Newton’s Laws

Newton-1: Law of Inertia Newton’s First Law inertial reference frameAn object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. –If no net forces act, there is no acceleration.

Minimizing Friction One way to minimize friction is to float objects on a cushion of air. You will use an air track in lab this week. Any horizontal force exerted on the cart is the net force acting on the cart.

Acceleration vs Force Experiments show that Acceleration is proportional to force

Acceleration vs Mass Acceleration is inversely proportional to mass

Or, more familiarly, Units: Mass has SI units of kg, and acceleration has SI units of m/s 2. The SI unit of force is: 1 newton = 1 N = 1kg m/s 2. Newton-2 Combining these two observations gives and by an appropriate choice of units

Example: Accelerated Mass A net force of 3.0 N produces an acceleration of 2.0 m/s 2 on an object of unknown mass. What is the mass of the object? m1m1

Newton-2 (Second Law of Motion)

Combining Forces Forces add as vectors.

Force Addition ACT (a)(b) (c) (d) Two forces are exerted on an object. Which third force would make the net force point to the left?

Free-body diagrams: A free-body diagram shows every force acting on an object. Isolate the object of interest Choose a convenient coordinate system Sketch the forces Resolve the forces into components Apply Newton’s second law in each coordinate direction Free Body Reprise

Free-body Diagram Example

Kinematics & Dynamics Combo You are stranded in space, away from your spaceship. Fortunately, you have a propulsion unit that provides a constant net force F for 3.0 s. You turn it on, and after 3.0 s you have moved 2.25 m. If your mass is 68 kg, find F. Since there is only one force, we call that direction positive x and only worry about magnitudes. Kinematics Dynamics

Free-body ACT

Example: Three Forces Moe, Larry, and Curley push on a 752 kg boat, each exerting a 80.5 N force parallel to the dock. (a) What is the acceleration of the boat if they all push in the same direction? (b) What is the acceleration if Moe pushes in the opposite direction from Larry and Curley as shown?

Newton’s Third Law of Motion Forces always come in pairs, acting on different objects: If Object 1 exerts a force F on Object 2, then object 2 exerts a force –F on Object 1. These forces are called action-reaction pairs.

Newton’s Third Law of Motion Some action-reaction pairs:

Contact forces: The force exerted by one box on the other is different depending on which one you push. Boxes 1 and 2 rest on a frictionless surface. What is the acceleration in each case? What is the force between the boxes in each of the cases? 3 kg 12 N 1 kg 3 kg 12 N