Newton’s Laws Forces and Motion

Laws of Motion formulated by Issac Newton in the late 17 th century formulated by Issac Newton in the late 17 th century written as a way to relate force and motion written as a way to relate force and motion Newton used them to describe his observations of planetary motion. Newton used them to describe his observations of planetary motion.

History Aristotle was an ancient Greek philosopher Aristotle was an ancient Greek philosopher Based on his observations the common belief was that in order for an object to continue moving, a force must be exerted in the direction of the motion Based on his observations the common belief was that in order for an object to continue moving, a force must be exerted in the direction of the motion This lasted until Issac Newton proposed his “Laws of Motion” based on observations made of bodies free from earth’s atmosphere. This lasted until Issac Newton proposed his “Laws of Motion” based on observations made of bodies free from earth’s atmosphere.

Newton’s 1 st Law Inertia An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity unless acted on by an unbalanced force. This statement contradicted Aristotle’s teaching and was considered a radical idea at the time. However, Newton proposed that there was, in fact, an unrecognized force of resistance between objects that was causing them to stop in the absence of an applied force to keep them moving. This new unseen resistance force became known as “friction”.

Newton’s 2 nd Law F net = ma If an unbalanced force acts on a mass, that mass will accelerate in the direction of the force. Newton’s 1 st Law says that without an unbalanced force objects will remain at constant velocity (a=0)…so it seems logical to say that if we apply a force we will see an acceleration. 2 N 8 N a Since 8N is greater than 2N, the unbalanced force is to the right so the acceleration is to the right.

Newton’s 3 rd Law Action - Reaction For every action force there is an equal and opposite reaction force. Example: If you punch a wall with your fist in anger, the wall hits your fist with the same force. That’s why it hurts! Action-reaction forces cannot balance each other out because they are acting on different objects.

A Force is… A “push” or “pull” A “push” or “pull” Measured in Newtons (N) in the metric (SI) system and pounds (lbs) in the English system Measured in Newtons (N) in the metric (SI) system and pounds (lbs) in the English system A vector quantity requiring magnitude and direction to describe it A vector quantity requiring magnitude and direction to describe it Represented by drawing arrows on a diagram Represented by drawing arrows on a diagram

Types of Forces Weight - force of gravity Weight - force of gravity Normal force – surface pushing back Normal force – surface pushing back Friction - resistance force Friction - resistance force Applied force - force you exert Applied force - force you exert Tension - applied through a rope or chain Tension - applied through a rope or chain Centripetal Force – any force that causes circular motion Centripetal Force – any force that causes circular motion Elastic Forces – applied force due to the stretch or compression of a rubberband, bungee, or spring Elastic Forces – applied force due to the stretch or compression of a rubberband, bungee, or spring Drag Forces – any resistance force caused by fluids (i.e. air resistance) Drag Forces – any resistance force caused by fluids (i.e. air resistance) Net force – total vector sum of all forces Net force – total vector sum of all forces Balanced forces – equal and opposite Balanced forces – equal and opposite Unbalanced forces – not equal and opposite Unbalanced forces – not equal and opposite

Weight The force of gravity acting on a mass. Weight always acts down! Weight = mass (kg) * acceleration due to gravity Weight is a force…so this is a special case of F=ma and the unit is a Newton.

Mass is… The amount of matter an object is made up of. The amount of matter an object is made up of. Measured in kilograms. Measured in kilograms. A universal value, independent of the influences of gravity. A universal value, independent of the influences of gravity. NOT a force. NOT a force.

Normal Force (F N ) Defined as the force of a surface pushing back on an object. Defined as the force of a surface pushing back on an object. Always directed perpendicular to the surface. Always directed perpendicular to the surface. This is a contact force. No contact…no normal force. This is a contact force. No contact…no normal force. NOT always equal to weight. NOT always equal to weight. Examples: FNFN Table WallWall FNFN

Friction A resistance force usually caused by two surfaces moving past each other. A resistance force usually caused by two surfaces moving past each other. Always in a direction that opposes the motion. Always in a direction that opposes the motion. Measured in Newtons Measured in Newtons Depends on surface texture and how hard the surfaces are pressed together. Depends on surface texture and how hard the surfaces are pressed together. Surface texture determines the coefficient of friction (μ) which has no units. Surface texture determines the coefficient of friction (μ) which has no units. Normal force measures how hard the surfaces are pressed together. Normal force measures how hard the surfaces are pressed together.

Types of friction Static friction is the force an object must overcome to start moving. Static friction is the force an object must overcome to start moving. Kinetic friction is the force an object must overcome to keep moving. Kinetic friction is the force an object must overcome to keep moving. Static friction is always greater than kinetic friction!

Calculating the Force of Friction Where f is the force of friction, μ is the coefficient of friction, and F N is the normal force For kinetic friction: For static friction:

Drag Forces Deriving expressions for drag forces such as air resistance will be the topic of an entire powerpoint of its own. Stay tuned for more to come to an AP Physics class near you.

