Forces Contact Forces - those resulting from physical contact between objects –Normal Force –Friction –Tension (spring/rope) –Compression Action at a Distance Force - Field Forces –Gravity –Electromagnetic –Strong Nuclear Force Holds Nucleus Together –Weak Nuclear Force Decay Process Force - The capacity to cause physical change in the motion of an object.

Newton’s First Law – Law of Inertia An object at rest will remain at rest –and an object in motion will continue in motion at a constant velocity ( Magnitude and Direction ) –unless acted upon by a nonzero net external force. Inertia – The tendency of a body to maintain its state of rest or constant velocity. Equilibrium - A condition during which the velocity of an object is constant or the object is at rest. The net force acting on the object is zero. Inertial Reference Frame –Place where Newton's Laws are valid. (at rest or constant velocity) –Non-inertial reference frames are accelerating.

Weight and Mass Mass - A term used to quantify/measure inertia. –Has SI units of kilogram. –The amount of a substance. –The quantity of matter. –Scalar Weight - Force exerted on an object while it is under the influence of a gravitational field. –Vector Density - The amount of a substance per unit volume.

Newton’s Second Law The acceleration of an object is –directly proportional to the net force acting on it –and inversely proportional to its mass. –The direction of the acceleration is in the direction of the net force acting on the object.

Units

Alternate Statement of the Second Law Momentum - The quantity of an object’s motion. The product of an object’s mass and velocity. The time rate of change of the momentum of an object is equal to the resulting net external force acting on the object.

Weight and Mass Mass - A term used to quantify/measure inertia. –Has SI units of kilogram. –The amount of a substance. –The quantity of matter. –Scalar Weight - Force exerted on an object while it is under the influence of a gravitational field. –Vector Density - The amount of a substance per unit volume.

Example 1 What constant net force must be used to bring a 1500 kg car to rest from a speed of 100 km/hr within a distance of 55 m?

Newton’s Third Law If two objects interact (contact or at a distance), the force exerted on body 1 by body 2 (F 12 ) is equal and opposite the force exerted on body 2 by body 1 (- F 21 ). On By

Cautions on the Third Law The forces of an action-reaction pair always act on different bodies. They do not combine to give a net force and cannot cancel each other.

Model Assumptions Surfaces are frictionless (*) The mass of a rope or string is zero. The tension in a rope is the same everywhere in the rope. ( The force(s) it exerts is(are) on the object(s) it is attached to). Ropes are non-extensive (do not get longer) A pulley has no friction or mass (*). It simply redirects the tension in another direction.

Problem Solving Approach Read the problem. Several times if necessary. Write down the information that is given or looked up in a table. Write down what is to be found. Draw a picture or sketch. Draw and label with forces, velocities, accelerations, etc. Isolate the object(s) of interest. –Free body diagram. –Specify your coordinate system. –Resolve forces along these coodinate axes. Write down the fundamental relationships/definitions/formula you need to solve the problem. – Apply Newton’s laws in component form along coordinate axes. Manipulate the equations. # Equations = # Unknowns. Check that your answer makes sense. Actually plug in numbers at the very end. Include unit analysis. Box your final answer. Include units and check for significant digits.

Big Picture If the object is at rest or moving at a constant velocity it is in equilibrium and the 1 st Law applies. If the the forces don’t seem balanced the object will accelerate and the second law applies

Example 2 A 10 kg box is sitting on the table. You pull up with a string attached to the box and apply 40 N. What is the normal force applied by the table on the box?

Example 3 Two boxes are connected by a cord and pulled by a second cord attached to the first box with a force of 40.0 N The two boxes have masses of 12.0 kg and 10.0 kg as shown. Find the acceleration of each box and the tension in the cord

Example 4 – Hanging Objects m

Resolve into components

Block on a smooth incline plane

Atwood’s Machine (a pulley) Object 1: Elevator Car Object 2: Counterweight

Incline plane (no friction) m 2 = 7 kg Which way do blocks move? What is acceleration? What is tension in cord?

Inside the elevator (non-inertial frame) While moving up at constant velocity: Scale reads correctly While slowing down: Scale reads light!