Chapter 4: Newton s Laws of Motion [A Tale of Force, Friction and Tension] 4.1. Newton s Laws of Motion

Force is a push or pull. Force Force is a vector it has magnitude and direction.

Newton s First Law of Motion An object moving with constant velocity continues to move at that velocity as long as no net force acts on it. An object at rest remains at rest as long as no net force acts on it. E.g.: A book does not start moving by itself. A force is required to make it move. An object stops moving only if there is friction, which is a force. (Demonstrate pushing a book and a steel ball.) Zero velocity is a constant velocity. Hence the first sentence includes the case of the second sentence. Also known as the Law of Inertia ( laziness ).

Newton s First Law of Motion An object moving with constant velocity continues to move at that velocity as long as no net force acts on it. An object at rest remains at rest as long as no net force acts on it. The net force is the vector sum of all forces. The law says no net force because typically more than one force acts on an object. For example, gravity is acting on all objects in this room. However a book on a table does not fall because the table is supporting it i.e. exerting a force on the book equal and opposite to gravity, resulting in no net force. Remove the table and the book will fall.

What surfaces have little friction, on which it can be observed that objects keep sliding at (nearly) constant velocity? Ice A wet or oily surface Exceptions: a golf ball on wet grass, a hockey puck on wet ice Air hockey table Outer space

Inertia

Newton s Second Law of Motion Force equals mass times acceleration. Or, equivalently, The SI units of Force are kg m/s 2 = N (Newtons).

Newton s Second Law of Motion

Newton s Second Law of Motion E.g. it takes more force to push a car than a baby carriage. Two equal weights exert twice the gravitational force of one.

Example A 1800-kg car has an acceleration of 3.8 m/s 2. What is the force acting on the car? F = ma F = (1800 kg)(3.8 m/s 2 ) F = 6840 kg m/s 2 = 6800 N

Newton s Second Law of Motion An object may have several forces acting on it. The net acceleration is due to the net force, determined by summing the x-, y- and z- components: Σ F x = m a x Σ F y = m a y Σ F z = m a z

Newton s Second Law of Motion To solve for the acceleration of an object, draw a free-body diagram which shows (with arrows) the direction of all the forces acting on that object only. The forces are considered to act on the object s center. Σ F x = m a x Σ F y = m a y Σ F z = m a z

Example 2 Moe, Larry and Curly push on a 752-kg boat that floats next to a dock. They each exert an 80.5-N force parallel to the dock. (a) What is the boat s acceleration if they all push in the same direction? (b) What is the boat s acceleration if Larry and Curly push in the opposite direction from Moe?

Answer

Vector Forces in Two Dimensions The easiest way to add forces in two dimensions is to (a) choose a coordinate system that simplifies resolving forces into perpendicular components, and (b) apply Newton s 2 nd Law (ΣF=ma) in each coordinate direction separately.

Newton s Third Law of Motion For every action force acting on object 1 by object 2, there is a reaction force acting on object 2 by object 1. The action and reaction forces are equal in magnitude and opposite in direction. Forces always come in pairs. If object 1 exerts a force F on object 2, then object 2 exerts the force F on object 1. These forces are called action-reaction pairs. E.g. if you push or pull someone, you both feel the same magnitude pressure.

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

Newton s Third Law of Motion For every action force acting on object by object 2, there is a reaction force acting on object 2 by object 1. The action and reaction forces are equal in magnitude and opposite in direction. Note: Forces equal in magnitude and opposite in direction acting on the same object cancel. However, forces equal in magnitude and opposite in direction acting on different objects do not cancel. Both objects will move---unless one is much more massive, or has other forces acting on it.

Example 3 Two groups of canoeists meet in the middle of a lake. After a brief visit, a person in canoe 1 pushes on canoe 2 with a force of 46 N to separate the canoes. The mass of canoe 1 and its occupants is 150 kg, and the mass of canoe 2 and its occupants is 250 kg. What is the acceleration of each canoe?

Answer

Newton s Third Law of Motion Rocket propulsion can also be explained using Newton s third law. Combustion causes gases at high pressure to push on the inside of the rocket. Because the gases are allowed to exit the tail, the net force on the rocket is upward. Note that the rocket does not need the ground or air to push against; it can accelerate in outer space.

The Limits of Newton s Laws

4.1 Clicker Questions