Newton’s Laws

Inertia

Force

Action Reaction

Isaac NewtonIsaac Newton (1642-1727)

• Life & Character– Born at Woolsthorpe in

Lincolnshire (England)– entered Cambridge

University in 1661 – Professor of

Mathematics in 1669 and Natural Philosopher

– President of the Royal Society of London in 1703 until death.

Scientific achievements

• GRAVITATION– calculated the relative

masses of heavenly bodies from their gravitational forces, calculated the force needed to hold the Moon in its orbit book: Principia I and III (1687)

• MECHANICS– calculated the

centripetal force needed to hold a stone in a sling, and the relation between the length of a pendulum and the time of its swing book: Principia I (1687)

Scientific achievements– OPTICS

– discovered measurable, mathematical patterns in the phenomenon of color, found white light as mixture of infinitely varied colored rays,…book: Opticks (1692).

• MATHEMATICS  – discovered general

methods of resolving problems of curvature, embraced in his "method of fluxions" and "inverse method of fluxions",..books: Principia I and II (1687)

Definitions

• Dynamics= the connection between force and motion

• Force= a push or pull upon an object, capable of accelerating that object, resulting from that object’s interaction with another object. Forces only exist as a result of interaction. Measured using the Newton (kg*m/s2).

Overview of Types of Forces

• 1. Applied Force= force applied to an object by a person or another object. Example: a person pushes a desk across the room, applied force acting upon the desk.

• 2. Gravity=force by which the earth, moon, or any other planet/massive object attracts another object toward itself. Downward pull towards the center, on earth.

• 3. Normal Force= support force exerted upon an object that is in contact with another stable object.

• Example: an object is resting on a surface, then the surface is exerting an upward force upon the object in order to support its weight.

• 4. Friction Force= force exerted by a surface as an object moves across it. The two types of friction are kinetic and static friction.

• 5. Air Resistance= acts upon objects as they travel through the air. Often opposes the motion of an object, but is frequently neglected due to negligible magnitude. Example: the force that slows a skydiver while he is falling.

• 6. Tension=transmitted through a string, rope, cable or wire when pulled tight by forces from opposite ends

• 7. Spring Force= force exerted by a compressed or stretched spring upon any object that is attached to it. The object that is compressed or stretched is also acted upon by a restoring force that restores it to rest or equilibrium position (Hooke’s Law)

Definitions

• Mass= refers to the amount of matter contained by the object; never altered by location, the pull of gravity, speed, or any other force. The unit of mass is the kilogram (kg) in SI units.

• Weight= the force of gravity acting on an object, depends on which planet is exerting the pull.  Weight is measured in Newtons or Pounds usually.

Newton’s First Law of Motion (the law of inertia)= An object at rest remains at rest, unless acted upon by some net force. An

object in motion remains in motion unless acted upon by some net force. Sometimes called the law of inertia.

• Inertia=the tendency of an object to move at a constant velocity

• Net force= sum of all forces acting on a body• Example 1: an ice hockey puck will continue to

move with the same velocity until it hits the boards.

• Example 2: A car comes to a sudden stop, a package in the car continues to slide forward because it continues in its state of motion, maintaining its velocity as the car decreases its velocity.

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

direction of the net force acting on it.

• Example (simple):  A 1.5 kg ball has an acceleration of 9.0 m/s2 to the left.  What is the net force acting on the ball?

• Givens/Formula: m=1.5kg and acceleration=9.0m/s2   -  F=ma

• Answer:  F=1.5kg*9.0m/s2= 13.5N or 14N (rounded)

Try it yourself

• Example (simple):  A 5.0kg bucket of water is raised from a well by a rope.  If the upward acceleration of the bucket is 3.0m/s2, find the force on the bucket by the rope.

• Givens:

• Answer:

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

direction of the net force acting on it.

• Example (more difficult): A parachute on a race car that weighs 8820N opens at the end of the quarter mile run when the car is traveling 35m/s.  What net retarding force must be supplied by the parachute to stop the car in a distance of 1100m?

• Givens: m=8820N  vi=35m/s   vf=0   d=1100m  

• Formulas:  F=ma    vf2=vi2+2(dy)(a)  rearranged for acceleration: a = vf2-vi2/2*dy 

• Answer:  Solve for the mass of the car.  Solve for a and then solve for retarding force.  

• F=ma   8820N=m*9.8m/s2   so   m=8820N/9.8m/s2 = 899.9kg  or 900kg (rounded)

• a = vf2-vi2/2*dy             a=(02-352) / 2*1100 = 1225/2200 = 0.557m/s2

• • F=900kg*(-0.557m/s2) = -501.3N or -5.0x102N (rounded)

Try it yourself

• - Example(simple) A 3.0kg block starts from rest at the top of a 30.0 degree incline and accelerates unifromly down the incline moving 2.00m in 1.50s.  Find the magnitude of acceleration of the block.   Find the force needed to stop the block after it has slid a distance of 2.00m.

• Givens:• Answer:

Newton’s Third Law of Motion = to every action, there is an equal and opposite reaction. Every push produces two forces. Example:

when you push a box forward, you also feel the box pushing at your hand.

• Example: When a person walks, with each step, he exerts force on the ground with his foot and the ground exerts force back on the person’s foot.

Newton’s Third Law Try it yourself

• A person on a scale rides in an elevator. If the mass of the person is 60.0 kg and the elevator accelerates downward with an acceleration of 4.90 m/s2, what is the reading on the scale?