Chapter 4 Section 3

Newton’s First Law
• From Newton’s 1 st 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 2 nd Law is created from.

Newton’s 2 nd 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/s ² to the right?
• Answer: 6.7 N to the right

Solving Problems With Multiple
Forces
• It is often easier to break the Newton’s 2 nd
Law into components.
– The sum of the forces in the x-direction equals the mass multiplied by the acceleration in the x-direction.
• ΣF x
= ma x
– The sum of the forces in the y-direction equals the mass multiplied by the acceleration in the y-direction.
• ΣF y
= ma y

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 3 rd 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/s ² forward

Example Problem #2
• A ball pushed with a force of 13.5N accelerates at 6.5m/s ² 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/s 2