AP Physics Chapter 6

Forces and Newton’s Laws of Motion

Kinematics: How objects moveDynamics: Why objects move

First studied by Isaac Newton

Isaac Newton

Sir Isaac Newton at 46 in Godfrey Kneller's 1689

portraitBorn 4 January [O.S. 25 December 1642] 1643

Woolsthorpe-by-Colsterworth, Lincolnshire, England

Died 31 March [O.S. 20 March] 1727Kensington, LondonResidence EnglandNationality English

Field Mathematics, physics, astronomy, alchemy, and natural philosophy

Institution University of CambridgeAlma Mater University of Cambridge

Doctoral Advisor Isaac BarrowKnown for Gravitation, optics, calculus,

mechanicsSocieties President of the Royal Society,

Master of the Royal MintPrizes Knighthood

Religion Prophetic Unitarianism, Church of England

Force

a push or a pullCan be a field force: gravity, magnetism

Does not involve physical contact.Or it can be a contact force like friction

4 types of forces

1. Gravitational: attractive force that exists between all objects that have mass, It is the weakest of all forcesBut holds the universe together

2. Electromagnetic: result of electric charge, gives materials their physical characteristics, strength, ability to bend, squeeze, stretch, shatter, malleability

Greater than gravity

3. Strong Nuclear: holds particles of nucleus togetherstrongest force

but only over a very, very small distance

4. Weak Force: involved in radioactive decay of some nuclei, may be a form of electromagnetic force

Force diagram

Sketch a free body diagramIsolate the objectAnd draw the forces acting on it

Normal Force

It is the force supplied by the surface supporting the objectIt is a contact forceUsually due to weight of the objectThe object pushes down The surface pushes up

Newton’s Laws of Motion

Newton’s 1st Law of Motion: an object with no outside force acting on it will move at a constant velocity in a straight line or remain at rest

Newton wrote the law, but Galileo speculated about this concept in his writings

Demo

Ballistic CarInertia apparatusCalled the Law of InertiaWhat is inertia?

Inertia is the tendency of a body or object to resist a change in its motionThe more mass a body has, the more inertia it has

Newton’s 1st Law of Motion

Law of Equilibrium (law of inertia): net sum of the forces is equal to zeroUniform MotionConstant velocityOr no motion

0F

Equilibrant

The equilibrant is equal to the resultant in magnitude but opposite in direction.When the vector sum is not zero, a force can be applied that will produce equilibrium. That is the equilibrant force.

Mass

Is a measurement of inertia, a body’s tendency to stay in equilibrium

Friction

The force that opposes motion between two surfacesIt is parallel to the surface and opposite the direction of motion

Static and Kinetic Friction

Static Friction: the force that opposes the start of motion, it is the maximum frictional force.Kinetic friction: the force that opposes motion between two surfaces in relative motion.

Coefficient of Static Friction

sDepends on the normal force and types of surfaces in contact

Coefficient of Kinetic Friction

kLess than static friction, object is in motionIs also called sliding friction

Frictional Force

Is the product of the coefficient and the normal

NFf

Free body diagram

All vectors are drawn at the center of massDraw a free body diagram of a box moving at constant velocity across the floor with frictionWhat does Net Force mean?

Newton’s Second Law of Motion

The acceleration of a body is directly proportional to the Net Force on it and inversely proportional to its mass.Net Force causes acceleration

ΣF = maUnit: the newton = 1kg meter/s2

Net Force

ΣF=ma

Weight

The magnitude of the force of gravity on an object.When the mass and acceleration due to gravity are known, the weight of an object can be calculatedWeight = mg

Example 1

Find the weight of a 2.25 kg bag of sugar. What direction is the force?

Mass

There are two kinds of mass:1. Gravitational – found on a scale

or balance2. Inertial mass – calculated using

Newton’s 2nd law of motion

Weight and Mass

Is your weight the same everywhere in the universe?What about your mass?

Example 2

Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Roberto. If the net external force acting on the book is 2.6 N to the right, what is the book’s acceleration?

Newton’s Third Law

If two object’s interact, the magnitude of the force exerted on Object #1 by Object #2 is equal to the magnitude of the force simultaneously exerted on Object #2 by Object #1, and these two forces are equal in magnitude and opposite in direction.Forces always exist in pairs.

F1,2 = F2,1

Action – Reaction pairsFor every action, there is an opposite and equal reaction

Newton’s 3rd Law of Motion

Terminal Velocity

Objects reach terminal velocity in free fall when the drag force of air resistance (friction) equals the force of gravityΣF = 0No acceleration, therefore, constant velocity Uniform Motion

Terminal Velocity

Example 3

A smooth wooden block is placed on a smooth table top. A 14.0 N force is exerted to keep the 40.0 N block moving at a constant velocity.What is the coefficient of kinetic friction?

If a 20.0 N brick is placed on top of the block, what force will be required to keep the block and brick system moving at a constant velocity?

Example 4

What net force is required to accelerate a 1500.0 kg car at +3.00 m/s2?

Example 5

An artillery shell has a mass of 55.0 kg. It is fired and leaves the barrel with a velocity of 770.0 m/s. The barrel is 1.50 meters long.What is the force of the shell inside the barrel?

Example 6

If a 10.0 kg object is on a frictionless surface and has a 100.0 N force acting on it, find the resulting acceleration.

If the same object rests on a rough surface where friction will oppose motion and the frictional force in -20.0 N. What is the acceleration now?

A Fish in the Elevator

A spring scale hangs from the ceiling of an elevator that is not moving.It supports a fish that weighs 25.0 N.What upward force does the scale exert?

What force must the scale exert when the elevator and fish accelerate upward at +1.50 m/s2

Example 8

A 24.0 kg crate initially at rest on a horizontal floor requires a 75.0 N horizontal force to set it in motion.Find the coefficient of static friction between the crate and the floor.

Simple Harmonic Motion

Repetitive motionIf a spring is vibrating, it has a restoring forceA force that wants to bring it back to equilibrium

Hooke’s Law

At equilibrium position, velocity is reaches a maximumAt maximum displacement, spring force and acceleration reach a maximumIn SHM, restoring force is proportional to displacementA stretched or compressed spring has elastic potential energy

Formula for Hooke’s Law

kxF

http://www.colorado.edu/physics/phet/simulations/massspringlab/MassSpringLab2.swf

Example #1

A mass of 0.55 kg is attached to a vertical spring. It stretches 2.0 cm from equilibrium position. What is the spring constant?

The Pendulum

For small angles, is repetitive motionThe restoring force of a pendulum is a component of the bob’s weightThe pendulum’s motion is SHMGravitational potential energy increases as the pendulum’s displacement increases

The Pendulum

Amplitude = maximum displacement from equilibriumPeriod = the time it takes to make one complete cycle of motion or waveFrequency = the number of cycles in one unit of time (usually the second)Period and frequency are inversely related

Period of a Pendulum

g

lT 2

Depends on the length of the pendulum and gravity

Example #2

You need to know the height of a tower, but darkness obscures the ceiling.You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 seconds.How tall is the tower?

Period of a mass-spring system

k

mT 2

Depends on the mass and the spring constant (k)

Example #3

You have a 1275kg car, you and your friend have a combined mass of 153 kg.You drive over a pothole that makes your car vibrate with a period of 0.840 seconds.Find the spring constant of one of your springs (shocks).