The Laws A section in the chapter of the study of Dynamics of motion

Program Line-up Take Aim Get Moving Building Momentum Let’s get impulsive What a pair! Conserve that momentum Rounding up

Taking Aim State Newton’s 3 Laws of motion in their complete forms Describe the qualities of momentum and impulse Solve impulse and momentum problems State the principle of conservation of linear momentum

Get Moving Newton’s First Law of Motion in your own words…

No… really, what is Newton’s First Law? Also known as the Law of Inertia When no net resultant force acts upon an object, then if that object is at rest, it will stay at rest and if it is moving, it will continue to move in a straight line with constant velocity

Building Momentum (1/2) From before: But that is not complete… Momentum (p)(p)

Building Momentum (2/2) Momentum is a vector Momentum is in the same direction as velocity Force need not be in the same direction as the momentum ROADBLOCK!!!

Roadblock 1: Air being pushed downwards by the blades of a helicopter travels at a velocity of v air m/s. Assuming the cross-section of the air being pushed away by the blades is A m 2, what is the average force that the blades are exerting on air? State any assumptions made.

Solution to Roadblock 1 (1/3) Assume that air being pushed out by the rotor blades takes the shape of a cylinder Cross-sectional area, A m 2 Length of cylinder, l m

Solution to Roadblock 1 (2/3) Volume of air being pushed away by the rotor blades per second can be written as: Now Newton’s Second Law of motion states:

Solution to Roadblock 1 (3/3) v remains constant but m changes Therefore: BINGO!!!

Let’s get IMPULSIVE (1/3) Newton’s Second Law: Therefore: Change in momentum, also known as Impulse This is the Impulse-momentum theorem

Let’s get IMPULSIVE (2/3) Force vs Time graph: Area under the curve gives Tells nothing of the initial and final momentum Force/N Time/s

Let’s get IMPULSIVE (3/3) Impulse is a Vector Direction of Impulse: ROADBLOCK!!! Initial Momentum Final Momentum Impulse

Roadblock 2 A baseball, mass m kg is moving horizontally at a velocity of v m/s when it is struck by a baseball bat. It leaves the bat horizontally at a velocity of v m/s in the opposite direction. (a) Find the impulse of the force exerted on the ball. (b) Assuming that the collision lasts for x ms, what is the average force?

Solution to roadblock 2 (1/3) Let the initial direction that baseball is travelling in be positive. Therefore, initial momentum, p initial, is: As the baseball is travelling horizontally in the opposite direction, the final momentum, p final, is:

Solution to roadblock 2 (2/3) Therefore impulse is: By the impulse-momentum theorem: And given time of impact, x ms, = x ms =

Solution to roadblock 2 (3/3) Therefore the average force, F ave, is: YEAH!!!!

What a pair (1/2)

What a pair (2/2) Newton’s Third law of motion: ROADBLOCK!!! Every action will produce an equal and opposite reaction

Roadblock 3 In roadblock 1, what is the force that air exerts on the rotor? Give other examples of action-reaction pairs that are useful

Solution to Roadblock 3 Force on rotor blades will be equal in magnitude but opposite in direction to that of the average force on air Other examples: – Jet engines – Walking – Swimming – Fans

Conserve that momentum (1/6) The principle of conservation of momentum: Extension of Newton’s Second and Third Laws of Motion The total momentum of a closed system is constant if no external resultant forces act on it.

Conserve that momentum (2/6) Consider two isolated particles m 1 and m 2 before and after they collide. Before the collision, the velocities of the two particles are v 1i and v 2i ; after collision, the velocities are v 1f and v 2f.

Before collision During collision After collision Conserve that momentum (3/6) Free body diagram: v 1i m1m1 v 2i m2m2 F1F1 F2F2 v 2f v 1f

Conserve that momentum (4/6) Applying the Impulse-Momentum Theorem to m 1 : Likewise, for m 2

Conserve that momentum (5/6) By Newton’s Third Law: Time of collision same for both masses: By Newton’s Second Law:

Conserve that momentum (6/6) From which we find: Total initial momentum = Final total momentum

Rounding up Dynamics: Newton’s Laws of Motion First Law Inertia Force required to change state of motion Second Law Force proportional to rate of change of momentum Momentum Impulse Third Law Principle of conservation of linear momentum Impulse-momentum theorem