Newton’s Second and Third Laws Chapter 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