Newton’s Second and Third LawsChapter 4 Section 3

Newton’s First Law

• From Newton’s 1st Law of Motion an object with balanced external forces acting on it is in a state of equilibrium.– ΣF = 0– No acceleration

• If the Forces are not balanced then there is a change in the motion of the object.– ΣF ≠ 0 – Acceleration occurs

Acceleration and Force

• Acceleration is directly Proportional to the Force– Acceleration ~ Force

• If the Force is increased, then the acceleration must increase by the same ratio as long as mass is held constant.

Force and Acceleration

• Acceleration is always in the direction of the net force.

Acceleration and Mass

• Acceleration is inversely proportional to the mass of the object.– Acceleration ~ 1 / Mass

• If the mass increases, then the acceleration decreases as long as the force remains constant.

– If the mass is doubled, then the acceleration is cut in half.

Force, Mass and Acceleration

• The acceleration is directly proportional to the Force divided by the Mass– Acceleration ~ Force / Mass

• This is where Newton’s 2nd Law is created from.

Newton’s 2nd Law of Motion

• Newton’s Second Law – The acceleration of an object is directly proportional to the net external force acting on the object and is inversely proportional to the mass of the object.– ΣF = ma

Equation Variables and Units

• Newton’s Second Law variables– Σ: Greek Letter Sigma meaning “The sum of”– F: Force (Newton – N)– m: Mass (Kilograms – kg)– a: Acceleration (meters per second² - m/s²)

What is a Newton?

• A Newton is the amount of force needed to move a 1 kilogram mass at an acceleration of 1 meter per second squared.

F = ma

N = kg • m/s²

N=kgm/s²

Example Problem

• What force is needed to move a 3.2kg book across a table with an acceleration of 2.1 m/s² to the right?

• Answer: 6.7 N to the right

Solving Problems With Multiple Forces

• It is often easier to break the Newton’s 2nd Law into components.– The sum of the forces in the x-direction

equals the mass multiplied by the acceleration in the x-direction.• ΣFx = max

– The sum of the forces in the y-direction equals the mass multiplied by the acceleration in the y-direction.• ΣFy = may

Net External Force equals Zero

• If the net external force is zero, then the acceleration is equal to zero regardless of how much mass is present.– ΣF = ma– ΣF = m • 0m/s²– ΣF = 0

Newton’s 3rd Law

• Newton’s Third Law – If two bodies interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction.

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

Forces Always Exist in Pairs

• Forces always exist in pairs, therefore there can not be a single isolated force.– If you push on a wall with 100N, the wall

presses back on you with 100N.• Equal and opposite, as long as there is no

acceleration.

• If Earth is pulling you down with a force equal to your weight, what is the second force?

Action-Reaction Pair

• Action-Reaction Pair – A pair of simultaneous equal but opposite forces resulting from the interaction of two objects.– The action and reaction occur at the same

exact time.

Field Forces

• Field Forces also exist in pairs as well.– Field forces such as gravity and

electromagnetism.• If you drop a ball the earth pulls down on

the ball, but the ball pulls up on the earth by the same amount.

• But why doesn’t the earth move and the ball does?

Example Problems #1

• The net external force on the propeller of a 0.75kg model airplane is 17N forward. What is the acceleration of the airplane?

Example Problem #1 Answer

• 23m/s² forward

Example Problem #2

• A ball pushed with a force of 13.5N accelerates at 6.5m/s² to the right. What is the mass of the ball?

Example Problem #2 Answer

• 2.1kg

Example Problem #3

• Two people push on a box resting on a frictionless floor. One person pushes to the left with a force of 17N and the other person pushed with a force of 37N to the right. If the mass of the box is 10kg, what is the acceleration of the box?

Example Problem #3 Answer

• 2 m/s2