May the Net Force be with you Total force acting on an object Total force acting on an object Vector sum of all the forces Vector sum of all the forces The unbalanced force referred to in Newton’s Law of Motion The unbalanced force referred to in Newton’s Law of Motion Net force is equal to the mass of an object times the acceleration of that object. Net force is equal to the mass of an object times the acceleration of that object.

Force Diagrams Force diagrams must include the object and all forces acting on it. Force diagrams must include the object and all forces acting on it. The forces must be attached to the object. The forces must be attached to the object. No other vectors may be attached to the object. No other vectors may be attached to the object. Components of forces, axis systems, motion vectors and other objects or surfaces may be included in force diagrams. Components of forces, axis systems, motion vectors and other objects or surfaces may be included in force diagrams.

Force Diagram Problem: A 10 kg crate with an applied force of 100 N slides across a warehouse floor where the coefficient of static friction is 0.3 between the crate and the floor. What is the acceleration of the crate. Weight = F g = (10 kg)*(9.81m/s 2 ) F applied = 100 N 10 kg FNFN f = μF N

To Solve the Problem Now that you have the force diagram! Problem: A 10 kg crate with an applied force of 100 N slides across a warehouse floor where the coefficient of static friction is 0.3 between the crate and the floor. What is the acceleration of the crate. F applied = 100 N 10 kg FNFN f = μF N Weight = F g = (10 kg)*(9.81m/s 2 ) Write the Newton’s 2 nd Law equation for the x- and y- directions. a Now plug in what you know and solve for what you don’t. Algebra…YUK!!

Centripetal Force Any force that causes an object to travel in a circular path Any force that causes an object to travel in a circular path Always toward the center of the circular path Always toward the center of the circular path Any of the forces we have identified could be the centripetal force, most commonly… gravity (weight), tension, friction, & elastic forces Any of the forces we have identified could be the centripetal force, most commonly… gravity (weight), tension, friction, & elastic forces r m FcFc v Note: an object’s velocity is tangent to the curved path it takes, so perpendicular to the centripetal force, acceleration and radius

Centripetal Forces in horizontal circles with tension m FcFc v Top view θ T F g =mg r FcFc m L When the plane of the circle traced out by the object is horizontal, gravity is perpendicular to the motion so the velocity remains constant. However, since the object will always hang below the point of support, only the component of the tension that is parallel to the plane of the circle can be considered as the centripetal force. Side view

Centripetal forces in vertical circles FcFc v v v v FTFT FcFc FcFc FcFc FTFT FTFT FTFT FgFg FgFg FgFg FgFg At the top of the circle: -velocity is the lowest -centripetal force is a combination of the tension and gravitational forces In a vertical circle, gravity does have an effect on the speed at different points on the circular path. At the sides: -velocity is vertical and changing with the acceleration due to gravity -centripetal force is supplied by the tension alone since the gravitational force is perpendicular. At the bottom: -velocity is the maximum -centripetal force is a combination of the tension and gravitational forces

Gravity as the Centripetal Force Satellite Motion (assuming circular orbits) m FgFg v r RERE MEME In the case of a satellite orbiting a planet, the centripetal force (net force required to keep the object moving in the circular path) is provided by the gravitational force (weight). Of course at orbital altitudes we can no longer use F g =mg to calculate weight of the satellite, so… We can solve this for v to get the orbital velocity associated with that particular radius. Note the orbital radius is measured to the center of the circular path of the orbit so … r = R E + H H

Friction as the centripetal force A car going around a curve m FcFc v For a car going around a curve on a road, the force that keeps the car in the circular path (Centripetal force) is the friction of the road pushing the tires in toward the center of the circle. Note: This is for a flat curve. If the curve is banked, the problem is a little trickier. Draw the force diagram and be careful about the components. It combines the best of Centripetal Motion and Inclined Planes…lots of vectors!

Normal Force as the centripetal force Amusement Park Rides m FcFc v Top view r FNFN FgFg fsfs In a ride where the rider is stuck to the wall due to the spinning motion while the floor drops away the Normal force provides the Centripetal Force to keep the rider moving in circular path. Meanwhile, static friction between the wall and the rider is the force that balances gravity allowing the rider to “hang” on the wall.

Elastic Forces and Hooke’s Law When a spring is stretched or compressed it exerts a restoring force. When a spring is stretched or compressed it exerts a restoring force. That force depends on the stiffness of the spring and the amount of deformation (stretch or compression) That force depends on the stiffness of the spring and the amount of deformation (stretch or compression) The direction of the force is always opposite to the direction of deformation. The direction of the force is always opposite to the direction of deformation. m k m x Hooke’s Law states: Where: F is the restoring force, k=spring constant (stiffness), x=stretch (or compression)

Spring force as centripetal force