Today: (Ch. 2 & 3) HDevelop the equations to describe motion  Look at some situations where we can apply them

Force A force is a push or a pull on an object Force is a vector quantity The magnitude of the force is the strength of the push or pull The direction of the force is the direction of the push or pull Denoted by

Fundamental Forces Gravity The strong and weak nuclear forces The electromagnetic Forces

Inertia The Principle of Inertia –An object will maintain its state of motion unless it is acted upon by a force –Inertia is also a measure of an object’s resistance to changes in its motion

Newton’s laws of motion The laws are statements about how things move Newton’s first law is a statement about inertia Newton’s Second Law gives the link between motion and forces Newton’s Third Law explains where forces come from

Newton’s laws of motion If no force acts on an object, then its speed and the direction of motion do not change. A non zero force action on an object causes its state of motion to change. In an interaction between two objects, the forces that each exerts on the other are equal in magnitude and opposite in direction

The acceleration of an object is directly proportional to the total force that acts on it. –Forces are vectors The direction of the acceleration is parallel to the sum of the forces Newton’s second law

The direction of the acceleration is always parallel to the direction of the total force The velocity and the total force do not need to be in the same direction Example –Initial velocity is upward –The total force is downward –The acceleration is downward Direction

Force applied on first object by second is equal in magnitude and opposite in direction –Often called the action- reaction principle Example –Force on ball –Force on bat Newton’s third law

Measuring Forces Hook’s law is applied for springs. Springs have property that is expansion and compression. Hook’s law says that expansion or compression is roughly proportional to the force exerted on the ends of the spring. Hooks law for ideal spring

Motion – Constant Velocity The velocity is zero –Position is constant (not necessarily zero) The velocity is non zero and constant –Position is changing steadily (v = 0)

Constant Acceleration The acceleration is a constant –On the graph, a straight horizontal line The velocity is changing –On the graph, this is an upward sloping straight line The position is changing –Not the same change each second

Equations to Describe Motion with Constant Acceleration v f = v o + a t –v o is the velocity at some initial time t = 0 –It depends on what happened prior to t = 0 x f -x o = v o t + ½ a t 2 –x o is the position at some initial time t = 0 v 2 = v o ² + 2 a (x f - x o ) –Eliminates t from the equation Which equation to use depends on what information you are given in the problem and what you are asked to find

Constant Acceleration Equations, Summary

Weight Weight is the force of gravity exerted by the Earth on an object : Denoted by If an object has a mass m, then –The force of gravity is a consequence of Newton’s Law of Universal Gravitation The value of g is approximately the same for all locations near the surface of the Earth, which is : g ≈ 9.8 m/s² The weight will be different on another planet –Since it is due to the gravitational attraction of that planet

Weight, cont. The value of g is independent of the mass of the object g is commonly referred to as the “acceleration due to gravity” Weight will be measured in Newtons –It is a force Since weight acts vertically, it will be along the y-axis Since the weight acts downward, F grav = - m g –It acts toward the center of the Earth

Weight and Normal Force, Example  ΣF = -m g + N = m a = 0  a = 0, since person is stationary  N = m g  Here, the normal is equal in magnitude to the weight and opposite in direction to the person’s weight

Free Body Diagram A free body diagram should be used for analysis using Newton’s Second Law It is a simplified diagram showing all the forces acting on each object involved in the problem

Free body diagram F 1y = W F 2y = N F 1y = W F 2y = N What is F net ?

Net Force: Vector addition F 1y = 40 N F 2y = 90 N F 2x = 60 NF 2x = 120 N F 1x = 60 NF 2x = 120 N F 1y = 40 N F 2y = 90 N F netx = ? N F nety = ? N

Contact forces

Tomorrow: (Ch. 3)  Develop the equations to describe motion  Look at some situations where we can apply them

Contact forces

Tension