force according to Newton's 3rd Law?

Answer: The gravitational force exerted by the apple on the earth

Example

If a mass of 10 kilograms is accelerated at 5 meters per second per second, what is the force acting on it?

Example: Answer

F 10 kg x 5 ms

s50 kg m

s2 = 50 newtons

Example

What acceleration will result when a 12-N net force applied to a 3-kg object?

(a) 0 m/s2

(b) 4 m/s2

(c) 36 m/s2

(d) Unable to determine

Example: Answer (b)

What acceleration will result when a 12-N net force applied to a 3-kg object?

F ma

a Fm

a 12N3kg 4 m

s2

Example

A 1-kg rock is thrown at 20 m/s straight upward. Neglecting air resistance, what is the net force that acts on it when it is half way to the top of its path?

(a) 0 N(b) 4.9 N(c) 9.8 N(d) 20 N(e) Unable to determine

Answer (c)

Answer: The only force acting on the rock is gravity.

F=ma F = (1) (9.8)=9.8N

Classical Mechanics…

The End

(for now…)